有限元四面体网格划分-英文
Sec04_有限元
S4 - 29
非协调 Topology
协调Topology
MSC.Patran FINITE ELEMENT 应用
S4 - 30
打开有限元窗口
在Elements 图标下,可以对曲线,曲面,和实体创建有限元 网格 检查单元质量 通过重划分网格或编辑网格 连接单元
S4 - 31
有限元划分菜单
Glide 1D to create 2D Glide curve 1D bar elements
S4 - 25
几何对网格划分的影响
几何特征
几何特征对单元生成的影响包括参数化,连贯性,和拓扑关系
参数化表达式 包括定义一个局部坐标系,可以定位几何实体中的任 一点 连贯性定义了几何方向, 例如曲面法线和边的次序 拓扑关系 描述了几何实体间的相邻关系
出色的网格控制:
生成的网格与相邻区域(2D 或 3D) 的网格一致 以实体边上的网格种子划分网格
S4 - 24
SWEEP MESHER
扫描低阶单元 (或节点) 生成高阶单元, 例如, 四边形扫描 生成六面体 多种扫描技术 (Extrude, Glide, etc.) 来处理复杂的几何形 状
TetMesh
Sweep mesh
S4 - 5
网格划分 基础和定义
S4 - 6
MSC.Patran 网格划分运算法则
IsoMesh Mesh
Sweep Mesh
Paver Mesh
S4 - 7
TetMesh Mesh
ISO (MAPPED) MESHER
使用范围
Iso-mesher (IsoMesh) 用来划分
ANSYS网格划分(强烈推荐)
比例因子
膨胀因子 过渡因子
有限元及ANSYS
Smartsize网格划分控制
2、Smartsize高级控制
[FAC]：用于计算默认网格尺寸的比例因子，取值范围0.2～5。
FAC=0.5 EXPAND＝1 TRANS＝2
FAC=1 EXPAND＝1 TRANS＝2
FAC参数控制效果(plane82 Free Tri Smartsize)
有限元及ANSYS
尺寸控制
MESHTOOL对话框
由于结构形状的 多样性，在许多情况 下，由缺省单元尺寸 或智能尺寸使产生的 网格并不合适，在这 些情况下，进行网格 划分时必须做更多的 处理。可以通过指定 下述的单元尺寸来进 行更多的控制。
有限元及ANSYS
设置单元尺寸优先等级
对应 MAP 方式
有限元及ANSYS
网格划分器选择－映射网格划分
2、指定尺寸和形状控制
选择单元形状非常简单. 在 MeshTool中,对 面的网格划分选择 Quad,对体的网格划分 选择 Hex, 点击 Mapped.
设置单元尺寸。
有限元及ANSYS
网格划分器选择－映射网格划分
若指定线的分割数, 切记:
对边的分割数必须匹配, 但只须指定一边的分割数. 映射网格划分器将把分割数自动传送到它的对边.若 对边均指定分割数且不一致，则取较多值。
有限元及ANSYS
网格划分器选择－自由网格划分
自由网格是面和体网格划分时的缺省设 置。生成自由网格比较容易：
• 导出 MeshTool 工具, 划分方式设为自由划分. • 推荐使用智能网格划分 进行自由网格划分，
激活它并指定一个尺寸级别。 存储数据库。 • 按 Mesh 按钮开始划分网格。按拾取器中
icem-cfd 四面体网格模块tetra介绍
z Choose Solver Input
− select desired domain(s) and click Done
z Options are specific to solver
Tetra 29
2 July 2008
Tetra 示例实践3
Tetra 19
2 July 2008
机翼例子：网格参数
z 细化
− integer, number of cells in 360 degrees of an arc
Tetra 20
2 July 2008
自然尺寸和细化
z Example, two rods in close proximity z 网格参数：:
2 July 2008
所有程序综述
z 创建或读入几何图形 z 将实体分配到几何图形数据库 z 定义网格全局尺寸和在所选实体上的尺寸 z 产生网格 z 提高网格质量（光滑，等） z 输出到分析软件
Tetra 4
2 July 2008
Tetra的几何图形
z 需要封闭的曲面模型
− 将曲面显示为实体 • 查找丢失的表面 • 查找洞或缺口
2 July 2008
机翼例子：设置
z 创建族
− 机翼 − 入口 − 出口 − Symm − 壁面
z 材料点
− live
Tetra 18
2 July 2008
机翼例子：网格参数
z Ref. size and max. size explained earlier z 自然尺寸
− factor times ref. size − represents a ‘minimum’ size
工程有限元分析英文课件：Shape Functions for 3D Elements
Ni
f1(i) (L1, L2 , L3, L4 ) f1(i) (L1i , L2i , L3i , L4i )
(5.8)
in which, f1(i) (L1, L2, L3, L4 ) denotes the left side of the equation for
one plane that pass through the remote nodes of node i, i.e.,
在右手坐标中，要使得右手螺旋在按照1-2-3的转向转动时是向4的方向前进。3
Volume CAonoardlyisnisatoefsT(Nhraeteu–r体aDl积iCm坐oe标onrs(d自ioin然naa坐lteP标sro))blems
To develop the shape functions for a tetrahedron element, we make
Analysis of Three – Dimensional Problems
Corresponding to node 1
f (1)
1
(
L1
,
L2 ,
L3, L4 )
L1
0
L1=0
Considering that L11 1, L21 L31 L41 0 , thus
Similarly
N1
8
AVnoalluysmiseoCf Tohorredein–aDteims ensional Problems
To get a2,b2, c2 and d2 we permute the indices(下标序列 改变) but must determine the proper sign(正确的符号) by
有限元英语
Preference ：Structural 结构分析Thermal 热分析Fluid 流场分析Electromagnetic 电磁场分析Preprocessor 前处理器Element type 单元类型Structural Mass 结构质量Link 杆Beam 梁Pipe 管道Solid 实体Quad 4 node 4 节点四边形单元Quad 8 node 8 节点四边形单元Brick 8 node 8 节点六面体单元Brick 20 node 20 节点六面体单元Tet 4 node 4 节点四面体单元Tet 10 node 10 节点四面体单元Shell 板壳Contact 接触Option 选择Full integration 完全积分Reduced integration 减缩积分Plane stress 平面应力Plane strain 平面应变Axisymmetric 轴对称Plane strs w/thk 平面应力(输入厚度)Real constant 实常数Thickness 厚度Beam 梁Cross-sectional area 横截面积Area moment of inertia 截面惯性矩Torsional moment of inertia 截面极惯性矩Beam height 梁高Material Props 材料特性Material model 材料模型Structural 结构Linear 线性Elastic 弹性Isotropic 各向同性EX 弹性模量PRXY 泊松比Orthotropic 各向正交Anisotropic 各向异性NonlinearDensity 密度（质量）Thermal expansion 热膨胀系数Damping 阻尼Friction coefficient 摩擦系数Thermal 传热CFD 计算流体动力学Electromagneties 电磁学Acoustics 声学Fluid 流体Section 截面Beam 梁Modeling 建模Create 创造Keypoint 关键点(几何)On Working Plane 在工作平面上On Active CS 在激活的坐标系上Hard point 硬点Line 线Straight Line 直线Arc 弧Through 3 KPs 通过3 点By End KPs & Rad 由端点和半径By Cent & Radius 由圆心和半径Full Circle 整圆Spline 样条Spline thru Locs 由点的坐标建立样条曲线Spline thru KPs 由关键点的坐标建立样条曲线Fillet 倒角Area 面，面积Triangle 三角形Square 矩形Pentagon 五边形Hexagon 六边形Heptagon 七角形Octagon 八角形Corner 角Center 中心Dimension 尺寸，维数Annulus 环状Arbitrary 