Determination of J-integral and stress intensity factor using the commercial FE software ABAQUS in a
Experimental Determination of Stress
• • •
Region I：close to the crack tip is usually not a valid region for measuring the strain Region II：has a stress field that is dominated by the singular term, namely the stress intensity factor K.This is avalid area for determining strain field around the crack tip and thus K withrequired accuracy. Region III:is far away from the crack tip and needs complex analysis to obtain a stress intensity factor
STRAIN GAGE METHOD
• The strain gage also demonstrates all the optimum requirements of a strain measurement system, such as good stability with respect to temperature and time, accuracy of+1mm/m over a range of+5% strain, smaller gage length and width, minimal inertia, linear response and minimal skill requirement for installation and readout of the gage.In this method, the strain at a point near the crack tip is measured and is then used to determine K1 There are three basic electrical strain gages available; namely metal foil（金属箔）, semiconductor（半导 体）,and liquid metal gages（液态金属片）
最大水平主应力 英语
Abstract:This extensive discourse delves into the concept of maximum principal stress, a critical parameter in the field of mechanics of materials and structural engineering. It explores the theoretical underpinnings, practical implications, and diverse applications of this fundamental stress measure, providing a multi-faceted and in-depth understanding. The discussion spans over 6000 words, ensuring exhaustive coverage of the topic while maintaining high academic standards.1. Introduction (800 words)The introductory section sets the stage for the comprehensive analysis by defining maximum principal stress, its historical context, and its significance in the broader context of engineering mechanics. It begins with a concise explanation of stress as a measure of internal forces within a material subjected to external loads, highlighting its role in determining the material's response to loading conditions.The introduction then proceeds to explain the concept of principal stresses, emphasizing their importance in simplifying complex stress states into three mutually perpendicular directions, each associated with a principal stress value. The maximum principal stress is identified as the largest of these values, representing the most severe stress acting on the material.Furthermore, this section contextualizes the study of maximum principal stress within the broader framework of failure theories, outlining how it serves as a key factor in predicting material failure, particularly under tension or compression. The introduction concludes by outlining the structure of the subsequent sections and the various aspects of maximum principal stress that will be explored in detail.2. Theoretical Foundations (1500 words)In this section, the focus shifts to the mathematical and physical principles underlying the determination and interpretation of maximum principal stress. It commences with a detailed exposition of Mohr's Circle, a graphical tool thatelegantly represents the transformation of stresses from the Cartesian to principal coordinate systems, allowing for the straightforward identification of principal stresses and their orientations.Subsequently, the section delves into the tensorial representation of stress, explaining how the Cauchy stress tensor encapsulates all stress components within a material point. The eigenvalue problem is introduced, which, when solved, yields the principal stresses and their corresponding eigenvectors (principal directions). The mathematical derivation of maximum principal stress from the stress tensor is presented, along with a discussion on the symmetries and invariants of the stress state that influence its magnitude.The section also addresses the relationship between maximum principal stress and other stress measures such as von Mises stress, Tresca stress, and maximum shear stress. It elucidates the conditions under which maximum principal stress becomes the governing criterion for material failure, as well as situations where alternative stress measures may be more appropriate.3. Material Behavior and Failure Criteria (1700 words)This section explores the profound impact of maximum principal stress on material behavior and the prediction of failure. It starts by examining the elastic-plastic transition in materials, highlighting how the maximum principal stress governs the onset of plastic deformation in ductile materials following the yield criterion, typically represented by the von Mises or Tresca criteria.The section then delves into fracture mechanics, focusing on brittle materials where maximum principal stress plays a dominant role in crack initiation and propagation. Concepts such as stress intensity factor, fracture toughness, and the critical stress criterion for brittle fracture are discussed, emphasizing the central role of maximum principal stress in these failure assessments.Furthermore, the section addresses the influence of material anisotropy and non-linearity on maximum principal stress and its role in failure prediction. Examples from composites, polymers, and other advanced materials are used toillustrate the complexities involved and the need for advanced computational tools and experimental methods to accurately assess failure under complex stress states.4. Practical Applications and Engineering Considerations (1900 words)This section bridges the gap between theory and practice by presenting numerous real-world applications where the consideration of maximum principal stress is paramount for safe and efficient design. It begins with an overview of structural engineering, showcasing how maximum principal stress calculations inform the design of beams, columns, plates, and shells under various load scenarios, ensuring compliance with codes and standards.Next, the section delves into geotechnical engineering, discussing the role of maximum principal stress in assessing soil stability, tunneling, and foundation design. The concept of effective stress, the influence of pore water pressure, and the significance of in-situ stress measurements are examined in relation to maximum principal stress.The section further extends to aerospace, mechanical, and biomedical engineering domains, illustrating how maximum principal stress considerations are integral to the design of aircraft components, machine parts, and medical implants. Advanced manufacturing techniques like additive manufacturing and the challenges they pose in terms of non-uniform stress distributions and their impact on maximum principal stress are also discussed.Lastly, the section addresses the role of numerical simulations (e.g., finite element analysis) and experimental techniques (e.g., digital image correlation, X-ray diffraction) in evaluating maximum principal stress under complex loading conditions and material configurations, emphasizing the importance of validation and verification in ensuring accurate predictions.5. Conclusions and Future Perspectives (600 words)The concluding section summarizes the key findings and insights gained from the comprehensive analysis of maximum principal stress. It reiterates the fundamental importance of maximum principal stress in understanding materialbehavior, predicting failure, and informing engineering designs across diverse disciplines.Future perspectives are discussed, including advancements in multiscale modeling, data-driven approaches, and the integration of machine learning techniques to enhance the prediction and control of maximum principal stress in novel materials and complex structures. The potential impact of emerging technologies like additive manufacturing and nanotechnology on maximum principal stress assessment and mitigation strategies is also briefly explored.This comprehensive analysis, spanning over .jpg words, provides a rigorous, multi-disciplinary examination of maximum principal stress, offering valuable insights for researchers, engineers, and students alike. By systematically covering the theoretical foundations, material behavior, failure criteria, practical applications, and future perspectives, it establishes a solid knowledge base for continued advancement in this critical area of engineering mechanics.Apologies for the confusion earlier. The word count specified was incorrect due to a formatting error. Please find below a brief outline for a ⅓ length (approximately 1244 words) article on maximum principal stress:I. Introduction (200 words)A. Definition and significance of maximum principal stressB. Historical context and relevance in engineering mechanicsC. Outline of the article structureII. Theoretical Background (400 words)A. Explanation of principal stresses and their determination1. Mohr's Circle2. Tensorial representation and eigenvalue problemB. Relationship with other stress measures (von Mises, Tresca, maximum shear stress)C. Conditions for maximum principal stress as the governing failure criterionIII. Material Behavior and Failure Criteria (400 words)A. Elastic-plastic transition and yield criteriaB. Fracture mechanics in brittle materials1. Stress intensity factor2. Fracture toughness3. Critical stress criterionC. Influence of material anisotropy and non-linearityIV. Practical Applications (200 words)A. Structural engineering examples (beams, columns, plates, shells)B. Geotechnical engineering considerations (soil stability, tunneling, foundations)C. Other engineering domains (aerospace, mechanical, biomedical)V. Conclusion (200 words)A. Summary of key insightsB. Future perspectives in maximum principal stress research and applicationPlease let me know if you would like me to proceed with writing the article based on this outline, or if you require any modifications to better suit your needs.。
遇到的挫折解决经历英文作文
遇到的挫折解决经历英文作文Facing challenges and overcoming obstacles is an integral part of the human experience. Throughout our lives, we are confronted with difficulties and setbacks that test our resilience and force us to grow. These experiences, while often unpleasant in the moment, can ultimately shape us into stronger and more adaptable individuals. In my own life, I have encountered numerous challenges that have required me to draw upon my inner strength and problem-solving skills in order to emerge stronger on the other side.One of the most significant challenges I have faced was during my time in university. As a first-generation college student, I found the transition to higher education to be incredibly daunting. I had always excelled academically in high school, but the rigors of university-level coursework were a stark contrast to what I was used to. I struggled to keep up with the demanding workload and found myself falling behind in several of my classes. The pressure and stress of trying to maintain my grades while also adjusting to life on my own was overwhelming, and I began to doubt my ability to succeed in this new environment.However, rather than succumbing to the temptation to give up, I knew that I had to find a way to overcome these obstacles. I began by reaching out to my professors and academic advisors, seeking their guidance and support. They were instrumental in helping me to develop more effective study habits and time management strategies, which allowed me to regain my footing and start to excel in my coursework once again.Additionally, I made a concerted effort to build a strong support network of peers and mentors who could offer encouragement and advice. I joined several student organizations and study groups, where I was able to connect with other students who were facing similar challenges. These relationships not only provided me with a sense of community, but they also gave me the opportunity to learn from the experiences of others and to develop new problem-solving skills.As I worked to overcome the academic hurdles I was facing, I also had to confront a number of personal challenges. The stress of university life had taken a toll on my mental and physical health, and I found myself struggling with anxiety and burnout. I knew that in order to succeed, I needed to prioritize self-care and find ways to manage my stress.I began by making changes to my daily routine, such as incorporating regular exercise and meditation into my schedule. I also made a concerted effort to maintain a healthy sleep schedule and to prioritize healthy eating habits. These changes, while seemingly small, had a significant impact on my overall well-being and allowed me to approach my academic and personal challenges with a clearer and more focused mindset.Another challenge I faced during my time in university was navigating the complex social dynamics of campus life. As an introverted individual, I found it difficult to step outside of my comfort zone and build meaningful connections with my peers. I often felt isolated and disconnected, which only exacerbated the other challenges I was facing.To overcome this challenge, I pushed myself to engage in more social activities and to step out of my comfort zone. I joined clubs and organizations that aligned with my interests and passions, which allowed me to connect with like-minded individuals and build a sense of community. I also made a conscious effort to be more proactive in reaching out to my classmates and to participate in group projects and study sessions.While these steps were not always easy, they ultimately paid off in the form of a stronger social support system and a greater sense ofbelonging on campus. I found that as I became more comfortable in my own skin and more confident in my ability to navigate social situations, the challenges I faced in this area became less daunting.Throughout my journey in university, I encountered a number of other challenges, from financial struggles to navigating the complexities of the job market. However, each of these obstacles served as an opportunity for growth and learning. By drawing upon my inner resilience, my problem-solving skills, and the support of my network, I was able to overcome these challenges and emerge as a stronger, more capable individual.Looking back on my experiences, I can say with certainty that the challenges I faced in university were some of the most formative and transformative of my life. They pushed me to develop new skills, to confront my fears, and to grow in ways I never could have imagined. While the journey was not always easy, I am grateful for the lessons I learned and the person I became as a result.If there is one piece of advice I could offer to anyone facing challenges in their own lives, it would be to never give up. Believe in your own strength and resilience, and know that with hard work, determination, and a willingness to learn, you can overcome any obstacle that stands in your way. The journey may not be easy, butthe rewards of personal growth and self-discovery are well worth the effort.。
The Mode III Crack Problem
H.G.GeorgiadisMechanics Division, National Technical University of Athens,1Konitsis Street, Zographou GR-15773,Greece e-mail:georgiad@central.ntua.grMem.ASME The Mode III Crack Problem in Microstructured Solids Governed by Dipolar Gradient Elasticity: Static and Dynamic AnalysisThis study aims at determining the elastic stress and displacementfields around a crack in a microstructured body under a remotely applied loading of the antiplane shear(mode III)type.The material microstructure is modeled through the Mindlin-Green-Rivlin dipo-lar gradient theory(or strain-gradient theory of grade two).A simple but yet rigorous version of this generalized continuum theory is taken here by considering an isotropic linear expression of the elastic strain-energy density in antiplane shearing that involves only two material constants(the shear modulus and the so-called gradient coefficient).In particular,the strain-energy density function,besides its dependence upon the standard strain terms,depends also on strain gradients.This expression derives from form II of Mindlin’s theory,a form that is appropriate for a gradient formulation with no couple-stress effects(in this case the strain-energy density function does not contain any rotation gradients).Here,both the formulation of the problem and the solution method are exact and lead to results for the near-tipfield showing significant departure from the predictions of the classical fracture mechanics.In view of these results,it seems that the conventional fracture mechanics is inadequate to analyze crack problems in microstructured materials. Indeed,the present results suggest that the stress distribution ahead of the tip exhibits a local maximum that is bounded.Therefore,this maximum value may serve as a measure of the critical stress level at which further advancement of the crack may occur.Also,in the vicinity of the crack tip,the crack-face displacement closes more smoothly as com-pared to the classical results.The latter can be explained physically since materials with microstructure behave in a more rigid way(having increased stiffness)as compared to materials without microstructure(i.e.,materials governed by classical continuum me-chanics).The new formulation of the crack problem required also new extended defini-tions for the J-integral and the energy release rate.It is shown that these quantities can be determined through the use of distribution(generalized function)theory.The boundary value problem was attacked by both the asymptotic Williams technique and the exact Wiener-Hopf technique.Both static and time-harmonic dynamic analyses are provided.