abaqus拓扑优化例题计算指导
拓扑优化设计的有限元分析使用教程
拓扑优化设计的有限元分析使用教程拓扑优化设计是一种优化设计方法，通过对结构的拓扑形状进行优化，以提高结构的性能和效率。
有限元分析是拓扑优化设计中常用的分析方法，能够对结构进行精确的应力和位移分析。
本篇文章将对拓扑优化设计的有限元分析使用进行详细介绍。
第一步：建立有限元模型在进行有限元分析之前，首先需要建立结构的有限元模型。
有限元模型是对实际结构进行离散化的模型，通过对结构进行网格划分，将结构分割成一系列小的单元。
常用的有限元单元包括三角形单元、四边形单元、六面体单元等。
根据实际情况选择适合的有限元单元进行建模。
第二步：定义材料属性和边界条件在建立有限元模型之后，需要为模型定义材料属性和边界条件。
材料属性包括材料的弹性模量、泊松比、密度等。
边界条件包括结构的支撑条件和施加的载荷条件。
根据实际情况为结构定义合适的材料属性和边界条件。
第三步：进行有限元分析有限元分析是对结构进行数值计算的过程，涉及到求解结构的位移和应力。
有限元分析可以通过商业软件实现，例如ABAQUS、ANSYS等。
在进行有限元分析之前，需要选择合适的求解算法和计算参数，并进行设置。
第四步：结果后处理有限元分析完成后，需要对分析结果进行后处理。
后处理包括对位移和应力结果进行可视化和分析。
可以使用后处理软件，如Paraview、Tecplot等，将结果导入进行可视化展示。
通过对结果进行分析，可以评估结构的性能以及进行结构的优化。
第五步：拓扑优化设计在进行有限元分析之后，可以根据分析结果进行拓扑优化设计。
拓扑优化设计的目标是优化结构的形态和拓扑结构，以满足特定的性能要求。
拓扑优化设计方法包括基于密度的方法、基于演化的方法、基于参数化的方法等。
根据实际情况选择适合的拓扑优化设计方法进行优化。
第六步：迭代优化拓扑优化设计是一个迭代的过程，需要进行多次优化迭代来逐步优化结构。
在每次优化迭代中，根据上次的优化结果进行结构的调整和更新，并重新进行有限元分析和后处理。
Abaqus作习题讲解3
出的对话框中定义载荷名称为 Load-Pressure，分 析步选择 Step-1，载荷类型选择 Mechanical： Pressure，单击 Continue，选择尚未确定的左侧的 三条边， 单击提示区中的 Done 按钮进入 Edit Load 对话框，输入 Magnitude:16e6,单击 Ok 完成内压 施加。 14. 在环境栏 Module 中选择 Mesh，Object 选择 Part 选项。执行 SeedEdge By Number， 在图形窗口选择底部横边和 X 坐标为 0 的竖直 边，单击提示区中的 Done 按钮，在 basic 选项 卡中选择 By Number：Number of elements，输 入种子数 5， 在 Constrains 选项卡中选择 Do not allow the number of elements to change，单击 Ok 完成设置。 同样方法设置内侧圆弧、 线段种 子数依次为 30、8、30。
15.单击工具箱中 （Mash Part） ，单击提示区 OK to mesh the part 后面的 Yes 完成网格划分。 16.在工具箱中单击 （Assign Element Type） ，在 弹出的 Element Type 对话框 中选择线性隐式四边形单元 CAX4R,单击 Ok 完成单元类 型的选择,保存模型。 17.在环境栏 Module 后 面选择 Job，进入该模块后， 单击工具箱中的 （Job
Manager） ，点击弹出的对话 框下部的 Create，在新的对 话框 Create Job 中定义作业 名称为 Pressure-vessel， 单击 Continue， 进入 Edit Job 对话 框，输入作业描述 Description： Static analysis of a pressure vessel，其他为默 认设置，单击 OK，在 Job Manager 中出现作业 Pressure-vessel，单击对话框 右部的 Write Input 可以输出 与作业同名的.inp 文件，单 击 Submit 提交作业， 进行计 算；单击 Monitor 弹出 Link Monitors 对话框， 可以对作业运行 情况进行监视。 18.执行 PlotContoursOn Both Shapes， 显示模型变形前后的 云图。 19.执行 OpinionsCommon， 在弹出的 Common Plot Opinions 对 话框，切换到 Basic 选项卡，选中 Deformation Scale Factor 栏中，默 认的时 Auto-compute， 即程序自动 选择变形放大系数，本例默认为放大 385.206 倍的结果。选择 Uniform 前面的单选按钮，在出现的 Value 后面自定义均匀放大系数为 150，单击 Apply 按钮即可；也可通过 Nonuniform 分别定义 X、Y、Z 方向的放 大系数。 20.执行 ReportField Output，在弹出的 Report Field Output 对话框输出变量 Output Variable 栏中 Position 下选择 Unique Nodal 然后在下拉列表中选择 U: Spatial displacement 下面的 U1，单击 Apply 按钮，
ABAQUS初学者使用算例
ABAQUS初学者使用算例ABAQUS/CAE实例教程我们将通过ABAQUS/CAE完成上图的建模及分析过程。
首先我们创建几何体一、创建基本特征：1、首先运行ABAQUS/CAE，在出现的对话框内选择Create Model Database。
2、从Module列表中选择Part，进入Part模块3、选择Part→Create来创建一个新的部件。
在提示区域会出现这样一个信息。
4、CAE弹出一个如右图的对话框。
将这个部件命名为Hinge-hole，确认Modeling Space、Type和Base Feature的选项如右图。
5、输入200作为Approximate size的值。
点击Continue。
ABAQUS/CAE初始化草图，并显示格子。
６、在工具栏选择Create Lines: Rectangle(4 Lines)，在提示栏出现如下的提示后，输入（20,20）和（-20,-20），然后点击３键鼠标的中键（或滚珠）。
７、在提示框点击OK按钮。
CAE弹出Edit Basic Extrusion对话框。
８、输入40作为Depth的数值，点击OK按钮。
二、在基本特征上加个轮缘１、在主菜单上选择Shape→Solid→Extrude。
２、选择六面体的前表面，点击左键。
３、选择如下图所示的边，点击左键。
４、如右上图那样利用图标创建三条线段。