任意Through KPs 通过关键点生成面By Lines 由线生成面Rectangle 四边形By 2 Corners 由2 个角点生成面By Centr & Cornr 由中心和角点生成面By Dimensions 由尺寸生成面Circle 圆面Solid Circle 实体圆面Annulus 圆环面Partial Annulus 部分环面By End Points 由端点生成圆面Polygon 多边形Volume 体Block 块体Cylinder 圆柱体Hollow 空心圆柱体Solid 固体，实体Prism 三棱体Sphere 球体Cone 圆锥体Node 节点Fill between Nds 在两个节点中填充节点Element 单元Attribute 特性Boolean 布尔运算Intersect 相交Add 加Subtract 减Divide 切分Glue 粘接Overlap 搭接Partition 分割Meshing 分网（离散化）Quadrilateral 四边形Triangle 三角形Hexahedral 六面体Tetrahedral 四面体Sweep 扫略Mapped 映射Surface load 表面力Body load 体积力Reaction 反力Force/ Moment 力/力矩Torque 扭矩Shear 剪力Pressure 压力Temperature 温度Inertia 惯性Angular velocity 角速度Angular acceleration 角加速度Gravity 重力Displacement 位移Constraint 约束Boundary condition 边界条件Symmetry B.C. 对称边界条件Antisymmetry B.C. 反对称边界条件Deflection 变形Coordinate System 坐标系Global 整体坐标系Local 局部坐标系Cartesian 笛卡尔（直角）坐标系Cylindrical 柱坐标系Spherical 球坐标系Element 单元坐标系Nodal 节点坐标系Active Cs 激活坐标系Select 选择Entity 实体List 列表Plot 绘图Plot control 绘图控制Work plane 工作平面Parameter 参数Resume 开始DB 数据库Elastic 弹性Plastic 塑性Linear 线性Nonlinear 非线性Contact 接触Delete 删除Couple 耦合Couple DOFS 耦合自由度Coincident node 重合节点Constraint equation 约束方程Solution 求解Static 静力学分析Modal 模态分析Harmonic 谐响应分析Transient 瞬态动力学分析Spectrum 谱分析Buckling 屈曲分析（稳定性分析）Postprocessor 后处理器Deformed shape 变形Contour plot 等高绘图DOF solution 自由度解Component 分量X-component ofdisplacement X 方向位移Displacement vector sum 位移矢量和Stress 应力X-component of stress X 方向正应力XY shear stress XY 剪应力Principal stress 主应力Stress intensity 应力强度Von Mises stress Mises 等效应力（基于第四强度理论）Bending stress 弯曲应力Axial direct stress 轴向应力Strain 应变Initial strain 初应变Frequency 频率。
Ansys基础培训-网格划分-MeshTool
Training Manual
INTRODUCTION TO ANSYS 11.0
建立有限元模型 — 生成网格和改变网格
•
Training Manual
演示：
– – – – 恢复 ribgeom.db。 用 SMRT,6划分网格 (并非很好的网格)。 用 SMRT,3 重新划分网格(好的网格)。 将 ESIZE 设为 0.2 后重新划分网格，由于智能网格划分考虑了ESIZE，即使 SMRT 设为 3，网格也变得很粗糙，届时，注意单元尺寸并不相同 (因为 SMRT为打开状态)。 – 关闭 SMRT 重新划分网格。单元尺寸现在完全相同。
Training Manual
INTRODUCTION TO ANSYS 11.0
不同的面可以有不同的 AESIZE。 • 边界线仅在未指定 LESIZE 或 KESIZE时， 采用指定尺寸。 • 智能网格划分打开时，为适应线的曲率或几 何近似，指定的尺寸可能无效。
建立有限元模型 —网格密度控制
• 网格工具MeshTool
0trainingmanual建立有限元模型网格密度控制125台湾地区的认证要求?台湾标准检验局bsmi为了岛内电子电机产品的电磁辐射干扰于1995年5月公布商品电磁兼容性管理办法?并于1996年7月正式公告自1997年1月1日起管制复印机等产品的电磁兼容性能?之后陆续管制信息周边产品家电与广播音响产品
• 可以指定边长比例 — 最后一个分割和 第一个分割的比率，使网格数偏向中间 或一边。
建立有限元模型 —网格密度控制
面尺寸 • 在面的内部控制单元尺寸：
– Main Menu > Preprocessor > Meshing > MeshTool; then select ―Size Controls‖, ―Areas‖, and [Set] – 或使用 AESIZE 命令 – 或 Main Menu > Preprocessor > Meshing > Size Cntrls > ManualSize > Areas
Digimat介绍资料511
Isotropic
逆向回归 FPGF 强度值
DIGIMAT-CAE
DIGIMAT-CAE 是 DIGIMAT 与其他 CAE 程序的 接口，工艺仿真软件能够通过 DIGIMAT-CAE 与 结构仿真软件连接起来，从而实现考虑工艺影 响的，多尺度耦合的结构有限元仿真。 在耦合分析每个增量步的求解中，各积分 点上的材料刚度都会根据该位置的微观结构特 征由 Digimat 通过场均匀化分别计算得出。在耦 合分析中，Digimat 以用户子程序形式参与耦合 迭代，不受有限元软件本身的材料模型限制。
DIGIMAT-MF 支持的虚拟实验加载：
DIGIMAT-FE
DIGIMAT 是通过建立反应材料微观结构特 征的代表性体积单元（RVE） ，并通过有限元分 析获取材料均化性能和微观尺度上局部应力应 变情况的模块。通过定义单相材料的本构模型， 微结构的几何特征即可采用随机算法生成材料 微观结构特征单元的几何模型，并通过调用内 部或外部商用有限元程序计算材料微观结构上 的应力应变分布情况，并可在后处理中分析应 力应变的分布概率以及材料的平均性能。
网格自动划分：低阶/高阶四面体单元、voxel 单元 有限元隐式非线性计算：支持多核并行 有限元结果后处理
DIGIMAT-FE 支持的外部求解器：
Marc：2013.1 Ansys workbench：15.0 Abaqus/ CAE：6.14
RVE 求解的后处理主要分为两部分。 首先在 FEA 软件的后处理中可以得到纤维和树脂上的
热弹粘塑性本构
DIGIMAT-MF 中的均化算法：
Mori-Tanaka法
单调加载、循环加载、自定义历程加载 多向应力应变载荷 力学载荷、热力学载荷 预测热传导和导电性能
MAXWELL第6讲
第六讲
Maxwell 3D 的网格剖分
目前的Maxwell仅支持四面体单元（也称作三 棱锥单元），该单元形状简单，对于复杂三维实 体和复杂曲面实体的网格剖分稳定，几乎可以在 所有的三维有限元软件中找到它的应用案例。所 以Maxwell 3D 中采用了四面体单元作为网格剖分 可以使得所计算的模型有一个更稳定更真实的结 果。
建一旦定义了旋转运动，以解决定子和转子部件之间的空气间隙
第六讲
Maxwell 3D —>Analysis Setup —>Apply Mesh Operations
Maxwell 3D/2D —>Fields —>Plot Mesh
Mesh Linking:
第六讲
第六讲
Mesh Failure 解决方法:
注意： Model Resolution必须谨慎使用，有时导致网格不能正确表示几何模型
第六讲
Cylindrical Gap Treatment网格剖分 Cylindrical Gap Treatment网格操作是一个近似的网格细化，
通常用于旋转运动的物体； 网格细化作用在封闭的物体的内部； 主要应用在涉及旋转运动的瞬态解算器，该网格操作是自动创
Initial Mesh Settings:
Maxwell 3D —>Mesh Operations —>Initial Mesh Settings
Meshing Methods: 3种方式
Auto (3D Only):自动选择合适的网格划分方法 Ansoft Tau Mesh:
工程有限元分析英文课件：Mesh Division (网格划分)
General Procedure of Finite Element Method
In structure analysis, the nodal degrees of freedom called nodal - displacement parameters (节点位移参量), normally refer to the displacements at each node.