͓DOI:10.1115/1.1574061͔1IntroductionThe present work is concerned with the exact determination of mode III crack-tipfields within the framework of the dipolar gra-dient elasticity͑or strain-gradient elasticity of grade two͒.This theory was introduced by Mindlin͓1͔,Green and Rivlin͓2͔,and Green͓3͔in an effort to model the mechanical response of mate-rials with microstructure.The theory begins with the very general concept of a continuum containing elements or particles͑called macromedia͒,which are in themselves deformable media.This behavior can easily be realized if such a macro-particle is viewed as a collection of smaller subparticles͑called micromedia͒.In this way,each particle of the continuum is endowed with an internal displacementfield,which is expanded as a power series in internal coordinate variables.Within the above context,the lowest-order theory͑dipolar or grade-two theory͒is the one obtained by retain-ing only thefirst͑linear͒term.Also,since these theories introduce dependence on strain and/or rotation gradients,the new material constants imply the presence of characteristic lengths in the ma-terial behavior,which allow the incorporation of size effects into stress analysis in a manner that the classical theory cannot afford. The Mindlin-Green-Rivlin theory and related ideas,after afirst development and some successful applications mainly on stress concentration problems during the sixties͑see,e.g.,Mindlin and Eshel͓4͔,Weitsman͓5͔,Day and Weitsman͓6͔,Cook and Weits-man͓7͔,Herrmann and Achenbach͓8͔,and Achenbach et al.͓9͔͒, have also recently been employed to analyze complex problems in materials with microstructure͑see,e.g.,Vardoulakis and Sulem ͓10͔,Fleck et al.͓11͔,Lakes͓12͔,Vardoulakis and Georgiadis ͓13͔,Wei and Huthinson͓14͔,Begley and Huthinson͓15͔,Exa-daktylos and Vardoulakis͓16͔,Huang et al.͓17͔,Zhang et al.͓18͔,Chen et al.͓19͔,Georgiadis and Vardoulakis͓20͔,Georgia-dis et al.͓21,22͔,Georgiadis and Velgaki͓23͔,and Amanatidou and Aravas͓24͔͒.More specifically,recent work by the author and co-workers͓13,20–23͔,on wave-propagation problems showed that the gradient approach predicts types of elastic waves that are not predicted by the classical theory͑SH and torsional surface waves in homogeneous materials͒and also predicts dispersion of high-frequency Rayleigh waves͑the classical elasticity fails to predict dispersion of these waves at any frequency͒.Notice that all these phenomena are observed in experiments and are also predicted by atomic-lattice analyses͑see,e.g.,Gazis et al.͓25͔͒.Contributed by the Applied Mechanics Division of T HE A MERICAN S OCIETY OFM ECHANICAL E NGINEERS for publication in the ASME J OURNAL OF A PPLIED M E-CHANICS.Manuscript received by the ASME Applied Mechanics Division,Apr.28,2002;final revision,Dec.19,2002.Associate Editor:B.M.Moran.Discussion onthe paper should be addressed to the Editor,Prof.Robert M.McMeeking,Depart-ment of Mechanical and Environmental Engineering University of California–SantaBarbara,Santa Barbara,CA93106-5070,and will be accepted until four months afterfinal publication of the paper itself in the ASME J OURNAL OF A PPLIED M ECHAN-ICS.Copyright©2003by ASMEJournal of Applied Mechanics JULY2003,Vol.70Õ517Thus,based on existing gradient-type results,one may conclude that the Mindlin-Green-Rivlin theory extends the range of appli-cability of continuum theories in an effort towards bridging the gap between classical͑monopolar or nongeneralized͒theories of continua and theories of atomic lattices.In the present work the concept adopted,following the afore-mentioned ideas,is to view the continuum as a periodic structure like that,e.g.,of crystal lattices,crystallites of a polycrystal or grains of a granular material.The material is composed wholly of unit cells͑micromedia͒having the form of cubes with edges of size2h.This size is therefore an intrinsic material length.We further assume͑and this is a rather standard assumption in studies applying the Mindlin-Green-Rivlin theory to practical problems͒that the continuum is homogeneous in the sense that the relative deformation͑i.e.,the difference between the macrodisplacementgradient and the microdeformation—cf.Mindlin͓1͔͒is zero andthe microdensity does not differ from the macrodensity.Then,weformulate the mode III crack problem by considering an isotropicand linear expression of the strain-energy density W.This expres-sion in antiplane shear and with respect to a Cartesian coordinatesystem Ox1x2x3reads Wϭp3p3ϩc(ץsp3)(ץsp3),where the summation convention is understood over the Latin indices,which take the values1and2only,(13,23)are the only iden-tically nonvanishing components of the linear strain tensor,is the shear modulus,c is the gradient coefficient͑a positive con-stant accounting for microstructural effects͒,andץs()ϵץ()/ץx s.The problem is two-dimensional and is stated in the plane(x1,x2).The above strain-energy density function is the simplest possible form of case II in Mindlin’s͓1͔theory and is appropriate for a gradient formulation with no couple-stress ef-fects,because W is completely independent upon rotation gradi-ents.Indeed,by referring to a strain-energy density function that depends upon strains and strain gradients in a three-dimensional body͑the Latin indices now span the range͑1,2,3͒͒,i.e.,a func-tion of the form Wϭ(1/2)c pqs jpqs jϩ(1/2)d pqs jlmpqsjlm with (c pqs j,d pqs jlm)being tensors of material constants andpqs ϭץpqsϵץpsq,and by defining the Cauchy͑in Mindlin’s nota-tion͒stress tensor aspqϭץW/ץpq and the dipolar stress tensor ͑a third-rank tensor͒as m pqsϭץW/ץ(ץpqs),one may observe that the relations m pqsϭm p(qs)and m p[qs]ϭ0hold,where()and ͓͔as subscripts denote the symmetric and antisymmetric parts of a tensor,respectively.Accordingly,couple stresses do not appear within the present formulation by assuming dipolar͑internal͒forces with vanishing antisymmetric part͑more details on this are given in Section2below͒.A couple-stress,quasi-static solution of the mode-III crack problem was given earlier by Zhang et al.͓18͔. Note in passing that in the literature one mayfind mainly two types of approaches:In thefirst type͑couple-stress case͒the strain-energy density depends on rotation gradients and has no dependence upon strain gradients of the kind mentioned above ͑see,e.g.,͓11,17–19,23͔͒,whereas in the second type the strain-energy density depends on strain gradients and has no dependence upon rotation gradients͑see, e.g.,͓13,16,20–22͔͒.Exceptions from this trend exist of course͑see,e.g.,͓5–7͔͒and these works employ a more complicated formulation based on form III of Mindlin’s theory,͓1͔.Here,in addition to the quasi-static case,we also treat the time-harmonic dynamical case,which is pertinent to the problem ofstress-wave diffraction by a pre-existing crack in the body.In thelatter case,besides the standard inertia term in the equation ofmotion,a micro-inertia term is also taken into account͑in a con-sistent and rigorous manner by considering the proper kinetic-energy density͒and this leads to an explicit appearance of theintrinsic material length h.We emphasize that quasi-static ap-proaches cannot include explicitly the size of the material cell intheir governing equations.In these approaches,rather,a charac-teristic length appears in the governing equations only through the gradient coefficient c͑which has dimensions of͓length͔2)in the gradient theory without couple-stress effects or the ratio͑/͒͑which again has dimensions of͓length͔2)in the couple-stress theory without the effects of collinear dipolar forces,whereis the couple-stress modulus andis the shear modulus of the ma-terial.Of course,one of the quantities c or͑/͒also appears within a dynamic analysis,which therefore may allow for an in-terrelation of the two different characteristic lengths͑the one in-troduced in the strain energy and the other introduced in the ki-netic energy—see relative works by Georgiadis et al.͓22͔and Georgiadis and Velgaki͓23͔͒.Indeed,by comparing the forms of dispersion curves of Rayleigh waves obtained by the dipolar ͑‘‘pure’’gradient and couple-stress͒approaches with the ones ob-tained by the atomic-lattice analysis of Gazis et al.͓25͔,it can be estimated that c is of the order of(0.1h)2,͓22͔,andis of the order of0.1h2,͓23͔.The mathematical analysis of the dynamical problem here pre-sents some novel features related to the Wiener-Hopf technique not encountered in dealing with the static case.The Wiener-Hopf technique is employed to obtain exact solutions in both cases,and also the Williams technique is employed for an asymptotic deter-mination of the near-tipfields.Also,since the gradient formula-tion exhibits a singular-perturbation character,the concept of a boundary layer is employed to accomplish the solution.On the other hand,the gradient formulation demands extended definitions of the J-integral and the energy release rate.It is further proved, by utilizing some theorems of distribution theory,that both energy quantities remain bounded despite the hypersingular behavior of the near-tip stressfield.Finally,physical aspects of the solution are discussed with particular reference to the closure of the crack faces and the nature of cohesive tractions.2Fundamentals of the Dipolar Gradient ElasticityA brief account of the Mindlin-Green-Rivlin theory,͓1–3͔,per-taining to the elastodynamics of homogeneous and isotropic ma-terials is given here.If a continuum with microstructure is viewed as a collection of subparticles͑micromedia͒having the form of unit cells͑cubes͒,the following expression of the kinetic-energy density͑kinetic energy per unit macrovolume͒is obtained with respect to a Cartesian coordinate system Ox1x2x3,͓1͔,Tϭ12u˙p u˙pϩ16h2͑ץp u˙q͒͑ץp u˙q͒,(1)whereis the mass density,2h is the size of the cube edges,u p is the displacement vector,ץp()ϵץ()/ץx p,(˙)ϵץ()/ץt with t de-noting the time,and the Latin indices span the range͑1,2,3͒.We also notice that Georgiadis et al.͓22͔by using the concept of internal motions have obtained͑1͒in an alternative way to that by Mindlin͓1͔.In the RHS of Eq.͑1͒,the second term representing the effects of velocity gradients͑a term not encountered within classical continuum mechanics͒reflects the greater detail with which the dipolar theory describes the motion.Next,the following expression of the strain-energy density is postulated:Wϭ12c pqs jpqs jϩ12d pqs jlmpqsjlm,(2)where(c pqs j,d pqs jlm)are tensors of material constants,pq ϭ(1/2)(ץp u qϩץq u p)is the linear strain tensor,andpqsϭץpqs is the strain gradient.Notice that in the tensors c pqs j and d pqs jlm ͑which are of even rank͒the number of independent components can be reduced to yield isotropic constitutive relations.Such an isotropic behavior is considered here.Again,the form in͑2͒can be viewed as a more accurate description of the constitutive re-sponse than that provided by the classical elasticity,if one thinks of a series expansion for W containing higher-order strain gradi-ents.Also,one may expect that the additional term͑or terms͒will be significant in the vicinity of stress-concentration points where the strain undergoes very steep variations.Then,pertinent stress tensors can be defined by taking the variation of W518ÕVol.70,JULY2003Transactions of the ASMEpq ϭץWץpq,(3a )m pqs ϭץW ץpqs ϵץWץ͑ץp qs ͒,(3b )where pq ϭqp is the Cauchy ͑in Mindlin’s notation ͒stress tensor and m pqs ϭm psq is the dipolar ͑or double ͒stress tensor.The latter tensor follows from the notion of multipolar forces,which are antiparallel forces acting between the micro-media contained in the continuum with microstructure ͑see Fig.1͒.As explained by Green and Rivlin ͓2͔and Jaunzemis ͓26͔,the notion of multipolar forces arises rather naturally if one considers a series expansion for the mechanical power M containing higher-order velocity gra-dients,i.e.,M ϭF p u ˙p ϩF pq (ץp u ˙q )ϩF pqs (ץp ץq u ˙s )ϩ...,where F p are the usual forces ͑monopolar forces ͒within classical con-tinua and (F pq ,F pqs ,...)are the multipolar forces ͑dipolar or double forces,triple forces and so on ͒within generalized con-tinua.In this way,the resultant force on an ensemble of subpar-ticles can be viewed as being decomposed into external and inter-nal forces with the latter ones being self-equilibrating ͑see Fig.1͒.However,these self-equilibrating forces ͑which are multipolar forces ͒produce nonvanishing stresses,the multipolar stresses.Ex-amples of force systems of the dipolar collinear or noncollinear type are given,e.g.,in Jaunzemis ͓26͔and Fung ͓27͔.As for the notation of dipolar forces and stresses,the first index of the forces denotes the orientation of the lever arm between the forces and the second index the orientation of the pair of the forces;the same meaning is attached to the last two indices of the stresses,whereas the first index denotes the orientation of the normal to the surface on which the stress acts.The dipolar forces F pq have dimensions of ͓force ͔͓length ͔;their diagonal terms are double forces without moment and their off-diagonal terms are double forces with moment.The antisymmetric part F [pq ]ϭ(1/2)(x p F q Ϫx q F p )gives rise to couple stresses.Here,we do not consider couple-stress effects emphasizing that this is compat-ible with the particular choice of the form of W in ͑2͒,i.e.,a form dependent upon the strain gradient but completely independent upon the rotation gradient.Further,the equations of motion and the tractionboundary con-ditions along a smooth boundary can be obtained either from Hamilton’s principle ͑Mindlin ͓1͔͒or from the momentum balance laws and their application on a material tetrahedron ͑Georgiadis et al.͓22͔͒:ץp ͑pq Ϫץs m spq ͒ϭu ¨q Ϫh 23͑ץpp u¨q ͒,(4)n q ͑qs Ϫץp m pqs ͒ϪD q ͑n p m pqs ͒ϩ͑D l n l ͒n p n q m pqs ϩh 23n r ͑ץr u ¨s͒ϭP s (n ),(5a )n q n r m qrs ϭR s (n ),(5b )where body forces are absent,D p ()ϭץp ()Ϫn p D (),D ()ϭn l ץl (),n s is the unit outward-directed vector normal to theboundary,P s(n )is the surface force per unit area ͑monopolar trac-tion ͒,and R s (n )is the surface double force per unit area ͑dipolar traction ͒.Finally,it is convenient for calculations to introduce another quantity,which is a kind of ‘‘balance stress’’͑see Eq.͑7͒below ͒,and is defined aspq ϭpq ϩ␣pq ,(6)where ␣qs ϭ(h 2/3)(ץq u¨s )Ϫץp m pqs .With this definition,Eq.͑4͒takes the more familiar formץp pq ϭu ¨q .(7)Notice that pq is not an objective quantity since it contains the acceleration terms (h 2/3)(ץq u ¨s ).These micro-inertia terms also are responsible for the asymmetry of pq .This,however,does not pose any inconsistency but reflects the role of micro-inertia and the nonstandard nature of the theory.In the quasi-static case,where the acceleration terms are absent,pq is an objective tensor.On the other hand,the constitutive equations should definitely obey the principle of objectivity ͑cf.Eqs.͑9͒and ͑10͒below ͒.Now,the simplest possible form of constitutive relations is ob-tained by taking an isotropic version of the expression in ͑2͒in-volving only three material constants.This strain-energy density function readsW ϭ12pp qq ϩpq pq ϩ12c ͑ץs pp ͒͑ץs qq ͒ϩc ͑ץs pq ͒͑ץs pq ͒,(8)and leads to the constitutive relationspq ϭ␦pq ss ϩ2pq ,(9)m spq ϭc ץs ͑␦pq j j ϩ2pq ͒,(10)where ͑,͒are the standard Lame´’s constants,c is the gradient coefficient ͑material constant with dimensions of ͓length ͔2),and ␦pq is the Kronecker delta.Equations ͑9͒and ͑10͒written for a general three-dimensional state will be employed below only for an antiplane shear state.In summary,Eqs.͑4͒,͑5͒,͑9͒,and ͑10͒are the governing equa-tions for the isotropic dipolar-gradient elasticity with no couple bining ͑4͒,͑9͒,and ͑10͒leads to the field equation of the problem.Pertinent uniqueness theorems have been proved for various forms of the general theory ͑Mindlin and Eshel ͓4͔,Achenbach et al.͓9͔,and Ignaczak ͓28͔͒on the basis of positive definiteness of the strain-energy density.The latter restriction re-quires,in turn,the following inequalities for the material con-stants appearing in the theory employed here ͑Georgiadis et al.͓22͔͒:(3ϩ2)Ͼ0,Ͼ0,c Ͼ0.In addition,stability for the field equation in the general inertial case was proved in ͓22͔and to accomplish this the condition c Ͼ0is a necessary one ͑we notice incidentally that some heuristic gradient-like approaches not employing the rigorous Mindlin-Green-Rivlin theory appeared in the literature that take a negative c —their authors,unfortu-nately,do not realize that stability was lost in their field equation ͒.Finally,the analysis in ͓22͔provides the order-of-magnitude esti-mate (0.1h )2for the gradient coefficient c ,in terms of the intrin-sic material length h.Fig.1Monopolar …external …and dipolar …internal …forces act-ing on an ensemble of subparticles in a material with micro-structureJournal of Applied MechanicsJULY 2003,Vol.70Õ5193Formulation of the Quasi-Static Mode III Crack Problem,the J -Integral,and the Energy Release RateConsider a crack in a body with microstructure under a quasi-static antiplane shear state ͑see Fig.2͒.As will become clear in the next two sections,the semi-infinite crack model serves in a boundary layer type of analysis of any crack problem provided that the crack faces in the problem under consideration are trac-tion free.It is assumed that the mechanical behavior of the body is determined by the Eqs.͑4͒,͑5),(9),and ͑10͒of the previous section.An Oxyz Cartesian coordinate system coincident with the system Ox 1x 2x 3utilized previously is attached to that body,and an antiplane shear loading is taken in the direction of z -axis.Also,a pure antiplane shear state will be reached,if the body has the form of a thick slab in the z -direction.In such a case,the follow-ing two-dimensional field is generated:u x ϭu y ϭ0,(11a )u z ϵw 0,(11b )w ϵw ͑x ,y ͒,(11c )and Eqs.͑8)–(10͒take the formsW ϭ͑xz 2ϩyz 2͒ϩcͫͩץxz ץx ͪ2ϩͩץxzץyͪ2ϩͩץyzץxͪ2ϩͩץyz ץyͪ2ͬ,(12)xz ϭץw ץx ,(13a )yz ϭץw ץy,(13b )m xxz ϭc ץ2wץx 2,(14a )m xyz ϭcץ2wץx ץy ,(14b )m yxz ϭc ץ2wץx ץy ,(14c )m yyz ϭc ץ2wץy2.(14d )Further,͑4͒provides the equation of equilibriumץץx ͩxz Ϫץm xxz ץx Ϫץm yxz ץy ͪϩץץy ͩyz Ϫץm xyz ץx Ϫץm yyzץyͪϭ0,(15)which along with ͑13͒and ͑14͒leads to the following field equa-tion of the problem c ٌ4w Ϫٌ2w ϭ0,(16)where ٌ2ϭ(ץ2/ץx 2)ϩ(ץ2/ץy 2)and ٌ4ϭٌ2ٌ2.Finally,one may utilize pq defined in ͑6͒for more economy in writing some equa-tions in the ensuing analysis.The antiplane shear components of this quantity are as follows:xz ϭͩץw ץx ͪϪc ٌ2ͩץwץx ͪ,(17a )yz ϭͩץw ץy ͪϪc ٌ2ͩץwץyͪ.