５、在工具栏中选择Create Arc: Center and 2 Endpoints６、移动鼠标到(40,0.0)，圆心，点击左键，然后将鼠标移到(40,20)再次点击鼠标左键，从已画好区域的外面将鼠标移到(40,20)，这时你可以看到在这两个点之间出现一个半圆，点击左键完成这个半圆。
７、在工具栏选择Create Circle: Center and Perimeter８、将鼠标移动到(40,0.0)点击左键，然后将鼠标移动到(50,0.0)点击左键。
９、从主菜单选择Add→Dimension→Radial，为刚完成的圆标注尺寸。
例题ABAQUS
对于梁的分析可以使用梁单元、壳单元或是固体单元。
Abaqus的梁单元需要设定线的方向，用选中所需要的线后，输入该线梁截面的主轴1方向单位矢量(x,y,z)，截面的主轴方向在截面Profile设定中有规定。
注意：因为ABAQUS软件没有UNDO功能，在建模过程中，应不时地将本题的CAE模型（阶段结果）保存，以免丢失已完成的工作。
简支梁，三点弯曲，工字钢构件，结构钢材质，E=210GPa，μ=0.28，ρ=7850kg/m3（在不计重力的静力学分析中可以不要）。
F=10kN，不计重力。
计算中点挠度，两端转角。
理论解：I=2.239×10-5m4，w中=2.769×10-3m，θ边=2.077×10-3。
文件与路径：顶部下拉菜单File, Save As ExpAbq00。
一部件1 创建部件：Module，Part，Create Part，命名为Prat-1；3D，可变形模型，线，图形大约范围10(程序默认长度单位为m)。
2 绘模型图：选用折线，从(0,0)→(2,0)→(4,0)绘出梁的轴线。
3 退出：Done。
二性质1 创建截面几何形状：Module，Property，Create Profile（剖面），命名为Profile-1，选I型截面，按图输入数据，l=0.1，h=0.2，b l=0.1，b2=0.1，t l=0.01，t2=0.01，t3=0.01，关闭。
2 定义梁方向：Module，Property，Assign Beam Orientation，选中两段线段，输入主轴1方向单位矢量(0,0,1)或(0,0,-1)，关闭。
3 定义截面力学性质：Module，Property，Create Section（截面），命名为Section-1，梁，梁，截面几何形状选Profile-1，输入E=210e9（程序默认单位为N/m2，GPa=109 N/m2），G=82.03e9，ν=0.28，关闭。
ABAQUS初学者使用算例
ABAQUS初学者使用算例ABAQUS/CAE实例教程我们将通过ABAQUS/CAE完成上图的建模及分析过程。
首先我们创建几何体一、创建基本特征：1、首先运行ABAQUS/CAE，在出现的对话框内选择Create Model Database。
2、从Module列表中选择Part，进入Part 模块3、选择Part→Create来创建一个新的部件。
在提示区域会出现这样一个信息。
4、CAE弹出一个如右图的对话框。
将这个部件命名为Hinge-hole，确认Modeling Space、Type和BaseFeature的选项如右图。
5、输入200作为Approximate size的值。
点击Continue。
ABAQUS/CAE初始化草图，并显示格子。
６、在工具栏选择Create Lines: Rectangle(4 Lines)，在提示栏出现如下的提示后，输入（20,20）和（-20,-20），然后点击３键鼠标的中键（或滚珠）。
７、在提示框点击OK按钮。
CAE弹出Edit Basic Extrusion对话框。
８、输入40作为Depth的数值，点击OK按钮。
二、在基本特征上加个轮缘１、在主菜单上选择Shape→Solid→Extrude。
２、选择六面体的前表面，点击左键。
３、选择如下图所示的边，点击左键。
４、如右上图那样利用图标创建三条线段。
５、在工具栏中选择Create Arc: Center and 2 Endpoints６、移动鼠标到(40,0.0)，圆心，点击左键，然后将鼠标移到(40,20)再次点击鼠标左键，从已画好区域的外面将鼠标移到(40,20)，这时你可以看到在这两个点之间出现一个半圆，点击左键完成这个半圆。
７、在工具栏选择Create Circle: Center and Perimeter８、将鼠标移动到(40,0.0)点击左键，然后将鼠标移动到(50,0.0)点击左键。
９、从主菜单选择Add→Dimension→Radial，为刚完成的圆标注尺寸。
ABAQUS初学者使用算例
ABAQUS/CAE实例教程我们将通过ABAQUS/CAE完成上图的建模及分析过程。
首先我们创建几何体一、创建基本特征：1、首先运行ABAQUS/CAE，在出现的对话框选择Create Model Database。
2、从Module列表中选择Part，进入Part模块3、选择Part→Create来创建一个新的部件。
在提示区域会出现这样一个信息。
4、CAE弹出一个如右图的对话框。
将这个部件命名为Hinge-hole，确认Modeling Space、Type和BaseFeature的选项如右图。
5、输入200作为Approximate size的值。
点击Continue。
ABAQUS/CAE初始化草图，并显示格子。
６、在工具栏选择Create Lines: Rectangle(4 Lines)，在提示栏出现如下的提示后，输入（20,20）和（-20,-20），然后点击３键鼠标的中键（或滚珠）。
７、在提示框点击OK按钮。
CAE弹出Edit Basic Extrusion对话框。
８、输入40作为Depth的数值，点击OK按钮。
二、在基本特征上加个轮缘１、在主菜单上选择Shape→Solid→Extrude。
２、选择六面体的前表面，点击左键。
３、选择如下图所示的边，点击左键。
４、如右上图那样利用图标创建三条线段。
５、在工具栏中选择Create Arc: Center and 2 Endpoints６、移动鼠标到(40,0.0)，圆心，点击左键，然后将鼠标移到(40,20)再次点击鼠标左键，从已画好区域的外面将鼠标移到(40,20)，这时你可以看到在这两个点之间出现一个半圆，点击左键完成这个半圆。
７、在工具栏选择Create Circle: Center and Perimeter８、将鼠标移动到(40,0.0)点击左键，然后将鼠标移动到(50,0.0)点击左键。
９、从主菜单选择Add→Dimension→Radial，为刚完成的圆标注尺寸。
ABAQUS拓扑优化手册