(xi , yi ), (x j , y j ) and (xm , ym ) . 10
General Procedure of Finite Element Method
( um, vm )
(ui, vi )
( u, v )
(uj , vj)
For a 2 - D triangular element, there are two
General Procedure of Finite Element Method
Substituting
the
nodal
coordinates
into
u 1 2x 3 y
v
4
5
x
6
y
one
after the other, we have
ui 1 2 xi 3 yi u j 1 2 x j 3 y j
(1)The continuum is divided into two- or three- dimensional (二维 或三维) finite elements, which are separated by straight or curved lines (直线或曲线) (two-dimensional) or by flat or curved surfaces (平面或曲面) (three-dimensional).
ANSYS-Workbench-网格划分
b) Curvature：是由曲率法确定、细化边和曲面处的网格大小
c) Proximity：是控制模型邻近区网格生成，主适用于窄、薄处网格的 生成。
确定全局网格的设置
d. Proximity and curvature：具有proximity和curvature二者的特点， 但所消耗的时间也多。
• 设置合适的全局网格参数可以减小后面具体网格参数的设置工作量， 对于结构场，其详细栏见上个PPT的mechanical，下面以结构分析为 例对其展开描述。Mechanical中的尺寸函数（sizing）下参数项是高 级尺寸函数（advanced sizing function,简称ASF）,这主要是控制 曲线、面在曲率较大的地方的网格。具体选项有：
Hex-Dominant网格
多域扫掠型
• 多域扫掠型（Multizone Sweep Meshing）主要用来划分六面体网格。 其特点就是具有几何体自动分解的功能，从而产生六面体网格。如下 图所示左边的几何体，若以常规的方式想划分成全六面体网格，则需 要先将几何体切分成四个规则体后，再扫掠成六面体网格。然而在 workbench中，只要直接使用多域扫掠法，程序就能自动处理划分成 六面体网格。
认识网格划分平台
网格文件具体地说主要有两类：有限元分析网格和计算流体力学 的网格。
认识网格划分平台
• 对于三维几何体，ANSYS共有下面六种不同的划分网格法
认识网格划分平台
• 对于二维几何体ANSYS有以下几种不同的划分网格法。
典型网格划分法
• 主要内容
四面体网格
• 在三维网格中，相对而言四面体网格划分是最简单的。在workbench 中，四面体网格的生成主要基于两种方法：RGRID算法和ICEM CFD tetra算法，具体如下：
IDESA有限元分析_第6篇第27章 自由网格划分
第27章MasterFEM 教程:自由网格划分本篇介绍了划分二维单元和实体单元的方方法。
用户将学会：∙划分二维单元。
∙根据曲率设置网格密度。
∙分配局部单元密度。
∙运用maximum area plane方法划分网格。
∙划分实体单元。
开始前必备知识：熟悉MasterFEM界面和创建零件。
熟悉在模型文件中管理零件。
熟悉拉伸特征和旋转特征的布尔运算。
熟悉仿真分析流程。
设置1/4如果还没有运行一个新的模型文件,创建一个新文件并命名。
FileOpen·1·打开模型文件菜单确信用户是在以下工作状态和任务当中:设置工作单位为毫米(mm)OptionsUnitsmm (milli newton)设置2/4工作内容：按照以下尺寸草绘封闭线框(拉伸距离50mm)。
提示：·2·工作内容：命名此零件提示：名称: Part设置3/4工作内容：创建此模型的有限元模型提示：创建有限元模型菜单OK注意事项：零件没有明显的改变，但是在抽屉里(Manage Bins)双击带省略号的零件名称就会看到对应的有限元模型文件。
设置4/4保存模型文件。
FileSave警告！如果软件提示用户保存模型文件，用户应选择：·3·No记住：只有教程中提示保存模型文件，而不是软件提示保存的时候，用户才可以执行保存文件操作。
为什么：在上一次保存以后的错误操作不能撤销恢复,用户可以选择重新打开文件，恢复到上一次保存时的状态。
提示：重新打开模型文件的快捷键：按Control-Z。
表面划分壳单元1/4本节介绍在表面上运用默认属性创建二维单元的方方法，后面将会介绍如何控制单元长度和局部密度。
当几何尺寸改变后，和几何相关的有限元模型也会自动更新。
表面划分壳单元2/4工作内容：在表面上定义单元属性，单元厚度为10mm的四边形壳单元。
怎样做：·4·选取表面Define Mesh 菜单Define Free Meshing Options 菜单Curvature Based Length:不要关闭Define Mesh 菜单.为什么：10mm长的单元至少能在25mm长的短边上定义两个单元，关闭Curvature-based选项是为了和下面的操作比较此参数的效果如何。
有限元、力学专业词汇汇总--中英文对照
有限元、力学专业词汇汇总拉力tensile force 正应力normal stress 切应力shear stress静水压力hydrostatic pressure 集中力concentrated force 分布力distributed force 线性应力应变关系linear relationship between stress andstrain弹性模量modulus of elasticity 横向力lateral force transverse force轴向力axial force 拉应力tensile stress 压应力compressive stress平衡方程equilibrium equation 静力学方程equations of static比例极限proportional limit 应力应变曲线stress-strain curve 拉伸实验tensile test‘屈服应力yield stress 极限应力ultimate stress 轴shaft 梁beam纯剪切pure shear 横截面积cross-sectional area 挠度曲线deflection curve 曲率半径radius of curvature 曲率半径的倒数reciprocal of radius of curvature纵轴longitudinal axis 悬臂梁cantilever beam 简支梁simply supported beam微分方程differential equation 惯性矩moment of inertia 静矩static moment扭矩torque moment 弯矩bending moment弯矩对x的导数 derivative of bending moment with respect to x弯矩对x的二阶导数the second derivative of bending moment with respect to x静定梁statically determinate beam 静不定梁statically indeterminate beam相容方程compatibility equation 补充方程complementary equation中性轴neutral axis 圆截面circular cross section两端作用扭矩twisted by couples at two ends 刚体rigid body 扭转角twist angle 静力等效statically equivalent 相互垂直平面mutually perpendicular planes通过截面形心through the centroid of the cross section 一端铰支pin support at one end 一端固定fixed at one end 弯矩图bending moment diagram剪力图shear force diagram 剪力突变abrupt change in shear force、旋转和平移rotation and translation虎克定律hook’s law边界条件boundary condition 初始位置initial position、力矩面积法moment-area method 绕纵轴转动rotate about a longitudinal axis 横坐标abscissa 扭转刚度torsional rigidity 拉伸刚度tensile rigidity剪应力的合力resultant of shear stress 正应力的大小magnitude of normal stress 脆性破坏brittle fail 对称平面symmetry plane 刚体的平衡equilibrium of rigid body 约束力constraint force 重力gravitational force实际作用力actual force 三维力系three-dimentional force system合力矩resultant moment 标量方程scalar equation、矢量方程vector equation 张量方程tensor equation 汇交力系cocurrent system of forces任意一点an arbitrary point 合矢量resultant vector 反作用力reaction force反作用力偶reaction couple 转动约束restriction against rotation平动约束restriction against translation 运动的趋势tendency of motion绕给定轴转动rotate about a specific axis 沿一个方向运动move in a direction控制方程control equation 共线力collinear forces 平面力系planar force system 一束光a beam of light 未知反力unknown reaction forces 参考框架frame of reference大小和方向magnitude and direction 几何约束geometric restriction刚性连接rigidly connected 运动学关系kinematical relations运动的合成superposition of movement 固定点fixed point平动的叠加superposition of translation 刚体的角速度angular speed of a rigid body 质点动力学particle dynamics 运动微分方程differential equation of motion 工程实际问题practical engineering problems 变化率rate of change 动量守恒conservation of linear momentum 定性的描述qualitative description点线dotted line 划线dashed line 实线solid line 矢量积vector product点积dot product 极惯性矩polar moment of inertia 角速度angular velocity角加速度angular acceleration infinitesimal amount 无穷小量definite integral 定积分a certain interval of time 某一时间段kinetic energy 动能conservative force 保守力damping force 阻尼力coefficient of damping 阻尼系数free vibration 自由振动periodic disturbance 周期性扰动viscous force 粘性力forced vibration 强迫震动general solution 通解particular solution 特解transient solution 瞬态解steady state solution 稳态解second order partial differential equation 二阶偏微分方程external force 外力internal force 内力stress component 应力分量state of stress 应力状态coordinate axes 坐标系conditions of equilibrium 平衡条件body force 体力continuum mechanics 连续介质力学displacement component位移分量additional restrictions 附加约束compatibility conditions 相容条件mathematical formulations 数学公式isotropic