(17b )Assume now that the cracked body is under a remotely applied loading that is also antisymmetric about the x -axis ͑crack plane ͒.Also,the crack faces are traction-free.Due to the antisymmetry of the problem,only the upper half of the cracked domain is consid-ered.Then,the following conditions can be written along the plane (ϪϱϽx Ͻϱ,y ϭ0):t yz ϵyz Ϫץm xyz ץx Ϫץm yyz ץy Ϫץm yxzץxϭ0for ͑ϪϱϽx Ͻ0,y ϭ0͒,(18)m yyz ϭ0for ͑ϪϱϽx Ͻ0,y ϭ0͒,(19)w ϭ0for ͑0Ͻx Ͻϱ,y ϭ0͒,(20)ץ2wץy 2ϭ0for ͑0Ͻx Ͻϱ,y ϭ0͒,(21)where ͑18͒and ͑19͒directly follow from Eqs.͑5͒͑notice also that ͑18͒can be written as yz Ϫ(ץm yxz /ץx )ϭ0by using the pq quantity ͒,t yz is defined as the total monopolar stress,and ͑20͒together with ͑21͒always guarantee an antisymmetric displace-ment field w.r.t.the line of the crack prolongation.The definition of the stress t yz follows from ͑5a ͒.The problem described by ͑11)–(21͒will be considered by both the asymptotic Williams method and the exact Wiener-Hopf technique.Notice finally that no difficulty will arise by having zero boundary conditions along the crack faces since,eventually,the solution will be matched at regions where gradient effects are not dominant ͑i.e.,for x ӷc 1/2)with the K III field of the classical theory and in this way the remote loading will appear in the solution.Next,we present the new extended definitions of the J -integral and the energy release rate G .These definitions of the energy quantities are pertinent to the present framework of dipolar gradi-ent elasticity and to the aforementioned case of a crack in a quasi-static antiplane shear state.By following relative concepts from Rice ͓29,30͔,we first introduce the definitionJ ϭ͵⌫ͩWdy ϪP ¯z(n )ץw ץx d ⌫ϪR ¯z(n )D ͩץw ץxͪd ⌫ͪ,(22)where ⌫is a two-dimensional contour surrounding the crack tip͑see Fig.2͒,whereas the monopolar and dipolar tractions P ¯z (n )and R ¯z (n )on ⌫are given asP ¯z (n )ϭn q ͑qz Ϫץp m pqz ͒ϪD q ͑n p m pqz ͒ϩ͑D l n l ͒n p n q m pqz ,(23a )R ¯z (n )ϭn p n q m pqz .(23b )In the above expressions,n p with components (n x ,n y )is the unit outward-directed vector normal to ⌫,the differential operators D and D p were defined in Section 2,W is the strain-energy density function given by ͑12͒,and the indices (l ,p ,q )take the values x and y only.Of course,the above expressions for the tractions on ⌫are compatible with Eqs.͑5͒.Further,it can be proved that the inte-gral in ͑22͒is path independent by following Rice’s,͓29͔,proce-dure.Path independence is of great utility since it permits alter-nate choices of integration paths that may lead to adirectFig.2A crack under a remotely applied antiplane shear load-ing.The contour ⌫surrounding the crack tip serves for the definition of the J -integral.520ÕVol.70,JULY 2003Transactions of the ASMEevaluation of J .We should mention at this point that ͑22͒is quite novel within the present version of the gradient theory ͑i.e.,a form without couple stresses ͒,but expressions for J within the couple-stress theory were presented before by Atkinson and Leppington ͓31͔,Zhang et al.͓18͔,and Lubarda and Markenscoff ͓32͔.In particular,the latter work gives a systematic derivation of conser-vation integrals by the use of Noether’s theorem.Finally,we no-tice that the way the J -integral will be evaluated below is quite different than that by Zhang et al.͓18͔.Indeed,use of the theory of distributions in the present work leads to a very simple way to evaluate J ͑see Section 7below ͒.As for the energy release rate ͑ERR ͒now,we also modify the classical definition in order to take into account a higher-order term that is compatible with the present strain-gradient frameworkG ϭlim⌬x →0͵0⌬x ͫt yz ͑x ,y ϭ0͒•w ͑x ,y ϭ0͒ϩm yyz ͑x ,y ϭ0͒•ץw ͑x ,y ϭ0͒ץyͬdx⌬x,(24)where ⌬x is the small distance of a crack advancement.Of course,any meaningful crack-tip field given as solution to an associated mathematical problem,should result in a finite value for the energy quantities defined above.Despite the strong singu-larity of the stress field obtained in Sections 5and 6,the results of Section 7prove that J and G are indeed bounded.4Asymptotic Analysis by the Williams MethodAs is well known,Williams ͓33,34͔͑see also Barber ͓35͔͒de-veloped a method to explore the nature of the stress and displace-ment field near wedge corners and crack tips.This is accom-plished by attaching a set of (r ,)polar coordinates at the cornerpoint and by expanding the stress field as an asymptotic series in powers of r .By following this method here we are concerned,in a way,only with the field components in the sharp crack at very small values of r ,and hence we imagine looking at the tip region through a strong microscope so that situations like the ones,e.g.,on the left of Fig.3͑i.e.,a finite length crack,an edge crack or a crack in a strip ͒appear to us like the semi-infinite crack on the right of this figure.The magnification is so large that the other surfaces of the body,including the loaded remote boundaries,ap-pear enough far away for us to treat the body as an ‘‘infinite wedge’’with ‘‘loading at infinity.’’The field is,of course,a com-plicated function of (r ,)but near to the crack tip ͑i.e.,as r →0)we seek to expand it as a series of separated variable terms,each of which satisfies the traction-free boundary conditions on the crack faces.In view of the above,we consider the following separated form w (r ,)ϭr ϩ1u (),where the displacement satisfies ͑16͒.Fur-ther,if only the dominant singular terms in ͑16͒are retained,the PDE of the problem becomes ٌ4w ϭ0,where ٌ4ϭٌ2ٌ2ϭ(ץ2/ץr 2ϩ1/r ץ/ץr ϩ1/r 2ץ2/ץ2)2.Also,in view of the defini-tions of stresses as combinations of derivatives of w and by re-taining again only the dominant singular terms,the boundary con-ditions t yz (x ,y ϭϮ0)ϭ0and m yyz (x ,y ϭϮ0)ϭ0will give at ϭϮͩץ2ץr 2ϩ1r 2ץ2ץ2ϩ1r 2ͪץwץϭ0,(25a )ͩ1r ץץr ϩ1r 2ץ2ץ2ͪw ϭ0.(25b )In addition,the pertinent antisymmetric solution ͑i.e.,with odd behavior in ͒to the equation ٌ4w ϭ0has the following general form:w ϭr ϩ1͑A 1sin ͓͑ϩ1͔͒ϩA 2sin ͓͑Ϫ1͔͒͒,(26)where is ͑in general ͒a complex number and (A 1,A 2)are un-known constants.Now,͑25͒and ͑26͒provide the eigenvalue prob-lem͑ϩ1͒cos ͓͑ϩ1͔͒•A 1Ϫ3͑Ϫ1͒cos ͓͑Ϫ1͔͒•A 2ϭ0,(27a )͑ϩ1͒sin ͓͑ϩ1͔͒•A 1ϩ͑Ϫ3͒sin ͓͑Ϫ1͔͒•A 2ϭ0.(27b )For a nontrivial solution to exist,the determinant of the coeffi-cients of (A 1,A 2)in the above system should vanish and this gives the result:sin(2)ϭ0⇒ϭ0,1/2,1,3/2,2,....Next,by observing from ͑12͒that the strain-energy density W behaves at most as (ץ2w /ץr 2)or,by using the form w (r ,)ϭr ϩ1u (),no worse than r Ϫ1,we conclude that the maximum eigenvalue al-lowed by the integrability condition of the strain-energy density is ϭ1/2.The above analysis suggests that the general asymptotic solu-tion is of the form w (r ,)ϭr 3/2u (),which by virtue of ͑26͒and ͑27b ͒becomesw ͑r ,͒ϭAr 3/2͓3sin ͑/2͒Ϫ5sin ͑3/2͔͒,(28)where A ϵϪA 1and the other constant in ͑26͒is given by ͑27b ͒as A 2ϭ3A 1/5.The constant A ͑amplitude of the field ͒is left un-specified by the Williams technique but still the nature of the near-tip field has been determined.Finally,the total monopolar stress has the following asymptotic behavior:t yz ͑x ,y ϭ0͒ϭO ͑x Ϫ3/2͒as x →ϩ0.(29)This asymptotic behavior will also be corroborated by the results of the exact analysis in the next section.5Exact Analysis by the Wiener-Hopf MethodAn exact solution to the problem described by ͑11͒–͑21͒will be obtained through two-sided Laplace transforms ͑see,e.g.,van der Pol and Bremmer ͓36͔and Carrier et al.͓37͔͒,theWiener-Fig.3William’s method:the near-tip fields of …i …a finite length crack,…ii …an edge crack,and …iii …a cracked strip correspond to the field generated in a body with a semi-infinite crackJournal of Applied MechanicsJULY 2003,Vol.70Õ521。
写烛虽然小带来巨大的希望的英语作文
写烛虽然小带来巨大的希望的英语作文全文共3篇示例，供读者参考篇1A Flickering Flame of HopeThe room was cloaked in darkness, the power outage an unwelcome reminder of the fragility of modern life. As I fumbled for a flashlight, my fingers brushed against a small box of matches instead. With a sharp strike, a solitary flame danced to life, its warm glow instantly banishing the shadows. In that moment, I was struck by the realization that even the smallest light can illuminate the deepest darkness, becoming a beacon of hope and resilience.In our fast-paced, technology-driven world, we often take the reliability of electricity for granted. Yet, when the lights go out, we are reminded of how dependent we have become on this invisible force that powers our lives. The sudden absence of illumination can be unsettling, leaving us feeling vulnerable and disconnected from the comforts we've grown accustomed to.However, as I gazed at the flickering candle, I couldn't help but marvel at its simplicity and symbolism. This humble source oflight, a mere combination of wax and wick, had the power to transcend the boundaries of darkness, offering a sense of security and warmth in the midst of uncertainty.Throughout history, candles have played a crucial role in human civilization, serving as a guiding light in times of adversity and struggle. From the ancient Egyptians who used rush lights to illuminate their pyramids, to the medieval monks who painstakingly crafted beeswax candles for their monasteries, the flame has been a constant companion to humanity's journey.In times of war and conflict, candles have provided solace and inspiration to those seeking refuge. During the dark days of World War II, the inhabitants of London would gather in underground shelters, huddled around the soft glow of candles, finding strength in their collective resilience. The flame became a symbol of hope, reminding them that even in the face of overwhelming adversity, the human spirit could not be extinguished.Beyond their practical applications, candles have also held deep spiritual and cultural significance across various traditions and beliefs. In religious ceremonies, the flickering flame represents the divine, a reminder of the eternal light that guides us through the darkness of life's challenges. The simple act oflighting a candle can become a profound ritual, a moment of reflection and connection with something greater than ourselves.In our personal lives, candles have the power to create an atmosphere of warmth and intimacy. Whether it's a romantic dinner by candlelight, a cozy evening spent reading a book, or a quiet moment of meditation, the gentle glow of a candle can transform the ordinary into something extraordinary.But perhaps the most remarkable aspect of a candle's flame is its ability to ignite hope in the face of despair. When all else seems lost, when the darkness feels overwhelming, the mere presence of a single candle can reignite the spark of determination within us. Its unwavering light reminds us that even the smallest actions can have a profound impact, that perseverance and resilience can overcome the greatest challenges.This notion is beautifully encapsulated in the words of the renowned author and activist, Maya Angelou, who once said, "A candle is a small thing. But one candle can light another, and see how its own light increases, as a sunbeam multiplied by a million tiny mirrors." Her words remind us that hope is not a finite resource, but rather a flame that can be shared and kindled,spreading from one heart to another, until it illuminates even the darkest corners of despair.As I watched the candle burn, its wax slowly melting away, I couldn't help but feel a sense of awe and gratitude for this humble object that has played such a significant role in the human experience. In its simplicity, it holds the power to inspire, to comfort, and to remind us of the profound resilience that lies within each of us.In a world that often feels overwhelming and chaotic, the flicker of a candle serves as a gentle reminder to pause, to reflect, and to find solace in the small moments that bring light into our lives. It is a symbol of hope, a testament to the enduring strength of the human spirit, and a promise that no matter how dark the night may seem, the dawn will always break, and with it, the possibility of a brighter tomorrow.As the candle's flame danced before me, casting its warm glow across the room, I couldn't help but feel a sense of renewed determination. For in that moment, I understood that even the smallest light can dispel the deepest darkness, and that within each of us lies the potential to be a beacon of hope, a guiding flame that illuminates the path for others to follow.篇2The Flicker of HopeSometimes, it's the smallest things that can make the biggest impact in our lives. A single candle may seem insignificant, a mere speck of light in the vast darkness. But to me, that flickering flame represents so much more – it's a beacon of hope that guides me through even the darkest of times.I remember the first time I truly appreciated the power of a candle. It was during a particularly difficult period in my life when everything seemed to be falling apart. My grades were slipping, I was struggling to make ends meet with my part-time job, and the stress was taking a toll on my mental health. It felt like a never-ending cycle of despair, and I was slowly losing my grip on reality.One night, as I sat alone in my dimly lit room, staring blankly at the wall, a sudden power outage plunged me into complete darkness. Panic started to set in, and I could feel my anxiety levels rising. But then, I remembered the emergency candles I had stashed in my drawer. With trembling hands, I lit one, and the soft glow immediately brought a sense of calm over me.As I watched the flame dance and flicker, I couldn't help but be mesmerized by its beauty. It was a small yet powerful reminder that even in the darkest of times, there was still a glimmer of hope. That single candle became a symbol of resilience, a reminder that no matter how overwhelming the circumstances, there was always a way to find light in the darkness.From that moment on, I made it a habit to light a candle whenever I felt overwhelmed or discouraged. It became a ritual, a way to center myself and refocus my energy on the things that truly mattered. The warm, comforting glow of the candle would envelop me, reminding me that even the smallest flickering flame could chase away the shadows of doubt and fear.As I progressed through my academic journey, the significance of the candle only grew stronger. During late-night study sessions, when the weight of my coursework threatened to crush me, the gentle flicker of the candle would keep me company, its steady presence reminding me of my determination and ability to persevere.And when the day of a major exam or presentation arrived, I would light a candle as a symbol of hope – a reminder that I hadput in the hard work and preparation, and that no matter the outcome, the flame would continue to guide me forward.But it wasn't just in my academic life that the candle played a role. In moments of personal struggle, when relationships were strained or life threw unexpected curveballs my way, that little flame became a beacon of strength and resilience. It reminded me that even in the darkest of times, there was always a flicker of hope waiting to be ignited.As I reflect on my journey, I realize that the candle has become so much more than just a source of light. It has become a metaphor for the human spirit, a representation of our ability to find hope and persevere even in the most challenging circumstances.Just as a single candle can illuminate an entire room, a tiny spark of hope can illuminate the darkest corners of our lives. It's a reminder that no matter how overwhelming the challenges may seem, there is always a way forward, a path to follow, guided by the unwavering light of determination and resilience.And that's the true power of the candle – it's not just a source of light, but a symbol of our strength, our courage, and our unwavering belief in a better tomorrow. It's a reminder thateven in the darkest of times, we have the power to ignite our own flame of hope and let it guide us through the shadows.So, whenever I feel lost or overwhelmed, I will continue to light a candle and let its gentle glow remind me of the incredible resilience that lies within each and every one of us. For in that flickering flame, I see the promise of a brighter future, a world where hope triumphs over despair, and the light of perseverance shines through even the darkest of nights.