设计循环 （Design cycle） : 优化分析是一种不断更新设计变量的迭代过程， 执行 Abaqus 进行模型修改、查看结果以及确定是否达到优化目的。 其中每次迭代叫做一个设计循环。 优化任务 （Optimization task） ： 一次优化任务包含优化的定义， 比如设计响应、 目标、 限制条件和几何约束。 设计响应（Design responses）: 优化分析的输入量称之为设计响应。设计响应可以直接 从 Abaqus 的结果输出文件.odb 中读取，比如刚度、应力、特征频率及位移等。或者 Abaqus 从结果文件中计算得到模型的设计响应，例如质心、重量、相对位移等。 一个设计响应与模型紧密相关，然而，设计响应必须是一个标量，例如区域内的最大应 力或者模型体积。另外，设计响应也与特定的分析步和载荷状况有关。 目标函数（Objective functions）: 目标函数决定了优化的目标。一个目标函数是从设计 响应中提取的一个标量， 如最大位移和最大应力。 一个目标函数可以用一个包含多个设计响 应的公式来表示。如果设定目标函数为最小化或者最大化设计响应，Abaqus 拓扑优化模块 则将每个设计响应值代入目标函数进行计算。另外，如果有多个目标函数，可以用权重因子 定义每个目标函数的影响程度。 约束（Constraints）: 约束亦是从设计响应中提取的一个标量值。然而，一个约束不能 由设计响应的组合来表达。约束限定了设计响应 ，比如可以指定体积必须降低 45%或者某 个区域的位移不能超过 1mm。也可以指定跟优化无关的加工约束或者几何约束，比如，一 个零件必须保证能够浇铸或者冲压，又比如轴承面的直径不能改变。 停止条件（Stop conditions）: 全局停止条件决定了优化的最大迭代次数。 局部停止条 件在局部最大/最小达成之后指定优化应该停止。 13.1.1.2 Abaqus/CAE 结构优化步骤
ABAQUS例题
对于梁的分析可以使用梁单元、壳单元或是固体单元。
Abaqus的梁单元需要设定线的方向，用选中所需要的线后，输入该线梁截面的主轴1方向单位矢量(x,y,z)，截面的主轴方向在截面Profile设定中有规定。
注意：因为ABAQUS软件没有UNDO功能，在建模过程中，应不时地将本题的CAE模型（阶段结果）保存，以免丢失已完成的工作。
简支梁，三点弯曲，工字钢构件，结构钢材质，E=210GPa，μ=0.28，ρ=7850kg/m3（在不计重力的静力学分析中可以不要）。
F=10kN，不计重力。
计算中点挠度，两端转角。
理论解：I=2.239×10-5m4，w中=2.769×10-3m，θ边=2.077×10-3。
文件与路径：顶部下拉菜单File, Save As ExpAbq00。
一部件1 创建部件：Module，Part，Create Part，命名为Prat-1；3D，可变形模型，线，图形大约范围10(程序默认长度单位为m)。
2 绘模型图：选用折线，从(0,0)→(2,0)→(4,0)绘出梁的轴线。
3 退出：Done。
二性质1 创建截面几何形状：Module，Property，Create Profile，命名为Profile-1，选I型截面，按图输入数据，l=0.1，h=0.2，b l=0.1，b2=0.1，t l=0.01，t2=0.01，t3=0.01，关闭。
2 定义梁方向：Module，Property，Assign Beam Orientation，选中两段线段，输入主轴1方向单位矢量(0,0,1)或(0,0,-1)，关闭。
3 定义截面力学性质：Module，Property，Create Section，命名为Section-1，梁，梁，截面几何形状选Profile-1，输入E=210e9（程序默认单位为N/m2，GPa=109 N/m2），G=82.03e9，ν=0.28，关闭。
最新Abaqus6.13拓扑优化atom-book超全学习资料-03
L3.1w w w .3d s .c o m | © D a s s a u l t S y s t èm e sLesson content:Abaqus Model Optimization Tasks Design Responses Objective Functions ConstraintsGeometric Restrictions Stop Conditions PostprocessingWorkshop 2a: Topology Optimization of a Cantilever Beam With Stamping Geometric Restrictions Workshop 2b: Topology Optimization of a Cantilever Beam With Demold Control Using the Central Plane TechniqueWorkshop 2c: Topology Optimization of a Cantilever Beam With Symmetry Geometric RestrictionsLesson 3: ATOM Workflow and Options2.5 hoursL3.2w w w .3d s .c o m | © D a s s a u l t S y s t èm e sAbaqus ModelThe Abaqus model must be ready prior to the setup of the optimizationAlthough not necessary, it is helpful to create sets that can be used later to define the optimization regionsShown on the right: A set was created to define the region (cell) where the stamping geometric restriction will be appliedw w w .3d s .c o m | © D a s s a u l t S y s t èm e sAn optimization task identifies the type of optimization and the design domain for the optimization.The task serves to configure the optimization algorithm to be usedCreate an optimization task from the Model Tree or the Optimization toolbox as shownChoose the type of optimization task accordinglyEach task also contains the design responses, objective functions, constraints, geometric restrictions and stop conditionsIn this lecture we discuss the setup of the task for topology optimizationL3.4w w w .3d s .c o m | © D a s s a u l t S y s t èm e sOptimization Tasks (2/6)For a topology optimization task, the optimization region is selected nextThe elements in the optimization region will constitute the design domainThe whole model is selected by defaultOften, the optimization region will only be a subset of the model.For example, on the right we have removed the deformable shaft from the display so that only the gear is selected as the optimization regionw w w .3d s .c o m | © D a s s a u l t S y s t èm e sHaving chosen the optimization type and region, it is now possible to configure the optimizationThe Basic tab of the optimization task editor allows the user to choose if the load and boundary regions are to be kept frozenFrozen areas are discussed further later in the context of geometric restrictionsL3.6w w w .3d s .c o m | © D a s s a u l t S y s t èm e sOptimization Tasks (4/6)The Density tab allows the user to change thedensity update strategy and configure other related parametersThese settings are only available for the sensitivity-based methodTip: These parameters rarely need to be changed; if necessary, use a more conservative strategy for a more stable optimizationw w w .3d s .c o m | © D a s s a u l t S y s t èm e sThe Advanced tab allows the user to switch to the condition-based approach if desiredThe condition-based approach is usually preferred for stiffness optimizationNote: the sensitivity-based approach is also able to optimize on stiffnessFor the condition-based approach, the user can configure the speed of the update scheme and the volume deleted in the first cycleThe advanced option “Delete soft elements in region” is recommended when solving problems where soft elements may distort excessively and cause convergence difficultyL3.8w w w .3d s .c o m | © D a s s a u l t S y s t èm e sOptimization Tasks (6/6)For sensitivity-based optimization the user may choose between the SIMP and the RAMP material interpolation techniquesRAMP is preferred for problems that are more dynamic in nature because the interpolation scheme is always concave.Criteria for convergence can be set here. Default criteria are usually sufficient.Note: the default penalty factor has been chosen carefully.Values less than 3 shouldn’t be used.Values greater than 3 significantly increase the chance of getting trapped in a local minimaw w w .3d s .c o m | © D a s s a u l t S y s t èm e sDesign responses are output variables that can be used to describe objective functions and constraintsAll available design responses forsensitivity-based optimization are shown on the rightCondition-based optimization can only have strain energy as the objective and volume as the constraintDesign responses can be a summation of values in the region or maximum/minimum of that regionDesign responses can also be summed across steps/load casesL3.10w w w .3d s .c o m | © D a s s a u l t S y s t èm e sDesign Responses (2/3)A design response can be a combination of previously defined