material 各向同性材料sufficient small 充分小state of strain 应变状态unit matrix 单位矩阵dilatation strain 膨胀应变the first strain invariant 第一应变不变量deviator stress components 应力偏量分量resonance frequency 谐振频率the first invariant of stress tensor 应力张量的第一不变量bulk modulus 体积模量constitutive relations 本构关系linear elastic material 线弹性材料mathematical derivation 数学推导 a state of static equilibrium 静力平衡状态Newton‘s first law of motion 牛顿第一运动定律directly proportional to 与……成正比stress concentration factor 应力集中系数state of loading 载荷状态st venant’ principle 圣维南原理uniaxial tension 单轴拉伸cylindrical coordinates 柱坐标buckling of columns 柱的屈曲critical value 临界值stable equilibrium 稳态平衡unstable equilibrium condition 不稳定平衡条件critical load 临界载荷a slender column细长杆fixed at the lower end下端固定free at the upper end上端自由critical buckling load 临界屈曲载荷potential energy 势能fixed at both ends 两端固定hinged at both ends 两端铰支tubular member 管型杆件transverse dimention 横向尺寸stability of column 柱的稳定axial force 轴向力elliptical hole 椭圆孔plane stress 平面应力nominal stress 名义应为principal stress directions 主应力方向axial compression 轴向压缩dynamic loading 动载荷dynamic problem 动力学问题inertia force 惯性力resonance vibration 谐振static states of stress 静态应力dynamic response 动力响应time of contact 接触时间length of wave 波长。
abaqus中英文
abaqus中英文ABAQUS专业术语中英文对照前后处理器模块——ABAQUS/CAE几何体建模——GeometryGeometry Creation Tools（几何体生成工具）2-D Sketcher（二维草图）Sketch T ools and Options（草图工具和选项）Geometry Import/Export（几何体导入和导出）Geometry Repair T ools（几何体修补工具）Mesh Edit（网格编辑）模型装配——AssemblyInstance Tools（实例工具）Sets and Surfaces（集合和表面）Display Groups（显式组）Merge/Cut T ools（合并/剪切操作）定义材料性质——PropertiesMaterial Models（材料模型）General（一般性质）Elasticity（弹性性质）Electrical properties(电性质)Mass diffusion（质量扩散）Plasticity（塑性性质）Pore fluid properties（孔隙流体性质）Thermal properties（热性质）Gasket（垫片）Acoustic medium（声学介质）Equation of state (EOS) materials（状态方程）User materials（用户自定义材料）Hyperelastic material evaluation（超弹性材料评估）Sections（截面性质）Solid（实体）homogeneous（各向同性的）, generalized plane strain（广义平面应变的Shell（壳）homogeneous（各向同性的）, composite（复合材料壳单元）, membrane （薄膜）,surface (rebar layers)（带钢筋层的曲面）Beam（梁） beam（梁）, truss（杆）Point（点）mass（质量单元）, rotary inertia（转动惯量）, damping（阻尼）, capacitance（电容）Gasket（垫片）Beam section profiles（梁截面形状）Skin（蒙皮）Orientations（材料方向）分析流程功能——AnalysisGeneral, Linear and Nonlinear Analyses（通用，线性和非线性分析）Static stress/displacement analysis（静力分析）Viscoelastic/viscoplastic response（粘弹/粘塑响应）Dynamic stress/displacement analysis（动力分析）Heat transfer analysis（热传导分析）Mass diffusion analysis（质量扩散分析）Acoustic analysis（声学分析）Coupled problems（耦合问题）– Thermo-mechanical（热固）– Thermo-electrical（热电）– Piezoelectric（压电）– Pore fluid flow-mechanical（孔隙流动）– Thermo-mechanical mass diffusion（热-固-质量扩散）– Shock and acoustic-structural（冲击和声固耦合）Linear Perturbation Analyses（线性摄动分析）Static stress/displacement analysis（应力位移静力分析）– Linear static stress/displacement analysis（应力位移线性静力分析）– Eigenvalue buckling estimates（特征值屈曲分析）Dynamic stress/displacement analysis（应力位移动力学分析）– Natural frequency extraction（自振频率提取）– Complex eigenvalue extraction（复频率提取）– Transient response via modal superposition（通过模态叠加法计算瞬态响应）–Steady-state response to harmonic loading （简谐载荷下的稳态响应）– Response spectrum analysis（响应谱分析）– Random response analysis（随机响应分析）Analysis Controls（分析控制）Output Requests（输出请求）定义约束和接触——Constraints and InteractionsContact（接触）General contact (ABAQUS/Explicit)（通用接触）Surface-to-surface contact（面面接触）Self-contact（自接触）Contact Properties（接触性质）Constraints（约束）Thermal（热）Loads（载荷）Mechanical（机械）Bolt load（螺栓预紧力）Thermal（热）Acoustic（声场）Fluid（流体）Electrical（电）Mass diffusion（质量扩散）Fields（场）Multiple load cases（多工况）Connectors（连接单元）Boundary Conditions（边界条件）Nodal（节点位移）Velocity（速度）Acceleration（加速度）Velocity/angular velocity（角速度）Submodel（子模型）Pore pressure（孔压）Electric potential（电势）Temperatures（温度）网格划分——MeshingMesh Seeding（网格种子）Structured Meshing（结构化分网）Surface Meshing（表面分网）Solid Meshing（实体分网）Virtual Topology（虚拟拓扑）单元库——Element Library Beam（梁单元）Truss（杆单元）Connector（连接单元）Shell（壳单元）Membrane（薄膜单元）Continuum（实体单元）Elbow（弯管单元）Gasket（垫片单元）Pipe（管道单元）后处理——VisualizationModel plotting（模型图）Deformed, contour, vector/tensor, path, tickmark, overlay, material orient ations, X–Y plots（变形图，云图、矢量/张量图、材料方向图、X-Y曲线图等）Animations（动画）Stress linearization（应力线性化）Tabular data reports（数据报表）Probe/query tools（查询工具）Diagnostics visualization（结果诊断）过程自动化——Process AutomationPython scripting（Python脚本）GUI toolkit（用户界面工具包）Macro manager（宏管理器）隐式求解器模块——ABAQUS/STANDARD分析类型——Analysis TypesGeneral, Linear and Nonlinear Analyses（通用，线性和非线性分析） Static stress/displacement analysis（静力分析）Direct cyclic analysis（直接载荷循环分析）Viscoelastic/viscoplastic response（粘弹性和粘塑性）Dynamic stress/displacement analysis（动力学分析）Steady-state transport analysis（稳态传输分析）Heat transfer analysis（热传导分析）Mass diffusion analysis（质量扩散分析）Acoustic analysis（声场分析）Coupled analysis（耦合分析）Linear Perturbation Analyses（线性摄动分析）分析和建模技术——Analysis and Modeling Techniques求解技术——Solution Techniques材料定义——Material DefinitionsElastic Mechanical Properties（弹性机械性质）Inelastic Mechanical Properties（非弹性机械性质）Additional Material Properties（其他材料性质）单元库——Element LibraryContinuum（实体单元）Membranes（薄膜单元）Beams（梁单元）Pipes（管道单元）Elbows（弯管单元）Frame Elements（框架单元）Trusses（杆单元）Gasket Elements（垫片单元）Inertial Elements（惯性单元）Rigid Elements（刚体单元）Capacitance Elements（热容单元）Connector Elements（连接单元）Springs, Dashpots, Flexible Joints（弹簧，阻尼器，柔性接头）Distributed Coupling（分布耦合）Special-Purpose Elements（特殊用途单元）User-Defined Elements（用户自定义单元）预设条件——Prescribed Conditions约束和接触——Constraints and Interactions Kinematic Constraints（自由度约束）Surface-Based Contact Modeling（基于表面的接触建模）Element-Based Contact Modeling（基于单元的接触建模）Cavity Radiation（空腔辐射）用户子程序——User Subroutines显式求解器模块——ABAQUS/EXPLICIT分析类型——Analysis Types非线性显示动力学分析分析和建模技术——Analysis and Modeling Techniques 材料定义——Material DefinitionsElastic Mechanical Properties（弹性机械性质）Inelastic Mechanical Properties（非弹性机械性质）Additional Material Properties（其他材料性质）单元库——Element LibraryContinuum（实体单元）Structural（结构单元）Inertial Elements（惯性单元）Rigid Elements（刚体单元）Capacitance Elements（热容单元）Connector Elements（连接单元）Springs, Dashpots（弹簧和阻尼器）预设条件——Prescribed Conditions约束和接触——Constraints and InteractionsKinematic Constraints（自由度约束）Contact Modeling（接触建模）。