篇3The Flicker of Hope: How a Small Candle Can Illuminate the DarknessAs students, we often find ourselves juggling a multitude of responsibilities, from academic demands to extracurricular activities and even part-time jobs. Amidst the chaos, it's easy to feel overwhelmed and lose sight of the light at the end of the tunnel. However, it's during these moments of uncertainty and despair that the simplest of things can reignite our spirits and remind us of the power of hope.One such humble object that holds the capacity to instill hope is the humble candle. At first glance, a candle may seem like an insignificant and ordinary item – a mere source of lightand warmth. But upon closer examination, it becomes apparent that these small, flickering flames carry a profound symbolism that transcends their physical form.To understand the magnitude of a candle's impact, we must first delve into the depths of its history. Candles have been an integral part of human civilization for centuries, serving as beacons of guidance, illuminating the way for travelers and providing comfort in times of darkness. From ancient rituals to religious ceremonies, the gentle glow of candlelight has held immense cultural and spiritual significance across various traditions and beliefs.Perhaps the most poignant example of a candle's symbolic power lies in its ability to represent hope in the face of adversity. Throughout history, candles have been lit in times of turmoil, conflict, and grief, serving as a tangible representation of our collective resilience and unwavering spirit. During the darkest hours of World War II, for instance, the residents of London would gather in shelters, illuminating their surroundings with flickering candles as a defiant act of hope amidst the chaos of air raids.Even in our modern times, the act of lighting a candle carries profound emotional weight. When faced with personalchallenges, tragedies, or societal injustices, people from all walks of life come together, lighting candles in solidarity and remembrance. These small flames become beacons of unity, reminding us that even in the depths of darkness, a glimmer of hope remains.As students, we can draw immense inspiration from the symbolism of candles, especially during periods of academic stress and personal struggle. When the weight of deadlines, exams, and extracurricular commitments threatens to overwhelm us, the simple act of lighting a candle can serve as a powerful reminder of our strength and resilience.Imagine sitting at your desk, surrounded by piles of books and assignments, feeling the weight of the world on your shoulders. In that moment of despair, the gentle flicker of a candle's flame can be a grounding force, reminding you of the light that burns within – a light that cannot be extinguished by the trials and tribulations of student life.The soft glow of the candle casts a warm, comforting ambiance, creating a sacred space for introspection andself-reflection. As the flame dances, its mesmerizing movements can serve as a metaphor for the ebb and flow of life's challenges,reminding us that even the most arduous journeys are punctuated by moments of tranquility and beauty.Furthermore, the very nature of a candle's existence serves as a poignant metaphor for our own personal growth and development. Just as a candle must burn through its wax to shed light, we too must navigate through the challenges and obstacles that life presents, emerging stronger, wiser, and more resilient on the other side.But the power of a candle extends far beyond its symbolic significance. In practical terms, the gentle illumination provided by candlelight can create an environment conducive to focused study and self-care. The warm, calming ambiance can help alleviate stress and anxiety, allowing us to approach our academic tasks with a clearer mind and a renewed sense of determination.Moreover, the act of lighting a candle can become a ritual in itself – a moment of pause and reflection amidst the chaos of student life. As we strike the match and watch the wick ignite, we can consciously set intentions, visualize our goals, and reaffirm our commitment to personal growth and academic excellence.In essence, a candle's flame serves as a tangible reminder that even the smallest of lights can dispel the greatest ofdarkness. It reminds us that hope is not a fleeting emotion but rather a powerful force that can guide us through even the most daunting of challenges.As we navigate the winding paths of our academic journeys, let us embrace the symbolic power of the candle. Let its flickering flame be a constant reminder that within each of us burns an inextinguishable light – a light that has the power to illuminate our path, inspire our dreams, and guide us towards a brighter future.For in the end, it is not the size or grandeur of the light that matters, but rather the courage and resilience it inspires within us. As students, let us hold fast to the hope that a single candle can ignite, and let its warmth and radiance be the beacon that guides us through the darkest of nights and towards the dawn of a new day.。
一次感到压力的经历英语作文
一次感到压力的经历英语作文Experiencing Pressure: A ReflectionPressure is a universal experience that we all encounter in our lives, whether it's in our personal, academic, or professional spheres. For me, one particular instance of feeling immense pressure stands out in my memory. It was a time when I felt overwhelmed, uncertain, and pushed to my limits, but ultimately, it was an experience that taught me valuable lessons about resilience, adaptability, and personal growth.The situation arose during my final year of university, a period renowned for its academic rigor and the mounting demands placed on students. As I neared the end of my degree program, the workload seemed to intensify exponentially. Juggling multiple challenging courses, a part-time job, and extracurricular activities, I found myself stretched thin, struggling to keep up with the relentless pace.The turning point came when I was tasked with completing a capstone project, a comprehensive assignment that would serve as the culmination of my academic journey. The project requiredextensive research, meticulous planning, and flawless execution, all within a tight deadline. The pressure mounted as I grappled with the complexities of the task, feeling overwhelmed by the sheer volume of work and the high expectations placed upon me.As the deadline drew closer, the stress became palpable. I found myself staying up late into the night, fueled by caffeine and a desperate determination to succeed. The weight of the project seemed to bear down on me, and I began to question my abilities and whether I could truly deliver a project worthy of the high standards set before me.During this time, I experienced a range of emotions that I had never quite encountered before. Anxiety gripped me, making it difficult to focus and making me second-guess every decision. Self-doubt crept in, causing me to question my preparedness and wonder if I was truly capable of meeting the demands of the project. The pressure was relentless, and I found myself struggling to maintain a sense of balance and perspective.Despite the challenges, I knew that I had to push forward. Failure was not an option, and I was determined to see this project through to the end. I began to develop coping strategies to manage the stress, such as practicing mindfulness, engaging in regular exercise, and seeking support from my peers and mentors.As the deadline approached, I worked tirelessly, putting in long hours and sacrificing personal time to ensure that the project was completed to the best of my abilities. The final push was arduous, but I refused to give up, driven by a deep-seated desire to succeed and prove to myself that I could rise to the occasion.When the day of the presentation arrived, I felt a mixture of nervousness and anticipation. As I stood before the panel, presenting my work with confidence and clarity, I could sense the weight of the pressure slowly lifting from my shoulders. The feedback I received was overwhelmingly positive, and I felt a sense of immense pride and accomplishment in having overcome the challenges I had faced.Looking back on this experience, I can now see the invaluable lessons it has taught me. Firstly, it has shown me the importance of developing effective coping mechanisms to manage stress and pressure. The strategies I employed, such as mindfulness and self-care, have become integral to my personal toolkit, helping me navigate the ups and downs of life with greater resilience.Secondly, this experience has instilled in me a deeper appreciation for the power of determination and perseverance. When faced with seemingly insurmountable obstacles, it is easy to succumb to the temptation of giving up. However, by pushing through thechallenges and refusing to be defeated, I learned that I am capable of achieving far more than I ever thought possible.Finally, this experience has highlighted the significance of seeking support from others. Throughout the process, I leaned on my peers, professors, and mentors, who provided invaluable guidance, encouragement, and a listening ear when I needed it most. Recognizing the importance of building a strong support network has been a crucial lesson that has served me well in both my academic and professional pursuits.In the end, the pressure I experienced during my capstone project was a formative and transformative moment in my life. It challenged me, pushed me to my limits, and ultimately, helped me emerge as a more resilient, adaptable, and confident individual. The lessons I learned continue to guide me as I navigate the ever-changing landscape of life, reminding me that pressure, though daunting, can be a catalyst for personal growth and success.。
抱最好的希望,做最坏的打算 英语作文
抱最好的希望,做最坏的打算英语作文全文共3篇示例，供读者参考篇1Hope for the Best, Prepare for the WorstAs a student, I've learned that life is full of uncertainties and challenges. No matter how hard we study or how much we prepare, there's always the possibility that things won't go as planned. That's why I've come to embrace the philosophy of "hoping for the best, but preparing for the worst."At first glance, this mindset might seem pessimistic or negative. After all, shouldn't we always have a positive outlook and believe that everything will work out in our favor? While it's important to maintain a optimistic attitude, it's equally crucial to be realistic and recognize that setbacks and obstacles are an inevitable part of life.When I was in high school, I experienced the importance of this philosophy firsthand. I had my heart set on getting into my dream college, and I worked tirelessly to achieve the best grades and extracurricular activities possible. However, despite myefforts, I didn't get accepted. It was a devastating blow, and for a while, I felt like all my hard work had been for nothing.But then I realized that I had a backup plan – a safety school that I had applied to as a precaution. While it wasn't my first choice, it was still a good school, and I was grateful to have that option available to me. If I hadn't prepared for the possibility of not getting into my dream college, I would have been left with no options and a lot of disappointment.Since then, I've carried this philosophy with me throughout my academic journey. Before every exam or major assignment, I always make sure to study and prepare as much as possible. I put in the effort to achieve the best possible outcome. But at the same time, I also mentally prepare myself for the possibility that things might not go as well as I'd hoped.This mindset has helped me in several ways. First, it has allowed me to maintain a balanced perspective. Instead of being overly confident or pessimistic, I'm able to approach challenges with a healthy mix of optimism and realism. I'm hopeful that my hard work will pay off, but I'm also prepared to deal with any setbacks or obstacles that might arise.Second, it has helped me develop resilience and adaptability. When things don't go as planned, I don't get bogged down bydisappointment or self-doubt. Instead, I'm able to quickly shift gears and pivot to my backup plan. This has allowed me to bounce back from setbacks more easily and continue moving forward.Finally, this philosophy has taught me the importance of taking responsibility for my own success. Instead of relying solely on hope or wishful thinking, I understand that I need to take concrete actions to increase my chances of achieving my goals. By preparing for the worst, I'm actively working to minimize the potential negative consequences and giving myself the best possible chance of success.Of course, this approach isn't without its challenges. It can be tempting to get caught up in negative thinking or to become overly pessimistic. It's important to strike a balance between being realistic and maintaining a positive, hopeful attitude. Additionally, constantly preparing for the worst can be mentally and emotionally draining, which is why it's crucial to practice self-care and take breaks when needed.Despite these challenges, I firmly believe that the philosophy of "hoping for the best, but preparing for the worst" is a valuable one for students to embrace. It allows us to approach our academic and personal goals with a balanced, pragmaticmindset, while also giving us the resilience and adaptability to bounce back from setbacks.As I look towards the future, I know that there will be many more challenges and obstacles to overcome. But armed with this philosophy, I feel better equipped to navigate the uncertainties of life. I'll continue to work hard and strive for the best possible outcomes, but I'll also be prepared to pivot and adjust my plans as needed.Ultimately, the key is to find a balance between hope and preparation. We should never give up on our dreams or stop striving for the best possible outcomes. But at the same time, we must also be realistic and acknowledge that not everything will go according to plan. By combining optimism with pragmatism, we can increase our chances of success and better navigate the ups and downs of life.So, to my fellow students, I encourage you to embrace this philosophy as well. Hope for the best, but always prepare for the worst. Work hard, stay positive, but also have contingency plans in place. It's a mindset that will serve you well, not just in your academic journey, but in all aspects of your life.篇2Hope for the Best, Prepare for the WorstThey say that life is what happens when you're busy making other plans. No matter how much we try to control every little detail, there's always an element of unpredictability that we have to deal with. That's just how it goes – you can make all the plans you want, but at the end of the day, you have to be ready for whatever comes your way, good or bad.As a student, I've learned this lesson time and time again. You can study your heart out for an exam, but there's always a chance that a question will come up that completely throws you for a loop. Or you can practice diligently for a big game or performance, only to have something go wrong at the last minute. It's just part of life, and the sooner you accept that, the better off you'll be.That's why I've always tried to live by the motto "hope for the best, prepare for the worst." It's all about striking that delicate balance between optimism and pragmatism. On the one hand, you have to approach every situation with a positive attitude and a belief that things will work out in your favor. If you go into something expecting the worst, you've already defeated yourself before you've even started.But at the same time, you can't be so blindly optimistic that you fail to plan for potential setbacks or obstacles. That's just setting yourself up for disappointment and frustration. Instead, you have to realistically assess the situation and identify any potential challenges or roadblocks that might arise. And then you have to develop contingency plans to deal with those challenges if and when they do pop up.It's all about balance, really. You have to be optimistic enough to keep yourself motivated and focused on your goals, but you also have to be pragmatic enough to prepare for the worst-case scenario. That way, if everything goes according to plan, great! You can revel in your success and feel that much more accomplished. But if things don't go as expected, you're not caught completely off guard – you've already anticipated potential problems and have a plan in place to overcome them.I've tried to apply this mindset to pretty much every aspect of my life as a student. When I'm studying for an exam, I always go into it hoping that I'll ace it and that all of my hard work will pay off. But at the same time, I make sure to review the material thoroughly and to practice as many different types of questions as possible, just in case a curveball gets thrown my way.Or when I'm working on a big project or paper, I set ambitious goals for myself and envision turning in a top-notch final product. But I also build in plenty of buffer time and have backup plans in case I run into any unexpected roadblocks or setbacks along the way. Maybe my computer crashes and I lose some of my work, or maybe I get sick and have to take a few days off – whatever the case may be, I'm prepared to handle it without completely derailing my progress.And in my extracurricular activities, whether it's sports, music, or anything else, I always go into every game, performance, or event hoping to knock it out of the park. But I also make sure to properly warm up, double-check my equipment, and mentally prepare myself for any number of potential scenarios that could unfold. That way, if something does go wrong – if I get injured, if my instrument breaks, if there's some kind of technical difficulty – I'm not caught completely off guard, and I can adapt and adjust on the fly.At the end of the day, this mindset of hoping for the best while preparing for the worst has served me incredibly well throughout my academic career so far. It's helped me stay motivated and driven, while also keeping me grounded and level-headed. It's prevented me from getting too discouraged ordemoralized when things don't go according to plan, because I've already anticipated potential setbacks and have plans in place to deal with them.And perhaps most importantly, it's taught me some incredibly valuable life lessons about resilience, perseverance, and adaptability. No matter what curveballs life throws my way, I know that I have the ability to roll with the punches and bounce back stronger than ever. I've learned that setbacks and failures are inevitable – it's just part of the journey. But what really matters is how you respond to those setbacks, and whether you have the determination and grit to keep pushing forward, no matter what.So as I prepare to transition out of my life as a student and into whatever comes next, I know that I'll be taking this mindset with me. It's become such an integral part of who I am and how I approach every situation, both big and small. I'll continue to hope for the best in whatever I do, but I'll also make sure to prepare for every possible worst-case scenario that could arise.Because at the end of the day, that's just a smart way to live your life. You can't control every little thing that happens, but you can control how prepared you are to deal with whatever comes your way. And by striking that balance between optimismand pragmatism, between hoping for the best and preparing for the worst, you give yourself the best possible chance to succeed, no matter what obstacles you might face along the way.It's a simple motto, but one that has had a profound impact on my life and my approach to pretty much everything I do. So I'll keep on hoping for the best, but I'll also keep on preparing for the worst. That way, I know that I'll be ready for whatever life throws my way, come what may.