design responsesFor example, on the right we have constructed design response D-Response-3 as aweighted combination of D-Response-1 and D-Response-2Sensitivity-based optimization supports the following operators:Weighted combinationDifferenceAbsolute differencew w w .3d s .c o m | © D a s s a u l t S y s t èm e sCondition-based optimization supports many more operators for creating combined termsL3.12w w w .3d s .c o m | © D a s s a u l t S y s t èm e sObjective Functions (1/2)Objective functions can be created from any previously defined design responsesDesign responses can be single term or combined termFurthermore, the objective function is always a weighted sum of the specified design responsesReference values are constants subtracted from the design responseReference values are meaningless for a condition-based topology optimizationL3.13w w w .3d s .c o m | © D a s s a u l t S y s t èm e sObjective Functions (2/2)Three objective target formulations are supported in topology optimizationMINMIN formulation minimizes the weighted sum of the specified design responsesMAXMAX formulation maximizes the sum of the specified design responsesMIN_MAX (minimize the maximum load case)MIN_MAX formulation minimizes the maximum of the two (or more) design responses specified in the objective function editorL3.14w w w .3d s .c o m | © D a s s a u l t S y s t èm e sConstraints (1/2)Constraints are an integral part of a topology optimizationAn unconstrained topology optimization is not allowed.An error is issued for such casesIn a condition-based topology optimization, only volume constraints are allowed and they are enforced as equality constraintsL3.15w w w .3d s .c o m | © D a s s a u l t S y s t èm e sConstraints (2/2)In sensitivity-based optimizations, many more constraints are allowedFilter by constraint while creating the design response to see what output variables can be chosen as constraints (shown below)Combined terms are allowed to be used as constraints (shown bottom right)Constraints are always inequalities in sensitivity-based optimizationL3.16w w w .3d s .c o m | © D a s s a u l t S y s t èm e sGeometric Restrictions (1/7)Geometric restrictions are additional constraints which are enforced independent of the optimizationGeometric restrictions can be used to enforce symmetries or minimum member sizes that are desired in the final designDemold control is perhaps the most important geometric restriction.It enables the user to place constraints such that the final design can be manufactured by casting.w w w .3d s .c o m | © D a s s a u l t S y s t èm e sFrozen areaFrozen area constraints ensure that no material is removed from the regions designated as frozen (relative density here is always 1)These constraints are particularly important in regions where loads and boundary conditions are specified since we don’t want these regions to become voids.In the gear example, the gear teeth and the inner circumference were kept frozen.Prevents