有限元计算与强度分析-(二)几何建模及网格划分
1.2 ANSYS Workbench建模技术
1.2.10 激活新平面
• New Sketch :在激活平面上新建草图。 • 新草图放在树形目录中，且在相关平面的下方。 • 通过树形目录或下拉列表操作草图（激活）。 • 注意：下拉列表仅显示以当前激活平面为参照的草图（示例如下）。
激活XY平面
下拉列表中仅显示XY平面内 的草图
关注于一个点
“Sphere of Influence” (红色 显示) 已经定义。球体内所关 注实体的单元大小是给定的平 均单元大小。
关注于两个面
1.4 划分网格
1.4.2.2 局部网格控制
刷新单元)。 • 需要更新:数据一改变单元的输出也要相应的更新。 • 最新的。 • 发生输入变动: 单元是局部时新的，但上行数据发生变
化也可能导致其发生改变。
1.2 ANSYS Workbench建模技术
1.2.1 DesignModeler概述 – DesignModeler (DM) 是ANSYS Workbench的一个组成， 类似CAD的建模器，具有参数建模能力:
1.1.1启动Workbench
• 两种方式启动Workbench:
– 从windows开始菜单启动:
– 从其支持的CAD系统中启动
1.1 ANSYS Workbench概述
1.1.2Workbench的图形用户界面
• Workbench 的图形用户界面主要分成工具箱和项目概图 两部分:
工具箱
项目概图
1.4 划分网格
1.4.2.1 网格划分方法
• Sweep（扫掠划分）：
– 扫掠划分单元（六面体，也可能是楔形体），否则就是四面体。 – 在mesh上点击鼠标右键选择Show Sweepable Bodies。 – Type ：扫掠方向上的划分数目或单元大小。 – Sweep Bias Type： 扫掠方向上的间隔比例 – Src/Trg Selection：
有限元网格划分技术
对于有限元分析来说，网格划分是其中最关键的一个步骤，网格划分的好坏直接影响到解算的精度和速度。
网格化有三个步骤：定义单元属性（包括实常数）、在几何模型上定义网格属性、划分网格。
定义网格的属性主要是定义单元的形状、大小。
单元大小基本上在线段上定义，可以用线段数目或长度大小来划分，可以在线段建立后立刻声明，或整个实体模型完成后逐一声明。
采用Bottom-Up方式建立模型时，采用线段建立后立刻声明比较方便且不易出错。
例如声明线段数目和大小后，复制对象时其属性将会一起复制，完成上述操作后便可进行网格化命令。
网格化过程也可以逐步进行，即实体模型对象完成到某个阶段就进行网格话，如所得结果满意，则继续建立其他对象并网格化。
网格的划分可以分为自由网格(free meshing)、映射网格(mapped meshing)和扫略网格(sweep meshing)等。
一、自由网格划分自由网格划分是自动化程度最高的网格划分技术之一，它在面上可以自动生成三角形或四边形网格，在体上自动生成四面体网格。
通常情况下，可利用ANSYS的智能尺寸控制技术（SMARTSIZE 命令）来自动控制网格的大小和疏密分布，也可进行人工设置网格的大小（AESIZE、LESIZE、KESIZE、ESIZE等系列命令）并控制疏密分布以及选择分网算法等（MOPT命令）。
对于复杂几何模型而言，这种分网方法省时省力，但缺点是单元数量通常会很大，计算效率降低。
同时，由于这种方法对于三维复杂模型只能生成四面体单元，为了获得较好的计算精度，建议采用二次四面体单元（92号单元）。
如果选用的是六面体单元，则此方法自动将六面体单元退化为阶次一致的四面体单元，因此，最好不要选用线性（一阶次）的六面体单元（没有中间节点，比如45号单元），因为该单元退化后为线性的四面体单元，具有过大的刚度，计算精度较差；如果选用二次的六面体单元（比如95号单元），由于其是退化形式，节点数与其六面体原型单元一致，只是有多个节点在同一位置而已，因此，可以利用TCHG命令将模型中的退化形式的四面体单元变化为非退化的四面体单元(如92号单元)，减少每个单元的节点数量，提高求解效率。
workbench 四面体网格膨胀
第五章四面体网格膨胀概述Training Manual •四面体网格划分算法•Patch Conforming的膨胀选项–算法–前处理和后处理–高级选项–冲突避免•Patch Independent 划分P t h I d d t–损伤外貌y–Proximity 细化–Curvature 细化•作业5.1 三通搅拌器的膨胀四面体网格(Patch Conforming)(P t h C f i)•作业5.2 汽车多支管的流体和结构网格划分(Patch Independent)(Patch Independent)四面体网格划分算法Training Manual •Patch Conforming–默认时考虑所有的面和边(尽管在收缩控制和虚拟拓扑时会改变且默认损伤外貌基于最小尺寸限制)–适度简化CAD (如. native CAD, Parasolid, ACIS, 等.)在体部件中结使扫共体棱柱体格–在多体部件中可能结合使用扫掠方法生成共形的混合四面体/棱柱和六面体网格–有高级尺寸功能–表面网格体网格•Patch Independent–对CAD 有长边的面, 许多面的修补, 短边等有用.–内置defeaturing/simplification 基于网格技术–基于ICEM CFD 四面体/棱柱Octree 方法–体网格表面网格Patch Conforming 四面体膨胀Training Manual •基本设置包括膨胀选项，前处理和后处理膨胀算法膨胀选项–平滑过渡Training Manual •平滑过渡(默认)–使用局部四面体单元尺寸计算每个局部的初始高度和总高度以达到平滑的体积变化比。
每个膨胀的三角形都有一个关于面积计算的初始高度，在节点处平均。
这意味着对一均匀网格，初始高度大致相同，而对变化网格初始高度也是不同的。
–过渡比•膨胀层最后单元层和四面体区域第一单元层间的体尺寸改变•当求解器设置为CFX时, 默认的Transition Ratio是0.77. 对其它物理选项, 包括SolverPreference设置为Fluent的CFD, 默认值是0.272.•因为Fluent求解器是单元为中心的，其网格单元等于求解器单元, 而CFX求解器是顶点为中心的，求解器单元是双重节点网格构造的，因此会发生不同的处理膨胀选项–厚度选项Training Manual •总厚度–创建常膨胀层，用Number of Layers的值和Growth Rate控制以获得Maximum Thickness值控制的总厚度。
hyperworks有限元仿真-第5章_1D网格划分
刚度矩阵的各列是一个节点力的平衡集合，节点力产生对应自由度的位移。
一个对称的刚度矩阵表示力与位移成正比。
矩阵的对角线项全是正值表示一个力指向左边就不能产生向右的位移。只有结构在不稳定的情况下，对
角线项才会是零或者负值。
rod单元只支持拉伸或压缩，不支持剪力、弯矩和扭矩。在上述方程中，刚度矩阵的阶数是2x2，未知量
|F|24x1 = |K|24x24 |δ|24x1 这就意味着求解一个quad4单元的问题，软件内部将会求解24个方程。
Tetra10 单元：
自由度/节点 = 3 总自由度 = 3*10 = 30 刚度矩阵阶数 = 30 x 30
|F|30x1 = |K|30x30 |δ|30x1
对于一个给定的有限元模型，软件需要求解多少个方程呢？
假设模型中只有薄壳单元，共20,000节点（6 自由度/节点）。
总自由度 = 20000*6 = 120,000
刚度矩阵阶数 = 120,000x120,000
有限元软件会在内部求解的方程数 = 120,000
固体力学中变分法有限元与加权残值法有限元的等效表格
问题：在一个1D的rod单元的一端（自由端）施加一个集中拉力，另一端固定。
5.2 刚度矩阵推导
什么是刚度以及为什么我们在FEA中需要它？ 刚度‘K’定义为力/长度（单位N/mm）。物理意义 – 刚度等于产生单位位移所需要的力。刚度取决于几何 形状以及材料属性。
铸铁
低碳钢
铝
考虑3个几何尺寸完全相同的二力杆 – 铸铁、低碳钢和铝。如果我们测量产生1mm位移所需要的力，铸
铁需要的力最大，然后依次是低碳钢和铝，即KCI > KMS > KAl。
你觉得承载垂直力需要哪些自由度？
ANSYS Workbench Mesh网格划分
Workbench Mesh 网格划分分析步骤网格划分工具平台就是为ANSYS 软件的不同物理场和求解器提供相应的网格文件，Workbench 中集成了很多网格划分软件/应用程序，有ICEM CFD，TGrid，CFX，GAMBIT，ANSYS Prep/Post 等。
网格文件有两类：①有限元分析（FEM）的结构网格：结构动力学分析，电磁场仿真，显示动力学分析（AUTODYN，ANSYS LS DYNA）；②计算流体力学（CFD 分析）分析的网格：用于ANSYS CFX，ANSYS FLUENT，Polyflow；这两类网格的具体要求如下：（1）结构网格：①细化网格来捕捉关心部位的梯度，例如温度、应变能、应力能、位移等；②大部分可划分为四面体网格，但六面体单元仍然是首选；③有些显示有限元求解器需要六面体网格；④结构网格的四面体单元通常是二阶的（单元边上包含中节点）；（2）CFD 网格：①细化网格来捕捉关心的梯度，例如速度、压力、温度等；②由于是流体分析，网格的质量和平滑度对结果的精确度至关重要，这导致较大的网格数量，经常数百万的单元；③大部分可划分为四面体网格，但六面体单元仍然是首选，流体分析中，同样的求解精度，六面体节点数少于四面体网格的一半。
④CFD 网格的四面体单元通常是一阶的（单元边上不包含中节点）一般而言，针对不同分析类型有不同的网格划分要求：①结构分析：使用高阶单元划分较为粗糙的网格；②CFD：好的，平滑过渡的网格，边界层转化（不同CFD 求解器也有不同的要求）；③显示动力学分析：需要均匀尺寸的网格；物理选项实体单元默认中结点关联中心缺省值Coarse Coarse Medium Coarse平滑度过渡Mechanical CFD Electromagnetic ExplicitKept Dropped Kept DroppedMedium Medium Medium FineFast Slow Fast Slow注：上面的几项分别对应Advanced 中的Element Midside Nodes，以及Sizeing 中的Relevance Center，Smoothing，Transition。
有限元中英文对照资料
The finite element analysisFinite element method, the solving area is regarded as made up of many small in the node connected unit (a domain), the model gives the fundamental equation of sharding (sub-domain) approximation solution, due to the unit (a domain) can be divided into various shapes and sizes of different size, so it can well adapt to the complex geometry, complex material properties and complicated boundary conditionsFinite element model: is it real system idealized mathematical abstractions. Is composed of some simple shapes of unit, unit connection through the node, and under a certain load.Finite element analysis: is the use of mathematical approximation method for real physical systems (geometry and loading conditions were simulated. And by using simple and interacting elements, namely unit, can use a limited number of unknown variables to approaching infinite unknown quantity