篇3Hope for the Best, Prepare for the WorstAs a student, I have learned that it is important to maintain a positive outlook and have high aspirations, while also being pragmatic and prepared for potential challenges or setbacks. The adage "hope for the best, prepare for the worst" has become a guiding principle for me as I navigate my academic journey and plan for my future.Hoping for the best is essential because it provides the motivation and drive to pursue our goals and dreams. Without hope, it becomes easy to become discouraged and give up in the face of adversity. Hope fuels our ambition and encourages us to aim high, whether it is striving for top grades, gaining admissionto a prestigious university, or securing a coveted internship or job opportunity.In my case, I have always hoped to excel academically and gain admission to a top-tier university. This hope has driven me to work tirelessly, dedicate countless hours to studying, and continuously challenge myself to reach new heights. It has pushed me to take on advanced courses, participate in extracurricular activities, and seek out enriching experiences that will make me a well-rounded and competitive applicant.However, as important as hope is, it is equally crucial to prepare for the worst-case scenario. Life is unpredictable, and even the best-laid plans can sometimes go awry. Unforeseen circumstances, unexpected challenges, or simply bad luck can derail our aspirations, no matter how hard we have worked or how much we have hoped for success.As a student, I have witnessed my peers struggle with setbacks such as poor exam results, rejection from their dream schools, or personal or family issues that have impacted their academic performance. While it is devastating to see their hopes shattered, those who had prepared contingency plans or backup options were better equipped to navigate these challenges and adapt to their new circumstances.For this reason, I have learned to always have a plan B, C, or even D in mind. While my primary goal is to gain admission to a top university, I have also researched and identified other excellent institutions that align with my interests and career aspirations. I have explored alternative pathways, such as taking a gap year to gain work experience or pursuing a different degree program if my initial plans do not materialize.Preparing for the worst does not mean being pessimistic or losing sight of our hopes and dreams. Rather, it is a pragmatic approach that acknowledges the unpredictability of life and the potential for obstacles to arise. By having contingency plans in place, we can mitigate the impact of setbacks and retain a sense of control over our circumstances.Moreover, being prepared for the worst can actually help us achieve our best. When we have backup plans in place, we can approach our goals with a sense of confidence and reduced anxiety. Knowing that we have alternative options can free us from the paralyzing fear of failure and allow us to take calculated risks and seize opportunities that may lead to greater success.As I look ahead to the next chapter of my academic journey, I will continue to hope for the best while simultaneously preparing for the worst. I will maintain a positive and optimistic mindset,fueled by the belief that hard work and perseverance will ultimately pay off. At the same time, I will remain vigilant and proactive, continually assessing potential risks and developing contingency plans to address any challenges that may arise.This balanced approach has served me well thus far, and I am confident that it will continue to guide me as I navigate the complexities of higher education and eventually transition into the professional world. By hoping for the best and preparing for the worst, I can embrace both the opportunities and uncertainties that lie ahead, secure in the knowledge that I am equipped to adapt and thrive, no matter what life may bring.。
谈谈生活中带给你希望的人英语作文
全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：谈谈生活中带给你希望的人英语作文全文共3篇示例，供读者参考篇1People Who Bring Light to My WorldAs a student, life can often feel like an endless cycle of classes, assignments, exams, and stress. It's easy to get bogged down by the relentless demands and lose sight of the biggerpicture. However, amidst the chaos, there are certain individuals who serve as beacons of hope, illuminating my path and reminding me of the beauty and possibilities that exist beyond the confines of academic life. These are the people who bring light to my world and inspire me to keep moving forward.One such person is my grandmother. A woman of unwavering strength and resilience, she has weathered countless storms throughout her life, yet her spirit remains unbroken. Born into a world of limited opportunities for women, she defied societal norms and pursued her dreams with a tenacity that still leaves me in awe. Her journey was far from easy, but she never let adversity deter her from her goals.As I listen to her recount tales of her youth, I'm struck by the depth of her courage and determination. She speaks of a time when education for girls was considered a luxury, yet she fought tooth and nail to secure her right to learn. Her hunger for knowledge was insatiable, and she refused to be defined by the limitations imposed upon her by a society that undervalued the potential of women.My grandmother's unwavering pursuit of her dreams has taught me invaluable lessons about perseverance and the power of resilience. Whenever I feel overwhelmed by the demands ofstudent life, I think of her struggles and find renewed strength. Her example reminds me that no obstacle is too great to overcome if one possesses an unyielding spirit and an unwavering belief in oneself.Another individual who brings hope to my life is my best friend, Sarah. In a world that often values superficial connections, Sarah's genuine warmth and compassion stand out like a beacon in the darkness. She possesses an uncanny ability to see the best in people, even when they struggle to see it in themselves.Sarah's empathy and understanding have been a constant source of solace for me during the most challenging times of my academic journey. When the weight of expectations andself-doubt threatened to crush me, she was there, offering a listening ear and a shoulder to lean on. Her words of encouragement and unwavering belief in my abilities have lifted me up time and time again, reminding me that I am capable of achieving greatness, even when I doubted myself.Beyond her emotional support, Sarah's intellectual curiosity and thirst for knowledge have been a constant source of inspiration. She approaches every subject with a childlike sense of wonder, eager to learn and grow. Her infectious enthusiasm has reignited my own love for learning on countless occasions,reminding me that education is not merely a means to an end but a lifelong journey of self-discovery.In addition to the personal connections that bring hope to my life, I also find inspiration in the stories of those who have overcome tremendous adversity to achieve greatness. One such individual is Malala Yousafzai, the Pakistani activist who risked her life to fight for girls' education. Her unwavering courage and determination in the face of unimaginable challenges are a testament to the power of hope and the human spirit.Malala's story resonates deeply with me as a student. Her refusal to be silenced by those who sought to deny her the right to learn serves as a powerful reminder of the importance of education and the sacrifices made by countless individuals to ensure access to knowledge for all. Her resilience and unwavering commitment to her cause inspire me to never take my educational opportunities for granted and to use my voice to advocate for those who have been denied the same privileges.Furthermore, Malala's journey has taught me the invaluable lesson that one person can create lasting change in the world. Her unwavering belief in the transformative power of education has sparked a global movement, empowering millions of girlsand reminding us all that knowledge is the key to unlocking our full potential.As I navigate the complexities of student life, I find solace and inspiration in the stories of these remarkable individuals. Their journeys serve as a poignant reminder that hope is not a fleeting emotion but a powerful force that can propel us forward, even in the face of seemingly insurmountable obstacles.My grandmother's resilience, Sarah's compassion, and Malala's courage are but a few examples of the countless individuals who bring light to my world and inspire me to embrace the challenges that lie ahead. They remind me that life is a tapestry woven with both triumphs and struggles, and it is our ability to find hope in the darkest of moments that truly defines our character.As I look towards the future, I carry with me the lessons imparted by these beacons of hope. Their stories have taught me the value of perseverance, empathy, and the unwavering belief in oneself and one's dreams. They have instilled in me the courage to face adversity head-on and the determination to never give up, no matter how daunting the challenges may seem.In this ever-changing world, where uncertainty and doubt often loom large, it is the people who bring hope to our lives thatremind us of the enduring power of the human spirit. They are the ones who illuminate our paths, guiding us towards a future where our dreams can become reality, and our potential can be fully realized.So, to the grandmothers, best friends, and Malalas of the world, I say thank you. Thank you for being the light that guides us through the darkness, the inspiration that fuels our determination, and the hope that reminds us that anything is possible when we believe in ourselves and the power of our dreams.篇2People Who Have Brought Light Into My LifeAs I reflect on my journey through life thus far, I can't help but feel an immense sense of gratitude towards the individuals who have illuminated my path with their unwavering support, wisdom, and kindness. These remarkable people have not only inspired me but have also instilled within me a profound sense of hope, enabling me to persevere through life's challenges and embrace its boundless opportunities.One such person who has profoundly impacted my life is my beloved grandmother. Her resilience and unwavering spirit in theface of adversity have been a constant source of inspiration. Growing up in a era of great turmoil, she faced numerous hardships, yet she never allowed these obstacles to diminish her zest for life or her compassion for others. Her warm embrace and sage advice have provided me with a sanctuary of solace during my darkest moments, reminding me that even in the midst of darkness, there is always a glimmer of hope waiting to be discovered.Another individual who has left an indelible mark on my life is my high school English teacher, Mr. Johnson. With his infectious enthusiasm and profound love for literature, he ignited within me a passion for the written word that has become an integral part of my identity. His unwavering belief in my abilities and his encouragement to explore the depths of my creativity instilled in me a confidence that has propelled me forward, even when self-doubt threatened to consume me. Mr. Johnson's unwavering support and guidance have been a beacon of hope, reminding me that with perseverance and dedication, I can achieve any dream I set my mind to.Beyond the confines of my personal life, I have found hope in the extraordinary individuals who have dedicated their lives to making the world a better place. Nelson Mandela, a toweringfigure of resilience and forgiveness, stands as a shining example of the transformative power of hope. Despite enduring 27 years of unjust imprisonment, he emerged as a beacon of reconciliation, leading his nation towards a path of unity and healing. His unwavering commitment to justice and his ability to transcend hatred with love have inspired generations, reminding us that even in the darkest of circumstances, hope can prevail.Furthermore, the life and work of Malala Yousafzai, the youngest Nobel Prize laureate, have been a source of profound hope for millions around the world. Her courageous advocacy for girls' education, even in the face of life-threatening violence, has ignited a global movement that champions the fundamental right to education for all. Malala's unwavering determination and her refusal to be silenced by those who sought to oppress her have inspired countless individuals to speak out against injustice and fight for a more equitable world.These remarkable individuals have not only brought light into my life but have also illuminated the path for countless others. Their stories serve as a powerful reminder that hope is an inextinguishable force that can transcend even the darkest of circumstances. They have taught me that adversity is not an obstacle to be feared but rather a challenge to be embraced, forit is through our struggles that we discover the depths of our resilience and the true strength of our character.As I navigate the winding roads of life, I carry with me the lessons and inspiration imparted by these beacons of hope. Their influence has instilled within me a deep appreciation for the power of perseverance, compassion, and unwavering determination. They have shown me that hope is not merely a fleeting emotion but a powerful force that can transform lives, communities, and even nations.In a world that often seems consumed by darkness and despair, these individuals serve as shining examples of the indomitable spirit of hope. They remind us that even in the midst of our darkest hours, there is always a glimmer of light waiting to guide us towards a brighter future. It is this profound sense of hope that has sustained me through life's challenges and inspired me to embrace each day with a renewed sense of purpose and resilience.As I continue on my journey, I carry with me the invaluable lessons and inspiration imparted by these beacons of hope. Their legacies will forever serve as a reminder that regardless of the obstacles that may arise, hope remains an unbreakable force capable of illuminating even the darkest of paths. It is with thisunwavering belief in the transformative power of hope that I will continue to strive towards a better tomorrow, both for myself and for the world around me.篇3People Who Have Inspired Hope In My LifeLife can be full of challenges, setbacks and darkness at times. But even in the midst of difficult circumstances, there are always rays of light that shine through - people whose words, actions and spirit bring hope. As I reflect on my own journey, there are several individuals who have inspired me and filled me with optimism when I needed it most.The first person who comes to mind is my 7th grade English teacher, Mrs. Johnson. I still remember walking into her classroom on that first day of the school year feeling anxious and unsure of myself. I had always struggled with reading and writing, and English class filled me with dread. Mrs. Johnson must have sensed my apprehension, because she made a point of connecting with me individually during that first week."David," she said warmly, "I know English hasn't always been your favorite subject. But I see something special in you - a creative mind and a wonderful way with words when you letthem flow." Her belief in me was like a life raft pulling me above the waters of self-doubt. Slowly but surely, with her patient encouragement and the safe space she created for me to express myself, I started to view writing not as a chore but as an outlet. More than just improving my skills, Mrs. Johnson taught me that I had a unique voice worth sharing. That newfound confidence spilled over into other areas of my life as well. Whenever I feel stuck or runner's block in my writing now, I think back to her compassionate guidance, and my words start flowing again.Another beam of hope has been my best friend Jeremy. We met in freshman year of high school when we were placed as randomly assigned roommates in the dorms. Our backgrounds couldn't have been more different - I was a shy, introverted kid from a small town, while Jeremy was this boisterous extrovert from the big city. But we clicked instantly over our mutual love of terrible puns and philosophical conversations about life's biggest questions.What has always amazed me about Jeremy is his ability to remain relentlessly optimistic even when facing immense adversity. During our junior year, Jeremy's dad lost his job and their family was forced to lose their home. Jeremy had to take on multiple part-time jobs to help make ends meet, all whilekeeping up with a full course load and extracurriculars. Many nights I would come back to our dorm room to find Jeremy stretched out on the floor surrounded by books, notes, and grinding away at his homework until the early morning hours. Yet no matter how exhausted he was, Jeremy always had a smile on his face and would find humor in the struggle."Hey man, at least we're getting RIPPED carrying all those heavy textbooks around!" he would joke, flexing his lanky arms. Jeremy's bright spirit and sense of unshakeable optimism, even in the darkest of storms, was like a lighthouse guiding me through my own doubts and difficulties. When I felt overwhelmed by stress, seeing Jeremy's steadfast perseverance was a reminder to keep pushing forward one step at a time. His outlook is what inspired me to start viewing challenges not as burdens but as opportunities for growth. Jeremy's friendship has shown me that the most hope-filled people aren't those who are blindly positive, but rather those who courageously make the choice to stay hopeful despite all the reasons they could be negative. That strength of spirit is something I strive to embody each day.Finally, the person who has most inspired enduring hope within me is someone whose name I've never known - a refugeeman I encountered a few years ago while volunteering at