losing contact with the shaft or losing the load path.FrozenL3.18w w w .3d s .c o m | © D a s s a u l t S y s t èm e sGeometric Restrictions (3/7)Member sizeTopology optimization can sometimes lead to thin or thick members that can be problematic to manufactureMember size restrictions provide filters to control the size of the membersUsers input a filter diameterNote:Maximum thickness restriction (and therefore enveloperestriction) is available only in sensitivity-based optimizationThe exact member size specified by the filter diameter isn’t guaranteedw w w .3d s .c o m | © D a s s a u l t S y s t èm e sDemold controlIf the topology obtained from the optimization is to be produced by casting, the formation of cavities and undercuts needs to be prevented by using demold controlDemold region: region where the demold control restriction is activeCollision check region: region where the removal of an element results in a hole or an undercut is checkedI.This region is same as the demold region by defaultII.This region should always contain at least the demold regionThe pull direction: the direction in which the two halves of the mold would be pulled in (as shown, bottom right)Center plane: central plane of the mold (as shown, bottom right)I.Can be specified or calculated automaticallyL3.20w w w .3d s .c o m | © D a s s a u l t S y s t èm e sGeometric Restrictions (5/7)Demold control (cont’d)The stamping option enforces the condition that if one element is removed from the structure, all others in the ± pull direction are also removedIn the gear example, a stamping constraint was used to ensure that only through holes are formed.Forging is a special case of casting. The forging die needs to be pulled in only one direction.The forging option creates a fictitious central plane internally on the back plane (shown below) so that pulling takes place in only one directionL3.21w w w .3d s .c o m | © D a s s a u l t S y s t èm e sGeometric Restrictions (6/7)SymmetryTopology optimization of symmetric loaded components usually leads to a symmetric designIn case we want a symmetric design but the loading isn’t symmetric, it is necessary to enforce symmetryPlane symmetryRotational symmetryCyclic symmetryPoint symmetryL3.22w w w .3d s .c o m | © D a s s a u l t S y s t èm e sGeometric Restrictions (7/7)It is possible to overconstrain the optimization.Care must be taken when specifying combinations of geometric restrictions.Examples:Planar symmetry can be combined with a pull direction if the pull direction is perpendicular or parallel to the symmetry plane.Rotation symmetry and the definition of a pull direction: this combination is possible if the pull direction is parallel to the axis of rotation.Two reflection symmetries can be combined if the planes are perpendicular.In general, begin the optimization study without geometric restrictions. Add them into the model one by one.L3.23w w w .3d s .c o m | © D a s s a u l t S y s t èm e sStop ConditionsThe