of the real system.Linear elastic finite element method is a ideal elastic body as the research object, considering the deformation based on small deformation assumption of. In this kind of problem, the stress and strain of the material is linear relationship, meet the generalized hooke's law; Stress and strain is linear, linear elastic problem boils down to solving linear equations, so only need less computation time. If the efficient method of solving algebraic equations can also help reduce the duration of finite element analysis.Linear elastic finite element generally includes linear elastic statics analysis and linear elastic dynamics analysis from two aspects. The difference between the nonlinear problem and linear elastic problems:1) nonlinear equation is nonlinear, and iteratively solving of general;2) the nonlinear problem can't use superposition principle;3) nonlinear problem is not there is always solution, sometimes even no solution. Finite element to solve the nonlinear problem can be divided into the following three categories:1) material nonlinear problems of stress and strain is nonlinear, but the stress and strain is very small, a linear relationship between strain and displacement at this time, this kind of problem belongs to the material nonlinear problems. Due to theoretically also cannot provide the constitutive relation can be accepted, so, general nonlinear relations between stress and strain of the material based on the test data, sometimes, to simulate the nonlinear material properties available mathematical model though these models always have their limitations. More important material nonlinear problems in engineering practice are: nonlinear elastic (including piecewise linear elastic, elastic-plastic and viscoplastic, creep, etc.2) geometric nonlinear geometric nonlinear problems are caused due to the nonlinear relationship between displacement. When the object the displacement is larger, the strain and displacement relationship is nonlinear relationship. Research on this kind of problemIs assumes that the material of stress and strain is linear relationship. It consists of a large displacement problem of large strain and large displacement little strain. Such as the structure of the elastic buckling problem belongs to the large displacement little strain, rubber parts forming process for large strain.3) nonlinear boundary problem in the processing, problems such as sealing, the impact of the role of contact and friction can not be ignored, belongs to the highly nonlinear contact boundary.At ordinary times some contact problems, such as gear, stamping forming, rolling, rubber shock absorber, interference fit assembly, etc., when a structure and another structure or external boundary contact usually want to consider nonlinear boundary conditions. The actual nonlinear may appear at the same time these two or three kinds of nonlinear problems.Finite element theoretical basisFinite element method is based on variational principle and the weighted residual method, and the basic solving thought is the computational domain is divided into a finite number of non-overlapping unit, within each cell, select some appropriate nodes as solving the interpolation function, the differential equation of the variables in the rewritten by the variable or its derivative selected interpolation node value and the function of linear expression, with the aid of variational principle or weighted residual method, the discrete solution of differential equation. Using different forms of weight function and interpolation function, constitute different finite element methods. 1. The weighted residual method and the weighted residual method of weighted residual method of weighted residual method: refers to the weighted function is zero using make allowance for approximate solution of the differential equation method is called the weighted residual method. Is a kind of directly from the solution of differential equation and boundary conditions, to seek the approximate solution of boundary value problems of mathematical methods. Weighted residual method is to solve the differential equation of the approximate solution of a kind of effective method.Hybrid method for the trial function selected is the most convenient, but under the condition of the same precision, the workload is the largest. For internal method and the boundary method basis function must be made in advance to meet certain conditions, the analysis of complex structures tend to have certain difficulty, but the trial function is established, the workload is small. No matter what method is used, when set up trial function should be paid attention to are the following:(1) trial function should be composed of a subset of the complete function set. Have been using the trial function has the power series and trigonometric series, spline functions, beisaier, chebyshev, Legendre polynomial, and so on.(2) the trial function should have until than to eliminate surplus weighted integral expression of the highest derivative low first order derivative continuity.