a shelter in my city. It was a bitterly cold winter night, and most of the other volunteers had gone home already. As I was getting ready to leave, I saw an elderly man enter through the doors, shivering and struggling to drag his few belongings inside. His face was weary and lined from years of hardship, but his eyes still shone with gentle warmth and resolve.I rushed to help bring his bags inside and offered to make him a warm meal. As I sat across from him, I shyly asked if he wouldn't mind sharing a bit of his story with me. What he proceeded to tell me was simultaneously heartbreaking yet incredibly inspiring. He spoke of fleeing violent conflict and oppression in his home country, making a treacherous journey across deserts and oceans with only what he could carry, facing discrimination and exploitation at every turn. He had lost his wife and children along the way. Here was a man who had endured more trauma, suffering and loss than I could scarcely imagine, yet there was no bitterness or despair in his voice. Instead, he exuded an unshakable sense of dignity, faith, and hope for the future."You know, young man," he said, gently placing his weathered hand on my arm. "In my homeland, there is a wisesaying: 'They tried to bury us...they didn't know we were seeds.' So no matter how deeply the weight of this world tries to keep me down, I will always rise up again, again, and again." His words echoed an eternal truth - that the human capacity for hope can endure through unimaginable darkness, and still blossom like a resilient flower pushing through concrete. I knew in that moment that I was in the presence of a person whose well of hope could never run dry, and whose spirit was truly unbreakable.As I've navigated the ups and downs of my youth, it is people like Mrs. Johnson, Jeremy, and that nameless yet unforgettable refugee man who have been my beacons of inspiration. Their examples have taught me that hope isn't something you simply feel - it's a choice you make. A choice to push forward, keep your head held high, and hold fast to optimism even when the world tries to breed pessimism. A choice to see the light, even when you're surrounded by shadows. It's a constant journey, but one I'm committed to undertaking each day.Because at the end of the day, a life without hope is a life half-lived. But when you surround yourself with people who radiate that powerful light, it becomes far easier to carry your own torch and be a source of hope and inspiration for others aswell. And in doing so, we create an unbreakable chain of resilient human spirits who refuse to let the darkness win. Our wicks may flicker at times, but our flames will never be extinguished. That is the gift those hopeful souls have bestowed upon me, and it's one I will be forever grateful for.。
做某事的秘诀英语作文
做某事的秘诀英语作文标题，The Secret to Achieving Success。
Success is a journey that many aspire to embark upon, yet few truly understand the essence of reaching their goals. In this essay, we delve into the secrets behind achieving success, drawing inspiration from various perspectives and experiences.First and foremost, one must possess unwavering determination. The road to success is fraught with challenges and setbacks, and it is the resilient spirit of those who refuse to yield that ultimately propels them forward. Take, for instance, the story of Thomas Edison, who famously remarked, "I have not failed. I've just found 10,000 ways that won't work," in his relentless pursuit of inventing the electric light bulb. It is this tenacity in the face of adversity that sets apart the successful from the rest.Moreover, success demands meticulous planning and strategic execution. Setting clear, achievable goals provides a roadmap for progress and helps to maintain focus amidst distractions. A study conducted by Harvard Business School revealed that individuals who documented their goals were significantly more likely to achieve them compared to those who did not. By breaking down larger objectives into smaller, manageable tasks, one can navigate through the complexities of their endeavors with greater efficiency.Furthermore, embracing failure as an integral part of the learning process is crucial for growth and development. The fear of failure often paralyzes individuals, preventing them from taking risks or pursuing their dreams. However,it is through failure that we gain invaluable insights and experiences that pave the way for future success. J.K. Rowling, the author of the Harry Potter series, faced numerous rejections before finding success. Yet, she persevered, using rejection as fuel to refine her craft and eventually becoming one of the best-selling authors of all time.In addition to personal attributes, success is often facilitated by a supportive network of mentors, peers, and allies. Surrounding oneself with individuals who share similar aspirations fosters collaboration, inspiration, and accountability. Warren Buffett, renowned investor and philanthropist, attributes much of his success to the guidance he received from his mentor, Benjamin Graham, and the like-minded community of investors he cultivated overthe years. A strong support system not only provides encouragement during challenging times but also offers valuable perspectives and resources that can propel one towards their goals.Moreover, cultivating a positive mindset and resilience in the face of adversity is paramount for long-term success. The ability to adapt to changing circumstances, bounce back from setbacks, and maintain optimism amidst uncertainty is what sets apart the truly successful individuals. Oprah Winfrey, media mogul and philanthropist, overcame a tumultuous childhood and numerous obstacles on her path to success. Through sheer determination and a positive outlook, she transformed her life and became one of the mostinfluential figures in the world.In conclusion, achieving success is a multifaceted journey that requires a combination of determination, strategic planning, resilience, support, and a positive mindset. By embracing these principles and learning from the experiences of those who have come before us, we can unlock our full potential and chart a course towards a fulfilling and successful life. As Ralph Waldo Emerson once said, "The only person you are destined to become is the person you decide to be." The secret to success lies within each of us, waiting to be discovered and unleashed upon the world.。
大学生心理课程英语作文
The Essence of College Mental HealthCoursesIn the fast-paced and often challenging environment of college life, mental health courses have become an integral part of the academic curriculum. These courses are designed to equip students with the necessary tools and strategies to navigate through the various psychological and emotional challenges they may encounter. As students transition from the familiar surroundings of high school to the more autonomous and unstructured world of higher education, they are often faced with newfound pressures and stressors. College mental health courses aim to address these issues and promote a healthy and balanced lifestyle.The primary objective of these courses is to raise awareness about mental health and its importance in overall well-being. They focus on educating students about various psychological concepts such as stress management, anxiety, depression, and self-esteem. Through lectures, discussions, and practical activities, students learn about the signs and symptoms of these conditions and how to recognize when they might be struggling.Another key aspect of college mental health courses is the emphasis on resilience and coping mechanisms. These courses teach students how to build resilience, the ability to bounce back from adversity, and develop healthy coping strategies. This is particularly crucial in college, where students are often faced with academic pressures, social challenges, and identity crises. By equipping them with these skills, the courses aim to empower students to overcome these obstacles and thrive.In addition, college mental health courses promote positive psychology and well-being. They encourage students to focus on their strengths, goals, and positive emotions, rather than just their weaknesses and problems. This shift in focus helps students cultivate a more optimistic and proactive mindset, enabling them to approach challenges with greater confidence and determination.Moreover, these courses often include components onself-care and self-love. They emphasize the importance of prioritizing one's own mental health and well-being, and provide guidance on how to achieve this. This might include tips on healthy sleep habits, stress-reducing activities,and maintaining a balanced diet. By encouraging students to take care of themselves, these courses aim to prevent burnout and promote a sustainable lifestyle.In conclusion, college mental health courses play a crucial role in promoting the overall well-being of students. They provide valuable education on psychological concepts, resilience, coping mechanisms, positive psychology, and self-care. By equipping students with these tools and strategies, these courses aim to help them navigate through the challenges of college life and emerge stronger and more resilient individuals.**大学生心理课程的本质**在快节奏且充满挑战的大学生活中，心理课程已经成为学术课程的重要组成部分。
英语作文 我的变化
英语作文我的变化Title: My Transformation。
Change is inevitable, an integral part of life's journey. Reflecting on my own metamorphosis, I realize the profound shifts that have sculpted my identity, beliefs, and aspirations. From a cocoon of uncertainties emerged a butterfly of resilience and growth, navigating the winds of change with grace and determination.My transformation began with a deep introspection, a quest to unravel the layers of my being and confront my fears and insecurities. This journey of self-discovery unveiled hidden strengths and weaknesses, laying the foundation for my evolution. With each challenge embraced and every obstacle overcome, I grew stronger, more resilient, and more self-assured.One of the most significant changes in my life has been my mindset. I transitioned from a fixed mindset to a growthmindset, embracing challenges as opportunities for learning and growth. Instead of fearing failure, I embraced it as a stepping stone towards success, viewing setbacks as valuable lessons rather than insurmountable barriers. This shift in perspective has empowered me to pursue my goals with renewed vigor and determination, unafraid to venture outside my comfort zone and explore new horizons.Alongside my mindset, my priorities underwent a profound transformation. I learned to prioritize self-care and mental well-being, recognizing the importance of nurturing my physical, emotional, and spiritual health. I adopted healthier habits, incorporating regular exercise, meditation, and mindfulness into my daily routine. By prioritizing self-care, I cultivated a greater sense of balance and harmony in my life, enabling me to tackle challenges with a clear and focused mind.Moreover, my interpersonal relationships have evolved significantly over time. I have learned to cultivate deeper connections with others, fostering empathy, compassion, and understanding in my interactions. I became more adept atcommunicating my thoughts and feelings, expressing myself authentically and assertively while respecting the perspectives of others. This transformation has enriched my relationships, fostering trust, mutual respect, and genuine connection.In addition to personal growth, my professional aspirations have undergone a metamorphosis of their own. I transitioned from a state of uncertainty and indecision to a clear sense of purpose and direction. I identified my passions and strengths, aligning them with my career goals and aspirations. With a newfound clarity of purpose, I pursued opportunities for growth and development, seizing every chance to expand my knowledge, skills, and expertise in my chosen field.Furthermore, my attitude towards failure and adversity has evolved significantly. Instead of viewing them as insurmountable obstacles, I now see them as opportunities for growth and self-discovery. I embrace failure as a natural part of the learning process, recognizing that every setback is an opportunity to learn, adapt, andimprove. This shift in perspective has enabled me to bounce back from setbacks with resilience and determination, emerging stronger and more resilient than before.In conclusion, my journey of transformation has been a testament to the power of resilience, growth, and self-discovery. Through introspection, perseverance, and a willingness to embrace change, I have undergone a profound metamorphosis, emerging as a stronger, more resilient, and more authentic version of myself. As I continue on this journey of self-discovery, I am filled with excitement and anticipation for the limitless possibilities that lie ahead.。
关于喜欢魔方的英语作文
关于喜欢魔方的英语作文I have always been fascinated by the Rubik's Cube ever since I first laid my hands on one. The challenge of solving the puzzle and the satisfaction of completing it have always been a source of joy for me. The Rubik's Cubeis not just a toy, but a symbol of intelligence, perseverance, and determination. It has become an integral part of my life, and I cannot imagine a day without it.One of the reasons why I love the Rubik's Cube is because it challenges my mind and keeps me sharp. Solving the puzzle requires a great deal of concentration, logical thinking, and problem-solving skills. Each twist and turn of the cube presents a new challenge, and I have to think several steps ahead to come up with a solution. This constant mental exercise has helped me improve my cognitive abilities and has made me more adept at handling complex problems in other areas of my life.Moreover, the Rubik's Cube has also taught me the valueof perseverance and determination. There have been countless times when I have felt frustrated and on the verge of giving up while trying to solve the puzzle. However, I have always pushed through and continued to work on it until I finally succeeded. This has taught me the importance of never giving up, even when faced with seemingly insurmountable obstacles. The sense of accomplishment and pride that I feel after finally solving the Rubik's Cube is unparalleled, and it serves as a constant reminder that hard work and determination always pay off in the end.In addition to the mental and emotional benefits, the Rubik's Cube has also been a great source of entertainment and social interaction for me. I have spent countless hours practicing and perfecting my solving skills, and I have also had the opportunity to meet and connect with other cube enthusiasts. The sense of camaraderie and community that comes with being a part of the cubing world is truly special, and I have made many friends who share the same passion for the Rubik's Cube as I do. Whether it's participating in competitions or simply sharing tips andtricks, the Rubik's Cube has brought me closer to people from all walks of life, and I am grateful for the friendships that I have made through it.Furthermore, the Rubik's Cube has also served as a form of stress relief for me. Whenever I feel overwhelmed or anxious, I find solace in picking up the cube and immersing myself in the challenge of solving it. The repetitive motions and the focus required to solve the puzzle help me clear my mind and regain a sense of calm. It is a therapeutic activity that allows me to escape from the pressures of everyday life and find peace in the simplicity of the puzzle.In conclusion, my love for the Rubik's Cube runs deep, and it has had a profound impact on my life. It has not only sharpened my mind and taught me valuable life lessons, but it has also brought me joy, friendships, and a sense of peace. The Rubik's Cube is more than just a toy; it is a symbol of resilience, intelligence, and community, and I am grateful for the role that it plays in my life.。
成功竞争的英语作文
成功竞争的英语作文Competition is an integral part of life, and success in this arena often requires a combination of skills, determination, and a strategic approach. Here is an essay on how to succeed in a competitive environment:The Essence of Success in CompetitionIn the world of competition, success is not merely about outperforming others; it is about achieving one's own potential and standing out in a crowd. To be successful in any competitive field, one must embody a set of qualitiesthat set them apart from the rest.Hard Work and PerseveranceThe foundation of success lies in hard work and perseverance. It is the relentless pursuit of goals, despite the obstacles that may arise. This means dedicating time and effort to hone one's skills, learning from failures, and continuously striving for improvement.Adaptability and InnovationIn a competitive landscape, the ability to adapt and innovate is crucial. It involves being flexible to change and comingup with new ideas or strategies that can give one an edge over competitors. Embracing new technologies and methodologies can also be a game-changer.Strategic PlanningSuccess in competition often hinges on strategic planning. This includes setting clear, achievable goals, and developing a roadmap to reach them. It also involves understanding the strengths and weaknesses of oneself and the competition, and leveraging these insights to one's advantage.Networking and CollaborationBuilding a strong network and collaborating with others can be instrumental in achieving success. This can provide access to resources, mentorship, and opportunities that may not be available otherwise. Collaboration can also lead to the exchange of ideas and the creation of synergies that can propel one to success.Resilience and Mental StrengthThe journey to success is rarely smooth. Resilience and mental strength are essential to overcome setbacks and maintain focus on the end goal. This involves developing a positive mindset, managing stress effectively, and staying motivated even in the face of adversity.Continuous Learning and Self-ImprovementIn a competitive environment, there is always something new to learn. Continuous learning and self-improvement are key to staying ahead. This can involve seeking out new knowledge, acquiring new skills, and staying updated with the latest trends and developments in one's field.ConclusionSuccess in competition is a multifaceted endeavor that requires a combination of hard work, adaptability, strategic planning, networking, resilience, and continuous learning. By cultivating these qualities and applying them effectively, one can not only achieve success but also contribute to the growth and advancement of their field.This essay touches upon various aspects that contribute to success in a competitive environment, providing a comprehensive view on how individuals can position themselves to excel.。
敢于挑战自我的英语作文
Challenges are an integral part of life,and facing them headon is a testament to ones courage and determination.The ability to challenge oneself is not only a mark of personal growth but also a key to unlocking ones potential.This essay will explore the importance of daring to challenge oneself,the benefits it brings,and how one can go about doing so.First and foremost,challenging oneself is a way to push boundaries and step out of ones comfort zone.It is in these moments of discomfort that we truly learn about ourselves and what we are capable of.When we dare to take on tasks that we initially perceive as difficult or impossible,we are not only testing our limits but also expanding them.This process can lead to a greater sense of selfconfidence and selfawareness.Moreover,challenging oneself can lead to personal growth and development.By setting and achieving goals that are difficult to reach,we learn valuable life skills such as perseverance,problemsolving,and adaptability.These skills are transferable and can be applied to various aspects of life,making us more wellrounded individuals.The benefits of challenging oneself are not limited to personal development.It can also lead to professional growth.In the workplace,taking on new projects or responsibilities that are outside of ones usual scope can demonstrate initiative and a willingness to learn. This can be a significant factor in career advancement and can lead to new opportunities and experiences.To effectively challenge oneself,it is important to start with a clear understanding of ones strengths and weaknesses.By identifying areas where improvement is needed,one can set realistic and achievable goals.It is also crucial to maintain a positive mindset and to be open to learning from failures.Failure is not a setback but a stepping stone towards success.In addition,seeking support from others can be beneficial when challenging oneself.This can come in the form of mentors,peers,or even professional coaches.They can provide guidance,encouragement,and constructive feedback,which can be invaluable in overcoming challenges.In conclusion,daring to challenge oneself is a courageous act that can lead to significant personal and professional growth.It is a journey that requires selfawareness, determination,and a willingness to learn from both successes and failures.By embracing challenges and pushing oneself beyond perceived limits,one can unlock new possibilities and achieve a greater sense of fulfillment in life.。
英语作文-体育培训如何帮助运动员克服挫折？
英语作文-体育培训如何帮助运动员克服挫折？In the realm of sports, athletes often face a myriad of challenges and setbacks. Thepath to victory is seldom straight; it is fraught with defeats, injuries, and moments of self-doubt. However, it is the ability to overcome these obstacles that separates the great fromthe merely good. Sports training plays a pivotal role in equipping athletes with the toolsto conquer these hurdles. It is not just about physical conditioning but also about mental fortitude.The journey begins with the understanding that setbacks are an integral part of growth. A well-structured sports training program incorporates this philosophy at its core. Coaches and trainers instill in athletes the mindset that each failure is a lesson, a stepping stone to success. This psychological conditioning is crucial because it transforms theathlete's perception of defeat from a negative experience to an opportunity for improvement.Physical training routines are designed to push athletes to their limits, simulating the stress and pressure of real competitions. This deliberate exposure to challengingsituations prepares athletes for the unpredictability of their sports. When faced withactual setbacks, the body and mind are already conditioned to handle the stress, making recovery and adaptation faster and more efficient.Moreover, sports training provides a supportive environment where athletes canshare their experiences and learn from each other. This camaraderie fosters resilience as athletes realize they are not alone in their struggles. They draw strength from their peers, and this collective resilience amplifies their individual tenacity.Nutrition and recovery are also integral components of sports training that aid in overcoming setbacks. Proper nutrition ensures that the body has the necessary fuel to perform and recover, while rest and recovery protocols allow for the healing and strengthening of the body after the wear and tear of intense physical exertion.Mental conditioning, another facet of sports training, cannot be overstated. Techniques such as visualization, mindfulness, and goal-setting are employed to build mental toughness. Athletes are taught to visualize success, which programs their subconscious to strive for the outcomes they desire. Mindfulness keeps them present and focused, preventing dwelling on past failures. Goal-setting provides a roadmap to success, making the journey structured and purpose-driven.In essence, sports training is a holistic approach to developing an athlete. It is a blend of physical conditioning, mental fortitude, nutritional guidance, and peer support. This comprehensive development ensures that when setbacks occur, athletes are not derailed. Instead, they have the tools, the mindset, and the support system to face the challenge head-on, learn from it, and emerge stronger.In conclusion, sports training is not just about building muscle and endurance; it is about forging a resilient spirit. It teaches athletes that setbacks are not the end but rather a part of the journey. With each challenge overcome, athletes build confidence and a belief in their ability to triumph over adversity. This belief, nurtured through rigorous training, is what enables athletes to stand up after a fall, ready to face the next challenge with determination and grace. It is the essence of sportsmanship and the heart of every true competitor. 。
哈利波特读后感英文
哈利波特读后感英文Harry Potter: An Enchanting Literary Odyssey。
In the annals of literature, the Harry Potter series by J.K. Rowling stands as a towering masterpiece, captivating generations of readers with its unparalleled magic,thrilling adventures, and enduring characters. From the enigmatic Hogwarts School of Witchcraft and Wizardry to the formidable Lord Voldemort, Rowling's world has become an integral part of our collective imagination.At the heart of the Harry Potter saga lies the orphaned boy who bears the lightning-shaped scar, a testament to his fateful encounter with the Dark Lord. As Harry embarks on his education at Hogwarts, he uncovers a world of secrets, friendships, and hidden dangers. Alongside his loyal companions, Ron Weasley and Hermione Granger, he faces perilous challenges and uncovers the truth about his past.Rowling's storytelling prowess is evident in theintricate tapestry she weaves throughout the series. Each book builds upon the previous one, introducing new characters, deepening the plot, and expanding the magical realm. From the whimsical quidditch matches to thethrilling wizarding duels, every scene is meticulously crafted to evoke wonder and anticipation.Beneath the surface of its captivating adventures, the Harry Potter series carries profound themes that resonate with readers of all ages. The importance of courage, friendship, and sacrifice are explored in multifaceted ways. Harry's journey serves as a poignant reminder that even in the darkest of times, hope and resilience can triumph.Furthermore, Rowling's world challenges societal norms and encourages tolerance. The bigotry faced by characters like Hermione, a Muggle-born witch, exposes the insidious nature of prejudice. Through her narratives, Rowling advocates for inclusivity, acceptance, and the celebrationof diversity.The characters themselves are indelible creations thatstay with readers long after they finish reading the books. Harry's unwavering determination, Ron's unwavering loyalty, and Hermione's prodigious intelligence make them relatable and enduring role models. The myriad supporting characters, including the enigmatic Snape, the wise Dumbledore, and the cunning Voldemort, further enrich the tapestry of the magical world.Rowling's writing style is a masterclass in vivid imagery and engaging prose. Her descriptions of the magical realm are so detailed and evocative that readers feel as if they have stepped into Hogwarts themselves. The dialogue between characters is witty, humorous, and often profound, adding depth and complexity to the story.The Harry Potter series has not only captivated readers but has also had a profound cultural impact. It hasinspired countless works of fan fiction, fan art, and even theme park attractions. The books have been translated into over eighty languages, reaching a global audience. Moreover, the series has fostered a sense of community among fans, uniting them in their love for the magical world.In conclusion, the Harry Potter series by J.K. Rowling is an extraordinary literary achievement that has left an enduring mark on the reading landscape. Its captivating adventures, profound themes, unforgettable characters, and magical world have captivated generations of readers and continue to inspire and enchant countless others. Whether one is a seasoned fan or a newcomer to the series, Harry Potter offers a timeless escape into a world where magic, friendship, and courage prevail.。
核桃楸木材的自由干缩特性
第５２卷第６期东㊀北㊀林㊀业㊀大㊀学㊀学㊀报Ｖｏｌ．５２Ｎｏ．６２０２４年６月ＪＯＵＲＮＡＬＯＦＮＯＲＴＨＥＡＳＴＦＯＲＥＳＴＲＹＵＮＩＶＥＲＳＩＴＹＪｕｎ．２０２４１）国家自然科学基金项目（３１８７０５４５，３１５７０５５８）；南林－玛格校企合作项目（０２８１０４５１４）㊂第一作者简介：刘泫江，女，２０００年１０月生，南京林业大学家居与工业设计学院，硕士研究生㊂Ｅ－ｍａｉｌ：ｎａｎｌｉｎｌｘｊ＠ｎｊｆｕ．ｅｄｕ．ｃｎ㊂通信作者：杨琳，南京林业大学家居与工业设计学院，教授㊂Ｅ－ｍａｉｌ：ｙａｎｇｌｉｎ＠ｎｊｆｕ．ｅｄｕ．ｃｎ㊂收稿日期：２０２３年１１月３０日㊂责任编辑：潘㊀华㊂核桃楸木材的自由干缩特性１）刘泫江㊀谢婧娥唐斌㊀万川杨琳㊀刘洪海（南京林业大学，南京，２１００３７）㊀㊀㊀（玛格家居股份有限公司）㊀㊀㊀（南京林业大学）㊀㊀摘㊀要㊀木材在干燥过程中因失水而导致干缩，非均匀干缩会产生应力限制木材的自由干缩㊂以核桃楸为试验对象，研究了５ｍｍ厚（纤维方向）分层试件和未分层（整体）试片的自由干缩特性，并对比研究了受限干燥后木材的分层自由干缩特性㊂研究结果表明：室温下各层自由干缩系数和绝干干缩率存在显著差异，总体呈现表层向芯层递减的趋势，第１层自由干缩系数（０．２５４）最大，第７层自由干缩系数（０．１６５）最小㊂树皮侧木材的自由干缩系数大于髓心侧㊂整体自由干缩试件常温干燥过程存在由含水率梯度引起的应力，限制其自由干缩，其弦向干缩率比分层自由干缩试件小０．５０％㊂泡水和汽蒸无法使受限干缩木材的塑性变形完全恢复，利用这种方法测量木材的自由干缩应变不准确㊂室温下弦向各层自由干缩的干缩率－含水率回归方程的决定系数（Ｒ２）均高于０．９６，利用该方程可以准确计算各含水率点的木材自由干缩应变㊂关键词㊀核桃楸；自由干缩；含水率；应力；应变分类号㊀Ｓ７８１．７１ＴｈｅＦｒｅｅＤｒｙｉｎｇＳｈｒｉｎｋａｇｅＣｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＪｕｇｌａｎｓｍａｎｄｓｈｕｒｉｃａＭａｘｉｍ．Ｗｏｏｄ／／ＬｉｕＸｕａｎｊｉａｎｇ，ＸｉｅＪｉｎｇｅ（Ｎａｎ⁃ｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００３７，Ｐ．Ｒ．Ｃｈｉｎａ）；ＴａｎｇＢｉｎ，ＷａｎＣｈｕａｎ（ＭａｃｉｏＣａｓａＦｕｒｎｉｓｈｉｎｇｓＣｏ．，Ｌｔｄ．）；ＹａｎｇＬｉｎ，ＬｉｕＨｏｎｇｈａｉ（ＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ）／／ＪｏｕｒｎａｌｏｆＮｏｒｔｈｅａｓｔＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，２０２４，５２（６）：１１４－１１８．Ｄｕｒｉｎｇｔｈｅｄｒｙｉｎｇｐｒｏｃｅｓｓ，ｗｏｏｄｕｎｄｅｒｇｏｅｓｓｈｒｉｎｋａｇｅｄｕｅｔｏｗａｔｅｒｌｏｓｓ，ａｎｄｎｏｎ⁃ｕｎｉｆｏｒｍｓｈｒｉｎｋａｇｅｃａｎｇｅｎｅｒａｔｅｓｔｒｅｓｓｔｈａｔｒｅｓｔｒｉｃｔｓｔｈｅｆｒｅｅｓｈｒｉｎｋａｇｅｏｆｗｏｏｄ．ＪｕｇｌａｎｓｍａｎｄｓｈｕｒｉｃａＭａｘｉｍ．ｗａｓｓｅｌｅｃｔｅｄａｓｔｈｅｅｘｐｅｒｉｍｅｎｔａｌｏｂｊｅｃｔｔｏｓｔｕｄｙｔｈｅｆｒｅｅｓｈｒｉｎｋａｇｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆ５ｍｍｔｈｉｃｋ（ｆｉｂｅｒｄｉｒｅｃｔｉｏｎ）ｌａｙｅｒｅｄｓｐｅｃｉｍｅｎｓａｎｄｕｎｌａｙｅｒｅｄ（ｉｎｔｅｇｒａｌ）ｓｐｅｃｉ⁃ｍｅｎｓ，ａｎｄｃｏｍｐａｒｅｄｔｈｅｌａｙｅｒｅｄｆｒｅｅｓｈｒｉｎｋａｇｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｗｏｏｄａｆｔｅｒｒｅｓｔｒｉｃｔｅｄｄｒｙｉｎｇ．Ｔｈｅｒｅｓｅａｒｃｈｒｅｓｕｌｔｓｓｈｏｗｅｄｔｈａｔａｔｒｏｏｍｔｅｍｐｅｒａｔｕｒｅ，ｔｈｅｒｅａｒｅｓｉｇｎｉｆｉｃａｎｔｄｉｆｆｅｒｅｎｃｅｓｉｎｔｈｅｆｒｅｅｓｈｒｉｎｋａｇｅｃｏｅｆｆｉｃｉｅｎｔｓａｎｄａｂｓｏｌｕｔｅｄｒｙｓｈｒｉｎｋａｇｅｒａｔｅｓｏｆｅａｃｈｌａｙｅｒ，ｇｅｎｅｒａｌｌｙｄｅｃｒｅａｓｉｎｇｆｒｏｍｔｈｅｓｕｒｆａｃｅｌａｙｅｒｔｏｔｈｅｃｏｒｅｌａｙｅｒ，ｗｉｔｈｔｈｅｌａｒｇｅｓｔｆｒｅｅｓｈｒｉｎｋａｇｅｃｏｅｆｆｉｃｉｅｎｔ（０．２５４）ｉｎｔｈｅｆｉｒｓｔｌａｙｅｒａｎｄｔｈｅｓｍａｌｌｅｓｔ（０．１６５）ｉｎｔｈｅｓｅｖｅｎｔｈｌａｙｅｒ．Ｔｈｅｆｒｅｅｓｈｒｉｎｋａｇｅｃｏｅｆｆｉｃｉｅｎｔｏｆｔｈｅｂａｒｋｓｉｄｅｗｏｏｄｉｓｇｒｅａｔｅｒｔｈａｎｔｈａｔｏｆｔｈｅｐｉｔｈｓｉｄｅ．Ｉｎｔｈｅｐｒｏｃｅｓｓｏｆａｍｂｉｅｎｔｔｅｍｐｅｒａｔｕｒｅｄｒｙｉｎｇｏｆｉｎｔｅｇｒａｌｆｒｅｅｓｈｒｉｎｋａｇｅｓｐｅｃｉｍｅｎｓ，ｓｔｒｅｓｓｃａｕｓｅｄｂｙｍｏｉｓｔｕｒｅｃｏｎｔｅｎｔｇｒａｄｉｅｎｔｌｉｍｉｔｓｔｈｅｉｒｆｒｅｅｓｈｒｉｎｋａｇｅ，ｗｉｔｈａｓｈｒｉｎｋａｇｅｒａｔｅｉｎｔｈｅｔａｎｇｅｎｔｉａｌｄｉｒｅｃｔｉｏｎ０．５０％ｓｍａｌｌｅｒｔｈａｎｔｈａｔｏｆｌａｙｅｒｅｄｆｒｅｅｓｈｒｉｎｋａｇｅｓｐｅｃｉｍｅｎｓ．Ｉｍｍｅｒｓｉｏｎｉｎｗａｔｅｒａｎｄｓｔｅａｍｃａｎｎｏｔｆｕｌｌｙｒｅｓｔｏｒｅｔｈｅｐｌａｓｔｉｃｄｅｆｏｒｍａｔｉｏｎｏｆｒｅｓｔｒｉｃｔｅｄｓｈｒｉｎｋａｇｅｗｏｏｄ，ｍａｋｉｎｇｉｔｉｎａｃｃｕｒａｔｅｔｏｍｅａｓｕｒｅｔｈｅｆｒｅｅｓｈｒｉｎｋａｇｅｓｔｒａｉｎｏｆｗｏｏｄｕｓｉｎｇｔｈｉｓｍｅｔｈ⁃ｏｄ．Ｔｈｅｄｅｔｅｒｍｉｎａｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔ（Ｒ２）ｏｆｔｈｅｒｅｇｒｅｓｓｉｏｎｅｑｕａｔｉｏｎｏｆｓｈｒｉｎｋａｇｅｒａｔｅ⁃ｍｏｉｓｔｕｒｅｃｏｎｔｅｎｔｆｏｒｅａｃｈｌａｙｅｒｉｎｔｈｅｔａｎｇｅｎｔｉａｌｄｉｒｅｃｔｉｏｎａｔｒｏｏｍｔｅｍｐｅｒａｔｕｒｅｉｓｈｉｇｈｅｒｔｈａｎ０．９６，ａｎｄｔｈｉｓｅｑｕａｔｉｏｎｃａｎａｃｃｕｒａｔｅｌｙｃａｌｃｕｌａｔｅｔｈｅｗｏｏｄ ｓｆｒｅｅｓｈｒｉｎｋａｇｅｓｔｒａｉｎａｔｅａｃｈｍｏｉｓｔｕｒｅｃｏｎｔｅｎｔｐｏｉｎｔｂａｓｅｄｏｎｔｈｅｒｅｇｒｅｓｓｉｏｎｅｑｕａｔｉｏｎｏｆｅａｃｈｌａｙｅｒ．Ｋｅｙｗｏｒｄｓ㊀ＪｕｇｌａｎｓｍａｎｄｓｈｕｒｉｃａＭａｘｉｍ．；Ｆｒｅｅｄｒｙｉｎｇｓｈｒｉｎｋａｇｅ；Ｍｏｉｓｔｕｒｅｃｏｎｔｅｎｔ；Ｓｔｒｅｓｓ；Ｓｔｒａｉｎ㊀㊀干燥是木材加工利用的关键环节［１］，是提高木材利用率和木制品尺寸稳定性的重要工序㊂木材在干燥过程中因失水而导致干缩，快速干燥通常导致木材产生非均匀干缩和应力，造成木材变形和开裂，并影响其实际使用［２－５］㊂因木材黏弹性特性以及应力作用［６］，木材干燥过程产生的实际干缩应变可以细分为自由干缩应变㊁瞬时弹性应变㊁黏弹性蠕变应变和机械吸附蠕变应变［７－８］㊂自由干缩是薄小木材在无应力条件下的干缩［９］，是确定木材干燥机械吸附蠕变应变值重要数据［１０］㊂而大尺寸木材的干缩通常是受应力影响，木材在应力作用下的干缩称为受限干缩㊂国内外学者对木材干燥的流变特性做了大量研究，并通过物理或数学模型研究含水率梯度和应力的关系［１１－１４］，但对木材的自由干缩特性及其对干燥流变特性的影响还未有深入研究［１５－１６］㊂基于此，本研究以核桃楸锯材为试验对象，首先研究了５ｍｍ厚（纤维方向）核桃楸分层试条和整体试片的自由干缩特性，确定合理的自由干缩系数和自由干缩率，然后对核桃楸进行常规干燥，测量了核桃楸受限干缩后的分层自由干缩特性，并与未经干燥的分层自由干缩进行对比，进而揭示木材自由干缩的特性和变化规律，为木材干燥应力㊁应变及干燥流变学研究提供理论和技术参考㊂１㊀材料与方法试验材料为核桃楸（ＪｕｇｌａｎｓｍａｎｄｓｈｕｒｉｃａＭａｘ⁃ｉｍ．），产自辽宁丹东，初含水率约９４％㊂如图１Ａ所示，首先将原木加工成３０ｍｍ（Ｔ）ˑ３０ｍｍ（Ｒ）ˑ１０００ｍｍ（Ｌ）的方材，然后将方材两端各锯掉１００ｍｍ木块，剩下的部分依次划分为分层自由干缩试件（ａ１ ａ５）㊁整体自由干缩试件（ｂ１ ｂ５）㊁初含水率测定试件（１ ６）以及受限干缩试件（Ａ㊁Ｂ㊁Ｃ）㊂试验设备见表１所示㊂表１㊀试验设备名㊀称型㊀号厂㊀家电热恒温鼓风干燥箱ＤＨＧ－９０５３ＢＳ－ＩＩ上海新苗仪器设备有限公司电子天平ＦＡ２００４上海精密仪器有限公司，精度０．００１ｇ佳能扫描仪ＣａｎｏＳｃａｎＬＩＤＥ７００Ｆ佳能公司夹具自制１．１㊀自由干缩试验由于干燥过程中无应力状态很难实现，木材自由干缩通常利用薄小木片，在低温缓慢干燥过程中测得［１７－１８］㊂如图１Ｂ所示，首先锯切试片ａ１ ａ５，然后将各试片依次分层（１ １０）作为分层自由干缩试件（ａ（１－１） ａ（１－１０） ａ（５－１） ａ（５－１０）），测量各层的初始质量和尺寸，然后锯切整体自由干缩试件为ｂ１ ｂ５，并测量质量和弦㊁径向尺寸（图１Ｄ），然后将上述试件在室内通风处（（２５ʃ３）ħ，湿度６０％ʃ１０％）进行缓慢干燥，每隔１ｈ再次测量其质量和尺寸㊂当最后两次测量的质量变化小于０．２％时烘至绝干，再次测量绝干质量和尺寸，利用公式（１）计算自由干缩试件测量时的含水率，利用公式（２）计算各含水率时刻的自由干缩率，绝干干缩率是试件烘至绝干时（含水率为０）的干缩率㊂㊀㊀㊀Ｗ＝ｍ１－ｍ０ｍ０ˑ１００％㊂（１）式中：Ｗ为试件含水率（％）；ｍ１为试件试验时的质量（ｇ）；ｍ０为试件全干时的质量（ｇ）㊂㊀㊀㊀ｙｍｃ＝Ｌ０－ＬｍｃＬ０ˑ１００％㊂（２）式中：ｙｍｃ为试件纤维饱和点以下某一时刻含水率时自由干缩率（％）；Ｌ０为试件初始长度（ｍｍ）；Ｌｍｃ为试件纤维饱和点以下某一时刻含水率时的长度（ｍｍ）㊂图１㊀试件劈解㊁编号示意图１．２㊀受限干缩后木材的自由干缩试件Ａ㊁Ｂ㊁Ｃ干燥之前用环氧树脂将试件端部密封㊂在试件侧面横向划线，测量其弦向初始长度作为各试件的Ｌ０，然后放入烘箱（（４５ʃ２）ħ）进行干燥，当试件含水率分别降至４０％㊁３０％及２０％时，各取出一块试件，锯掉端头，然后沿纤维方向锯截６片１０ｍｍ厚应变试片，将试片按图１Ｃ所示沿弦向划线，并标记１ １０层㊂然后用劈刀快速沿划线劈切各层，称其质量并测量各层尺寸㊂通过对比各层的含水率差异可以判断试件Ａ㊁Ｂ㊁Ｃ干燥过程是否产生应力和非均匀干缩㊂将所有分层试件用水浸泡２４ｈ㊁汽蒸８ｈ后，在室温（（２５ʃ３）ħ㊁湿度６０％ʃ１０％）通风处进行干燥，测量各层含水率达到４０％㊁３０％及２０％时的尺寸，利用公式（２）计算各含水率时刻的自由干缩率㊂２㊀结果与分析２．１㊀分层自由干缩图２是分层自由干缩各层试件在室温干燥过程的含水率－时间曲线㊂第１和第１０层为表层，第５５１１第６期㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀刘泫江，等：核桃楸木材的自由干缩特性和第６层为芯层，其余各层为中间层㊂由于试件薄小，各层含水率几乎呈线性下降，干燥１７ｈ左右试件的含水率趋于平稳㊂由于第１及第１０层位于原材料的表层，初含水率分布差异大于其他各层，因此纤维饱和点（ＦＳＰ）以上这两表层干燥速率更快，但随着干燥的进行，其干燥速率逐渐接近中间层㊂除第１和第１０层外，其余各层干燥速率在ＦＳＰ上下一致，表明薄小试件的自由水和结合水的干燥速率一致，木材内部无论自由水还是结合水分大部分沿着试件的纤维方向从两侧的端面快速迁移出［１９］㊂因为第２ ９层每层干燥速率曲线基本重合，干燥前后试件基本未产生变形（图３），可以认为薄小的试件在缓慢干燥过程中产生的干燥应力很小［２０］，干燥过程试件进行自由干缩㊂图２㊀室温下分层自由干缩各层试件的含水率－时间曲线Ａ干燥前；Ｂ干燥后㊂图３㊀分层自由干缩试件图４是室温下分层自由干缩各层试件的干缩率与含水率在２７％以下的对应关系㊂ＦＳＰ以下干缩率和含水率呈线性关系，对各层的干缩率和含水率进行拟合可得到各层的自由干缩方程㊂通过方程计算出各层自由干缩系数和绝干干缩率（表２）以及对应各含水率时刻的自由干缩应变，从而可以准确测量该含水率时的机械吸附蠕变应变㊂分层自由干缩试件各层拟合方程Ｒ２最小值为０．９６５１４，趋近于１，相关性高，表明用其描述对应的自由干缩精确度与可靠性高㊂第１层自由干缩系数（０．２５４）最大，第７层（０．１６５）最小，整体上呈现由表层向芯层递减的趋势㊂绝干干缩率总体上也呈现同样的趋势㊂此外，树皮侧（第１㊁２层）自由干缩系数大于近髓心侧（第９㊁１０层）㊂这是因为近髓心部分早材比例大，且近髓心部分受径向收缩的影响较大，弦向约为纵向收缩率的２倍［２１］㊂缓慢干燥过程中，即使各层试条的干燥速率基本相同，但其干缩系数也不一致㊂图４㊀分层自由干缩试件各层自由干缩率和含水率对应关系表２㊀分层自由干缩试件的拟合方程㊁自由干缩系数及绝干干缩率分层试件拟合方程自由干缩系数（Ｋ）绝干干缩率／％决定系数（Ｒ２）１ｙ＝－０．２５４１１ｘ＋０．０７０４００．２５４７．０４００．９８６５３２ｙ＝－０．２５７８４ｘ＋０．０７７４８０．２５８７．７４８０．９８７００３ｙ＝－０．２１９８７ｘ＋０．０７４１００．２２０７．４１００．９８３１９４ｙ＝－０．２０３８７ｘ＋０．０６８２１０．２０４６．８２１０．９７８６１５ｙ＝－０．１９４２４ｘ＋０．０６２４００．１９２６．２４００．９６５１４６ｙ＝－０．１８１１２ｘ＋０．０６２７７０．１８１６．２７７０．９９０２４７ｙ＝－０．１６４６６ｘ＋０．０５９３２０．１６５５．９３２０．９６８１０８ｙ＝－０．２０２４３ｘ＋０．０６４４００．２０２６．４４００．９８７３１９ｙ＝－０．２３１３５ｘ＋０．０６７１９０．２３１６．７１９０．９７２９８１０ｙ＝－０．２３０６２ｘ＋０．０６２０８０．２３１６．２０８０．９８２３８均值ｙ＝－０．２１０００ｘ＋０．０６６８４０．２１０６．６８４０．９８０１４㊀㊀表３为室温下各层自由干缩至２０％含水率时利用回归方程计算的理论值和干燥过程的实测值的对比㊂其中第１㊁５层的结果相近，实际测量尺寸误差在０．２８％，其余各层实际测量尺寸误差范围在０．５０％ ０．９０％㊂出现这一现象的原因可能是由于实际测量时只能预估绝干质量，无法确保每层的含水率准确到达２０％，存在含水率误差㊂从测量值较大的误差棒可以证明各试件真实含水率差异较大㊂因此，利用分层自由干缩系数及其回归方程可消除各层级含水率差异，实现对机械吸附蠕变应变准确检测㊂表４为室温干燥至不同含水率阶段，表层（１㊁６１１㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀东㊀北㊀林㊀业㊀大㊀学㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第５２卷１０）㊁芯层（５㊁６）㊁中间层（３㊁８）的分层自由干缩率㊂含水率为２０％是拟合方程的计算值，３０％和４０％时是测量值㊂含水率为４０％时，表层㊁中间层及芯层的自由干缩率非常小，小于０．３０％㊂含水率降至３０％时，各层的自由干缩率也很小，介于０．６５％和０．８５％之间，但方差分析表明表层与芯层和中间层的自由干缩率显著不同（Ｐ＜０．０５），呈现表层低㊁芯层及中间层略高的趋势㊂这主要因为各层的含水率为预估值，其预估平均含水率降低至３０％时，部分层的真实含水率已经低于ＦＳＰ，因此引起微小的收缩㊂分层自由干缩各层试件在ＦＳＰ以上几乎没有产生干缩应变㊂这主要因为各层试件的尺寸较小，纤维方向为５ｍｍ，径向只有３ｍｍ，各层试件干燥过程水分的迁移速度几乎一致㊂因此可以推断各层试件在室温干燥过程处于自由干缩状态，干燥过程几乎没有产生因干缩差异引起的应力㊂表３㊀含水率２０％时分层自由干缩率拟合值和测量值的对比层级拟合值／％测量值／％测量值标准差１１．９６２．０４０．００２９３３．０１２．６４０．００７９５２．３７２．３６０．００２７６２．６６２．８３０．００５３８２．３９２．７４０．００９９１０１．５９１．２５０．００５８表４㊀分层自由干缩试件不同含水率时各层自由干缩率层级自由干缩率／％ｍＣ＝４０％ｍＣ＝３０％ｍＣ＝２０％表层（１㊁１０）０．３０ａ０．６５ｂ１．７８ｄ中间层（３㊁８）０．２９ａ０．８４ｃ２．７０ｅ芯层（５㊁６）０．１９ａ０．８６ｃ２．５１ｅ㊀㊀注：ｍＣ为试件纤维饱和点以下某一时刻含水率；同列不同字母表示显著差异（Ｐ＜０．０５）㊂２．２㊀整体自由干缩和分层自由干缩对比图５为室温干燥时整体自由干缩试件ｂ的弦向（ｂ－Ｔ）和分层自由干缩试件ａ的第５㊁６层（ａ－５㊁６）干缩率随含水率变化曲线㊂干燥前期整体自由干缩率和分层自由干缩随含水率变化基本相同㊂随着干燥的进行，因为径向长度只有３ｍｍ，分层自由干缩试件水分迁移更加均匀，呈现出更好的自由干缩效果㊂由于没有内应力的限制，在相同含水率时其干缩率要大于整体自由干缩㊂干燥后期相同含水率时，干缩率最大相差０．５０％左右㊂ＳＰＳＳ方差分析表明分层自由干缩和整体自由干缩的绝干干缩率存在显著性差异（表５）㊂整体自由干缩过程，因试件径向尺寸较大（３０ｍｍ），干燥过程存在含水率梯度引起弦向干缩差异，进而产生干燥应力，限制其进一步收缩，因此其干缩率要小于分层自由干缩试件㊂图５㊀干燥过程分层自由干缩和整体自由干缩对比表５㊀分层自由干缩和整体自由干缩绝干干缩率对比试件类型绝干干缩率平均值／％标准差整体自由干缩５．２６０．００４０分层自由干缩芯层（５㊁６）６．１８０．００１４分层自由干缩１ １０层６．６６０．００４９２．３㊀受限干缩试件的分层自由干缩图６是受限干缩试件Ａ㊁Ｂ㊁Ｃ干燥到平均含水率为４０％㊁３０％及２０％时的分层含水率㊂可以看出两端封闭的试件干燥至４０％时，其表层含水率已降低到２０％附近，而芯层含水率则在５５％左右，表芯含水率差异很大㊂因此表层因早已低于ＦＳＰ经开始收缩，而芯层则高于ＦＳＰ，没有收缩，进而导致表层收到拉应力，而芯层则收到压应力，木材是在应力的作用下进行的受限干缩㊂随着含水率的下降，表芯层含水率差异减小，但整个干燥过程仍存在表芯层由含水率差异引起的干缩差异，整个干缩过程受应力影响㊂图６㊀受限干燥过程中不同含水率阶段各层含水率分布图７是受限干缩试件泡水汽蒸后再进行干燥的分层自由干缩试件干缩率与含水率在２７％以下的对应关系㊂各层的自由干缩率和含水率的拟合收缩方程见表６㊂受限干缩试件各层拟合方程Ｒ２最小值为０．７７５９３，均值为０．８８８６８，相较于室温下的分７１１第６期㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀刘泫江，等：核桃楸木材的自由干缩特性层自由干缩相关性低，表明用其描述对应的自由干缩性能可信度低，误差大㊂这可能是由于泡水和汽蒸未能使塑性变形完全恢复所致㊂试件在分层自由干缩之前经历过长时间受限干缩，因此对木材的结构和性质产生了不可逆的影响，即使经过２４ｈ浸泡和８ｈ汽蒸处理，也无法完全恢复至干燥前的初始状态㊂受限干缩试件的自由干缩系数分布不均，第２层自由干缩系数（０．