(3) the trial function should be special solution with analytical solution of the problem or problems associated with it. If computing problems with symmetry, should make full use of it. Obviously, any independent complete set of functions can be used as weight function. According to the weight function of the different options for different weighted allowance calculation method, mainly include: collocation method, subdomain method, least square method, moment method and galerkin method. The galerkin method has the highest accuracy.Principle of virtual work: balance equations and geometric equations of the equivalent integral form of "weak" virtual work principles include principle of virtual displacement and virtual stress principle, is the floorboard of the principle of virtual displacement and virtual stress theory. They can be considered with some control equation of equivalent integral "weak" form. Principle of virtual work: get form any balanced force system in any state of deformation coordinate condition on the virtual work is equal to zero, namely the system of virtual work force and internal force ofthe sum of virtual work is equal to zero. The virtual displacement principle is the equilibrium equation and force boundary conditions of the equivalent integral form of "weak"; Virtual stress principle is geometric equation and displacement boundary condition of the equivalent integral form of "weak". Mechanical meaning of the virtual displacement principle: if the force system is balanced, they on the virtual displacement and virtual strain by the sum of the work is zero. On the other hand, if the force system in the virtual displacement (strain) and virtual and is equal to zero for the work, they must balance equation. Virtual displacement principle formulated the system of force balance, therefore, necessary and sufficient conditions. In general, the virtual displacement principle can not only suitable for linear elastic problems, and can be used in the nonlinear elastic and elastic-plastic nonlinear problem.Virtual mechanical meaning of stress principle: if the displacement is coordinated, the virtual stress and virtual boundary constraint counterforce in which they are the sum of the work is zero. On the other hand, if the virtual force system in which they are and is zero for the work, they must be meet the coordination. Virtual stress in principle, therefore, necessary and sufficient condition for the expression of displacement coordination. Virtual stress principle can be applied to different linear elastic and nonlinear elastic mechanics problem. But it must be pointed out that both principle of virtual displacement and virtual stress principle, rely on their geometric equation and equilibrium equation is based on the theory of small deformation, they cannot be directly applied to mechanical problems based on large deformation theory. 3,,,,, the minimum total potential energy method of minimum total potential energy method, the minimum strain energy method of minimum total potential energy method, the potential energy function in the object on the external load will cause deformation, the deformation force during the work done in the form of elastic energy stored in the object, is the strain energy.The convergence of the finite element method, the convergence of the finite element method refers to when the grid gradually encryption, the finite element solution sequence converges to the exact solution; Or when the cell size is fixed, the more freedom degree each unit, the finite element solutions tend to be more precise solution. Convergence condition of the convergence condition of the finite element finite element convergence condition of the convergence condition of the finite element finite element includes the following four aspects: 1) within the unit, the displacement function must be continuous. Polynomial is single-valued continuous function, so choose polynomial as displacement function, to ensure continuity within the unit. 2) within the unit, the displacement function must include often strain. Total can be broken down into each unit of the state of strain does not depend on different locations within the cell strain and strain is decided by the point location of variables. When the size of the units is enough hours, unit of each point in the strain tend to be equal, unit deformation is uniform, so often strain becomes the main part of the strain. To reflect the state of strain unit, the unit must include the displacement functions often strain. 3) within the unit, the displacement function must include the rigid body displacement. Under normal circumstances, the cell for a bit of deformation displacement and displacement of rigid body displacement including two parts. Deformation displacement is associated with the changes in the object shape and volume, thus producing strain; The rigid body displacement changing the object position, don't change the shape and volume of the object, namely the rigid body displacement is not deformation displacement. Spatial displacement of an object includes three translational and three rotational displacement, a total of six rigid body displacements. Due to a unit involved in the other unit, other units do rigid body displacement deformation occurs willdrive unit, thus, to simulate real displacement of a unit, assume that the element displacement function must include the rigid body displacement. 4) the displacement function must be coordinated in public boundary of the adjacent cell. For general unit of coordination is refers to the adjacent cell in public node have the same displacement, but also have the same displacement along the edge of the unit, that is to say, to ensure that the unit does not occur from cracking and invade the overlap each other. To do this requires the function on the common boundary can be determined by the public node function value only. For general unit and coordination to ensure the continuity of the displacement of adjacent cell boundaries. However, between the plate and shell of the adjacent cell, also requires a displacement of the first derivative continuous, only in this way, to guarantee the strain energy of the structure is bounded. On the whole, coordination refers to the public on the border between neighboring units satisfy the continuity conditions. The first three, also called