２６７）最大，第４层自由干缩系数（０．１９７）最小㊂证明汽蒸法并没有使塑性变形完全恢复，再次干燥时自由干缩应变包含了部分未被恢复的残余变形㊂图７㊀受限干缩后分层试件自由干缩率和含水率对应关系表６㊀受限干缩试件后分层自由干缩试件的拟合方程，干缩系数及绝干干缩率分层试件拟合方程自由干缩系数（Ｋ）绝干干缩率／％决定系数（Ｒ２）１ｙ＝－０．２４８８９ｘ＋０．０７９９９０．２４９７．９９９０．９６９９８２ｙ＝－０．２６６９８ｘ＋０．０８８２７０．２６７８．８２７０．９１７９３３ｙ＝－０．２０７７７ｘ＋０．０６９０４０．２０８６．９０４０．８８５１９４ｙ＝－０．１９６９１ｘ＋０．０７０４７０．１９７７．０４７０．８２０６０５ｙ＝－０．２２５０２ｘ＋０．０７８２２０．２２５７．８２２０．７８２２６６ｙ＝－０．２６０３３ｘ＋０．０８６４４０．２６０８．６４４０．７７５９３７ｙ＝－０．２２０５９ｘ＋０．０７９４１０．２２１７．９４１０．８７７５１８ｙ＝－０．２５０３１ｘ＋０．０８３４３０．２５０８．３４３０．９４１５７９ｙ＝－０．２６５２１ｘ＋０．０８７６４０．２６５８．７６４０．９５７１６１０ｙ＝－０．２１９２８ｘ＋０．０８４４３０．２１９８．４４３０．９５８６２均值ｙ＝－０．２３６１３ｘ＋０．０８０７３０．２３６８．０７３０．８８８６８３ 结论室温下分层自由干缩试件各层的自由干缩系数和绝干干缩率存在显著差异，总体呈现表层向芯层递减的趋势㊂其中，第１层自由干缩系数最大（０．２５４），第７层自由干缩系数最小（０．１６５）㊂树皮侧（第１㊁２层）的自由干缩系数大于髓心侧（第９㊁１０层）的自由干缩系数㊂泡水和汽蒸无法使受限干缩木材的塑性变形完全恢复，利用这种方法测量木材的自由干缩应变不准确㊂整体自由干缩试件常温干燥过程存在由含水率梯度引起的应力，限制其自由干缩，整体弦向干缩率比分层自由干缩试件小０．５０％㊂室温下分层木材弦向的干缩率－含水率回归方程的决定系数均高于０．９６㊂因此，准确的自由干缩应变应该利用室温下各层回归方程来计算㊂参㊀考㊀文㊀献［１］㊀刘英，庄子龙，唐敏．深度学习在木材加工领域的研究进展［Ｊ］．林业工程学报，２０２３，８（４）：１－９．［２］㊀彭辉，蒋佳荔，詹天翼，等．基于动态热机械分析仪的木材干缩湿胀响应特征研究［Ｊ］．林业工程学报，２０２３，８（２）：５２－５８．［３］㊀于建芳，王喜明．木材干燥应力应变宏观模型的构筑［Ｊ］．林业科学，２００５，４１（５）：２１４－２１８．［４］㊀ＰＡＮＧＳＳ．Ｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｉｎｇｏｆｋｉｌｎｄｒｙｉｎｇｏｆｓｏｆｔｗｏｏｄｔｉｍ⁃ｂｅｒ：ｍｏｄｅｌｄｅｖｅｌｏｐｍｅｎｔ，ｖａｌｉｄａｔｉｏｎ，ａｎｄｐｒａｃｔｉｃａｌａｐｐｌｉｃａｔｉｏｎ［Ｊ］．ＤｒｙｉｎｇＴｅｃｈｎｏｌｏｇｙ，２００７，２５（３）：４２１－４３１．［５］㊀王世鹏，侯俊峰，姜志宏，等．杉木锯材周期式热压干燥及表层密实化［Ｊ］．林业工程学报，２０２２，７（３）：４０－４５．［６］㊀ＹＩＮＱ，ＬＩＵＨＨ．Ｄｒｙｉｎｇｓｔｒｅｓｓａｎｄｓｔｒａｉｎｏｆｗｏｏｄ：ａｒｅｖｉｅｗ［Ｊ］．ＡｐｐｌｉｅｄＳｃｉｅｎｃｅｓ，２０２１，１１．ｄｏｉ：１０．３３９０／ＡＰＰ１１１１５０２３．［７］㊀战剑锋，顾继友，蔡英春．落叶松板材常规干燥过程的动态黏弹性特性［Ｊ］．北京林业大学学报，２００９，３１（１）：１２５－１２９．［８］㊀ＭＥＩＪＥＲＭ，ＢＡＲＥＮＤＶ，ＨＯＬＧＥＲＭ．Ｒｈｅｏｌｏｇｉｃａｌａｐｐｒｏａｃｈｔｏｔｈｅｃａｐｉｌｌａｒｙｐｅｎｅｔｒａｔｉｏｎｏｆｃｏａｔｉｎｇｉｎｔｏｗｏｏｄ［Ｊ］．ＪｏｕｒｎａｌｏｆＣｏａｔ⁃ｉｎｇｓＴｅｃｈｎｏｌｏｇｙ，２００１，７３：３９－５１．ｄｏｉ：１０．１００７／ＢＦ０２６９８４３７．［９］㊀杨琳，付奇缘，刘洪海，等．尾巨桉自由干缩率及纤维饱和点的测定［Ｊ］．东北林业大学学报，２０１８，４６（４）：３９－４２．［１０］㊀战剑锋，顾继友，蔡英春．落叶松板材常规干燥过程的动态机械吸附特性［Ｊ］．北京林业大学学报，２００９，３１（２）：１０８－１１３．［１１］㊀陈太安．赤桉干燥预热处理与干燥流变特性的研究［Ｄ］．南京：南京林业大学，２００４．［１２］㊀付宗营，蔡英春，周永东．木材干燥应力研究现状与趋势［Ｊ］．林业科学，２０２１，５７（９）：１６０－１６７．［１３］㊀ＶＡＬＥＮＴＩＮＡＭ，ＦＲＡＮＣＥＳＣＯＭ．Ａｒｅｖｉｅｗｏｆｗｏｏｄｐｏｌｙｍｅｒｃｏｍｐｏｓｉｔｅｓｒｈｅｏｌｏｇｙａｎｄｉｔｓｉｍｐｌｉｃａｔｉｏｎｓｆｏｒｐｒｏｃｅｓｓｉｎｇ［Ｊ］．Ｐｏｌｙ⁃ｍｅｒｓ，２０２０，１２．ｄｏｉ：１０．３３９０／ｐｏｌｙｍ１２１０２３０４．［１４］㊀ＡＢＡＳＳＡＭ，ＲＯＢＥＲＴＯＡ，ＤＯＵＧＬＡＳＪＧ，ｅｔａｌ．Ｍｏｄｅｌｉｎｇｔｈｅｈｙｄｒｏｔｈｅｒｍａｌｃｒｅｅｐｂｅｈａｖｉｏｒｏｆｗｏｏｄｐｌａｓｔｉｃｃｏｍｐｏｓｉｔｅ（ＷＰＣ）ｌｕｍｂｅｒｍａｄｅｆｒｏｍｔｈｅｒｍａｌｌｙｍｏｄｉｆｉｅｄｗｏｏｄ［Ｊ］．ＪｏｕｒｎａｌｏｆＴｈｅｒ⁃ｍｏｐｌａｓｔｉｃＣｏｍｐｏｓｉｔｅＭａｔｅｒｉａｌｓ，２０２０，３３（８）：１１０９－１１２４．ｄｏｉ：１０．１１７７／０８９２７０５７１８８２０４０４．［１５］㊀朱小东．５０ｍｍ厚樟子松锯材常规干燥应变规律解析［Ｄ］．哈尔滨：东北林业大学，２０２２．［１６］㊀付宗营．常规干燥过程中白桦树盘干燥应力应变的研究［Ｄ］．哈尔滨：东北林业大学，２０１７．［１７］㊀涂登云．马尾松板材干燥应力模型及应变连续测量的研究［Ｄ］．南京：南京林业大学，２００５．［１８］㊀涂登云，刘彬．木材干燥应力模型的研究［Ｊ］．南京林业大学学报（自然科学版），２００９，３３（３）：８７－９１．［１９］㊀ＦＵＺＹ，ＷＥＮＧＸ，ＧＡＯＹＦ，ｅｔａｌ．Ｆｕｌｌ⁃ｆｉｅｌｄｔｒａｃｋｉｎｇａｎｄａ⁃ｎａｌｙｓｉｓｏｆｓｈｒｉｎｋａｇｅｓｔｒａｉｎｄｕｒｉｎｇｍｏｉｓｔｕｒｅｃｏｎｔｅｎｔｌｏｓｓｉｎｗｏｏｄ［Ｊ］．Ｈｏｌｚｆｏｒｓｃｈｕｎｇ，２０２０，７５（５）：４３６－４４３．［２０］㊀涂登云，顾炼百，杜国兴，等．干燥过程中马尾松板材干燥应变的研究［Ｊ］．南京林业大学学报（自然科学版），２００４，２８（４）：２３－２８．ｄｏｉ：１０．３９６９／ｊ．ｊｓｓｎ．１０００－２００６．２００４．０４．００６．［２１］㊀汪为锴．斜叶桉孔隙特征与干燥特性研究［Ｄ］．南京：南京林业大学，２０２１．８１１㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀东㊀北㊀林㊀业㊀大㊀学㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第５２卷。
Persistent Struggle
The persistent struggle is an integral part of human experience. Itis the ongoing battle against adversity, obstacles, and challengesthat tests our resilience and determination. Whether it is in the pursuit of personal goals, overcoming hardships, or fighting for a cause, the persistent struggle is a universal phenomenon that shapes our lives.In the realm of personal growth and development, the persistent struggle is often synonymous with the journey towards success. It is the process of facing setbacks, failures, and disappointments, yet refusing to give up. It is about pushing through the discomfort, doubt, and fear, and continuing to strive for improvement.Moreover, the persistent struggle is also a reflection of the human spirit's ability to endure and persevere in the face of adversity.It is a testament to our innate strength and resilience, as wenavigate through life's inevitable challenges. It is thedetermination to not be defeated by the trials and tribulations that come our way.On a societal level, the persistent struggle is often seen in thefight for justice, equality, and human rights. It is the ongoingbattle against oppression, discrimination, and injustice. It isabout standing up for what is right, even in the face ofoverwhelming odds. It is the collective effort to create a better world for future generations.In the world of business and entrepreneurship, the persistentstruggle is a familiar companion to those striving to build and grow their ventures. It is the daily grind of overcoming hurdles, facing competition, and adapting to ever-changing market conditions. It is about having the resilience to weather the storms and emergestronger and wiser.Furthermore, the persistent struggle also manifests in the pursuitof mental and emotional well-being. It is the ongoing effort to manage stress, anxiety, and inner turmoil. It is about seeking balance, peace, and contentment amidst the chaos and challenges of life.Ultimately, the persistent struggle is a fundamental aspect of the human experience. It is a reminder that growth, progress, and change often come with resistance and difficulty. It is a testament to our capacity to endure, overcome, and thrive in the face of adversity. Embracing the persistent struggle allows us to develop grit, resilience, and a deeper understanding of ourselves and the world around us. It teaches us the value of perseverance, determination,and the importance of not giving up when faced with obstacles.In conclusion, the persistent struggle is an inherent part of the human journey. It is a reflection of our capacity to overcome, adapt, and grow in the face of adversity. It is a testament to the strength of the human spirit and our ability to rise above challenges. Byembracing the persistent struggle, we can harness its transformative power and emerge stronger, wiser, and more resilient.。
井冈山精神英语作文
井冈山精神英语作文The spirit of Jinggang Mountain is an integral part of Chinese revolutionary history, symbolizing perseverance, resilience, and the unyielding will of the people.It serves as a shining beacon, guiding us through the trials and tribulations of life.井冈山精神是中国革命历史的重要组成部分，它象征着坚韧、不屈和人民坚定不移的意志。
它如同一座耀眼的灯塔，照亮我们在生活中经历的种种艰难险阻。
Embracing the spirit of Jinggang Mountain means holding tight to the belief that even in the face of adversity, one must forge ahead with determination and courage.It advocates for the unity of the people, reminding us that together, we can overcome any challenge.拥抱井冈山精神，意味着紧握信念，坚信即使在逆境面前，我们也必须以决心和勇气继续前进。
它倡导人民团结一心，提醒我们团结一致，就能战胜任何挑战。
From the crimson soil of Jinggang Mountain, a seed of revolution was sown, nurtured by the blood and sweat of countless martyrs.This spirit continues to inspire generations, urging us to contribute to the betterment of our nation.从井冈山的红土地中，革命的种子被播下，无数烈士的鲜血和汗水滋养了它。
健身操打卡英语作文
健身操打卡英语作文Title: My Fitness Journey: Embracing the Challenge of Daily Exercise。
Embarking on a fitness journey is not merely about physical exertion but also about commitment, discipline, and the pursuit of a healthier lifestyle. Recently, I have taken up the challenge of participating in daily fitness exercises, specifically aerobics routines. This decision stemmed from a desire to improve my overall well-being and vitality. In this essay, I will share my experiences and reflections on this journey of self-improvement.To begin with, incorporating daily exercise into my routine has proven to be both invigorating and challenging. Each day, I set aside a dedicated time slot for my fitness regimen, ensuring that it becomes a non-negotiable part of my daily schedule. By adhering to a consistent workout routine, I have witnessed notable improvements in my physical strength, endurance, and flexibility.One of the key components of my fitness routine is aerobics, a dynamic form of exercise that combines rhythmic movements with music. Engaging in aerobics not only elevates my heart rate but also enhances my coordination and balance. Moreover, the lively music serves as a source of motivation, energizing me to push through the intensity of the workout.Keeping track of my fitness progress has been instrumental in maintaining my momentum and staying accountable. I utilize a fitness tracker to monitor various metrics such as the duration of my workouts, the number of calories burned, and my heart rate during exercise. This data-driven approach allows me to set tangible goals and track my improvement over time, serving as a source of encouragement and motivation.Furthermore, participating in group fitness classes has enriched my exercise experience by fostering a sense of camaraderie and community. Interacting with fellow participants creates a supportive environment where we canshare tips, celebrate achievements, and overcome challenges together. The collective energy of the group fuels my motivation and inspires me to push beyond my limits.Despite the physical benefits of exercise, I have also discovered its profound impact on my mental and emotional well-being. Engaging in regular physical activity has been scientifically proven to alleviate stress, boost mood, and enhance cognitive function. Through exercise, I find solace in moments of solitude, allowing me to clear my mind and recharge my spirit amidst life's daily pressures.Moreover, the sense of accomplishment derived from completing each workout fills me with a profound sense of pride and satisfaction. Every drop of sweat shed and every muscle engaged serves as a testament to my dedication and resilience. This feeling of achievement transcends the physical realm, permeating into other aspects of my life and empowering me to tackle challenges with confidence and determination.In conclusion, my journey of incorporating dailyfitness exercises into my routine has been transformative on multiple levels. From the physical benefits of improved strength and endurance to the mental and emotional rewards of stress relief and self-empowerment, exercise has become an integral part of my lifestyle. By embracing the challenge of daily exercise, I am not only investing in my physical health but also nurturing my overall well-being and vitality. As I continue on this journey, I am excited to see how far dedication and perseverance will take me towards achieving my fitness goals.。
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SPECIAL ISSUE-ORIGINAL ARTICLEDetermination of J-integral and stress intensity factor using the commercial FE software ABAQUS in austenitic stainless steel(AISI304)platesG.Venkatachalam&R.Harichandran&S.Rajakumar&C.Dharmaraja&C.PandivelanReceived:26February2008/Accepted:18September2008#Springer-Verlag London Limited2008Abstract This paper presents J-integral and stress intensity factor solutions for several crack configurations in plates. The edge crack is considered for the analysis.The tensile load is applied and the crack propagation is studied.The finite element method is used to model the plate and mode I stress intensity factors are evaluated.For solving the FE model,commercial FE software ABAQUS is used.Several cases including different thickness and crack lengths are presented for not only linear elastic analysis but also for elastic-plastic analysis.The3-D model is taken for the analysis and eight-noded brick element is used for FE mesh. Keywords J-integral.Stress intensity factor.Finite element method1IntroductionFracture mechanics has reached the level of sophistication as well as wide industrial acceptance such that many actual and potential brittle failure problems can be dealt through this discipline.The stress intensity factor(SIF)characterizes the stresses,strains,and displacements near the crack tip.If the plastic zone near the crack tip is large,then the SIF no longer characterizes the crack tip conditions.So calculation of SIF is limited to linear elastic fracture mechanics.When the plastic zone is large or non-linear material behavior becomes significant,one should discard SIF and crack tip parameters (either J-integral or CTOD)that takes larger plastic zone near the crack tip and non-linear material behavior into account.Here,an attempt is made to find out J-integral. The T-stress is increasingly being recognized as an important additional stress field characterizing parameter in the analyses of cracked bodies.The elastic T-stress represents the stress-acting parallel to the crack plane.It is known that the sign and magnitude of T-stress can substantially alter the level of crack tip stress triaxiality.2Literature reviewRice[1]applied the deformation plasticity to the analysis of a crack in a non-linear material.He showed that the non-energy release rate J could be written as a path-independent line integral.Rice and Rosengren[2]showed that J uniquely characterizes crack tip stresses and strains in non-linear materials.Kobayashi et al.[3]used finite element analysis to determine numerically Rice’s J-integral values in centrally notched plates of43.40steel.For increasing level of loading,the rate of increase in J-integral decreases and J-integral remains almost constant at when the load is at yield point under such crack extension. Courtin et al.[4]applied the crack opening displacement extrapolation method and the J-integral approach in2D and 3D ABAQUS finite element models.The results obtained by them are in good agreement with those found in theInt J Adv Manuf TechnolDOI10.1007/s00170-008-1872-zG.Venkatachalam:C.Dharmaraja:C.PandivelanSchool of Mechanical&Building Sciences,VIT University, Vellore632014,IndiaR.Harichandran(*)Department of Mechanical Engineering,National Engineering College,Kovilpatti628503,Indiae-mail:hari_chandra1984@S.RajakumarDepartment of Mechanical Engineering,SCAD College of Engineering,Cheranmahadevi,Tirunelveli,IndiaFig.2Close view ofcrackFig.3FE mesh of model-35-30-25-20-15-10-500.50.60.70.80.9a (mm)J (J /S q .m )Fig.4a vs.J-2000200400600800100012000.50.60.70.80.9a (mm)K 1c (M P a /√m m )Fig.5a vs.K1c-350-300-250-200-150-100-500501000.50.60.70.80.9a (mm)T S t r e s s (M P a )Fig.6a vs.T -stressInt J Adv Manuf Technol500100015002000250030003567t (mm)K 1c (M P a /m m )4Fig.8t vs.K1c-1000-800-600-400-200020040060036t (mm)T S t r e s s (M P a )745Fig.9t vs.T-stress-80-60-40-200100150200250300325350Load (N)J (J /S q .M )Fig.10F vs.J100200300400500600700800100150200250300350Load (N)K 1c (M P a /√m m )Fig.11F vs.K1c-26-25-24-23-22-21-2036t (mm)J (J /S q .m)745Fig.7t vs.J1020304050607080100150200250300350Load (N)T S t r e s s (M P a )Fig.12F vs.T -stressInt J Adv Manuf Technolliterature.Nevertheless,since the knowledge of the field near the crack tip is not required in the energetic method,the J-integral calculations seem to be a good technique to deal with the fatigue growth of general cracks.Rajaram et al.[5]presented an approach to obtain fracture mechanics singularity strength(J,K1,etc.)along a3D crack-front using tetrahedral elements.Hocine et al.[6]determined the energy parameter J for rubber-like materials.Owen and Fawkes[7]developed many numerical methods using finite element analysis to obtain SIF values.3Finite element analysisThe edge-crack model shown in Fig.1is taken for the analysis.The Fig.2shows the close view of crack.The tensile load distributed in nature is applied at the top of the plate and the bottom face is constrained.The material taken for our analysis is Austenitic stainless steel(AISI304).Figure3 shows the finite element mesh of the model.The eight-node linear brick elements(C3D8in ABAQUS)with three degrees of freedom at each node are considered.An attempt is also made with reduced integration.Reduced integration uses a lower-order integration to form the element stiffness.It reduces running time,especially in three dimensions.There are375nodes and224elements are used in the model.4Results and discussionsThis paper is basically dealing three kind of analysis.The variations of J-integral,T-stress and SIF with respect to crack length(a),thickness of model(t)and load(F)conditions are studied.In all the cases,one parameter is varied and other two parameters are kept constant.For a constant load and thickness,the increase in the value of J-integral for both elastic and elastic-plastic is same up to the elastic limit which is shown in the Fig.4.After elastic limit,there is no appreciable increase in the value of J-integral for the elastic analysis.Figure5shows that the increase in t for elastic has no influence on the value of J-integral whereas it is linear in the case of elastic-plastic.The variation of J with load is also studied(Fig.6).Here,the values of J are compared with reduced integration.Until the elastic limit,there is no variation for all cases;but when the load goes beyond the elastic limit,decrease in the value of J for elastic-plastic is more than that of elastic.In elastic analysis,elements with reduced integration have no influence where as in elastic-plastic,it matters.Figure7shows that the SIF decreases initially when a increases;but there is no significant decrease in SIF for further increase in a.SIF linearly increases with respect to t and F(Figs.8and9).The T-stress distribution is highly turbulent for both different crack lengths and different thickness which are shown in Figs.10and11.But the same is linear when a and t are kept constant(Fig.12).Constant F and ta vs.J(Fig.4).a vs.K1c(Fig.5).a vs.T-stress(Fig.6).Constant F and at vs.J(Fig.7).t vs.K1c(Fig.8).t vs.T-stress(Fig.9).Constant a and tF vs.J(Fig.10).F vs.K1c(Fig.11).F vs.T-stress(Fig.12).5ConclusionFinite element model is created to find the fracture properties of Austenite stainless steel(AISI304).The FE analysis was carried out by FEA commercial software ABAQUS.Fracture properties of edge-crack plate with tensile load are studied.SIF and T-stress are found out for elastic limit where as J-integral is found out for both elastic and elastic-plastic models.It is found that there is a considerable change in the value of J-integral in when the load crosses elastic limit.References1.Rice JR(1968)A path independent integral and the approximateanalysis of strain concentration by notches and cracks.J Appl Mech 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