completeness conditions, meet the conditions of complete unit is complete unit; Article 4 is coordination requirements, meet the coordination unit coordination unit; Otherwise known as the coordinating units. Completeness requirement is necessary for convergence, all four meet, constitutes a necessary and sufficient condition for convergence. In practical application, to make the selected displacement functions all meet the requirements of completeness and harmony, it is difficult in some cases can relax the requirement for coordination. It should be pointed out that, sometimes the coordination unit than its corresponding coordination unit, its reason lies in the nature of the approximate solution. Assumed displacement function is equivalent to put the unit under constraint conditions, the unit deformation subject to the constraints, this just some alternative structure compared to the real structure. But the approximate structure due to allow cell separation, overlap, become soft, the stiffness of the unit or formed (such as round degree between continuous plate unit in the unit, and corner is discontinuous, just to pin point) for the coordination unit, the error of these two effects have the possibility of cancellation, so sometimes use the coordination unit will get very good results. In engineering practice, the coordination of yuan must pass to use "small pieces after test". Average units or nodes average processing method of stress stress average units or nodes average processing method of stress average units or nodes average processing method of stress of the unit average or node average treatment method is the simplest method is to take stress results adjacent cell or surrounding nodes, the average value of stress.1. Take an average of 2 adjacent unit stress. Take around nodes, the average value of stressThe basic steps of finite element method to solve the problemThe structural discretization structure discretization structure discretization structure discretization to discretization of the whole structure, will be divided into several units, through the node connected to each other between the units; 2. The stiffness matrix of each unit and each element stiffness matrix and the element stiffness matrix and the stiffness matrix of each unit (3) integrated global stiffness matrix integrated total stiffness matrix integrated overall stiffness matrix integrated total stiffness matrix and write out the general balance equations and write out the general balance equations and write out the general balance equations and write a general equation 4. Introduction of supporting conditions, the displacement of each node 5. Calculate the stress and strain in the unit to get the stress and strain of each cell and the cell of the stress and strain and the stress and strain of each cell.For the finite element method, the basic ideas and steps can be summarized as: (1) to establishintegral equation, according to the principle of variational allowance and the weight function or equation principle of orthogonalization, establishment and integral expression of differential equations is equivalent to the initial-boundary value problem, this is the starting point of the finite element method. Unit (2) the area subdivision, according to the solution of the shape of the area and the physical characteristics of practical problems, cut area is divided into a number of mutual connection, overlap of unit. Regional unit is divided into finite element method of the preparation, this part of the workload is bigger, in addition to the cell and node number and determine the relationship between each other, also said the node coordinates, at the same time also need to list the natural boundary and essential boundary node number and the corresponding boundary value.(3) determine the unit basis function, according to the unit and the approximate solution of node number in precision requirement, choose meet certain interpolation condition basis function interpolation function as a unit. Basis function in the finite element method is selected in the unit, due to the geometry of each unit has a rule in the selection of basis function can follow certain rules. (4) the unit will be analysis: to solve the function of each unit with unit basis functions to approximate the linear combination of expression; Then approximate function generation into the integral equation, and the unit area integral, can be obtained with undetermined coefficient (i.e., cell parameter value) of each node in the algebraic equations, known as the finite element equation.(5) the overall synthesis: after the finite element equation, the area of all elements in the finite element equation according to certain principles of accumulation, the formation of general finite element equations. (6) boundary condition processing: general boundary conditions there are three kinds of form, divided into the essential boundary conditions (dirichlet boundary condition) and natural boundary conditions (Riemann boundary conditions) and mixed boundary conditions (cauchy boundary conditions). Often in the integral expression for natural boundary conditions, can be automatically satisfied. For essential boundary conditions and mixed boundary conditions, should be in a certain method to modify general finite element equations satisfies. Solving finite element equations (7) : based on the general finite element equations of boundary conditions are fixed, are all closed equations of the unknown quantity, and adopt appropriate numerical calculation method, the function value of each node can be obtained.有限元分析有限元法求解区域是由许多小的节点连接单元（域），该模型给出了切分的基本方程（子域名）的近似解，由于单位（域）可以分为不同的形状和大小不同的尺寸，所以它能很好的适应复杂的几何形状、材料特性和边界条件复杂，复杂有限元模型：它是真实系统的理想化的数学抽象。