optimization may be stopped before convergence is achieved if the stop conditions are achievedStop conditions can be constructed on displacements and stressesStop conditions are only supported in shape optimizationL3.24w w w .3d s .c o m | © D a s s a u l t S y s t èm e sPostprocessing (1/10)The relative densities of the elements in the optimization region are available in the field output variable MAT_PROP_NORMALIZEDw w w .3d s .c o m | © D a s s a u l t S y s t èm e sIn order to access the field output showing the relative densities of elements, switch to the step named ATOM OPTIMIZATIONFrom the main menu bar, select Results →Step/FrameSelect ATOM OPTIMIZATION as the step to visualizePlot contours of MAT_PROP_NORMALIZEDNote: Only the undeformed shape will be plotted. If the deformed shape is desired, switch back to Step-1_Optimization (or as named in your model)L3.26w w w .3d s .c o m | © D a s s a u l t S y s t èm e sPostprocessing (3/10)IsosurfacesThe soft elements can be visualized as voids using the Opt_surface cut in the View Cut ManagerRelative densities of the elements are centroidal quantities that are extrapolated and averaged at the nodes in order to obtain field outputAn isosurface is created that separates the soft elements from the hard elementsw w w .3d s .c o m | © D a s s a u l t S y s t èm e sWhat went wrong here?Can we tell by looking at stress or displacement plots?Iso value = 0.9 Iso value = 0.3L3.28w w w .3d s .c o m | © D a s s a u l t S y s t èm e sPostprocessing (5/10)Iso value = 0.9 Iso value = 0.3Note: Always plot MAT_PROP_NORMALIZED as field output and ensure that the isosurface is not cutting through fully dense elementsw w w .3d s .c o m | © D a s s a u l t S y s t èm e sBelow, isosurfaces are generated on element output (MAT_PROP_NORMALIZED) that is averaged at nodes with the averaging threshold at 100%Iso value = 0.9Iso value = 0.3L3.30w w w .3d s .c o m | © D a s s a u l t S y s t èm e sPostprocessing (7/10)ExtractionExtraction is a process of obtaining a surface mesh (STL format or its equivalent in an Abaqus input file) from a topology optimization resultOnce the isosurface is identified, new interior edges and surfaces are identified.Nodes are created on interior faces and a triangular mesh is created on the portion of the model to be retained.SmoothingThe isosurface provides first-order smoothing of a topology optimization resultDuring extraction the nodes on the interior surfaces are moved to achieve additional smoothing of the isosurfacew w w .3d s .c o m | © D a s s a u l t S y s t èm e sExtraction (cont’d)Reduction is the process of reducing the number of triangles in the STL representationThis is useful when converting a large STL file to a SAT file which can be imported and meshed in Abaqus for further analysisNote: you will need to use other DS tools such as SOLIDWORKS or CATIA for this conversionL3.32w w w .3d s .c o m | © D a s s a u l t S y s t èm e sPostprocessing (9/10)Optimization reportEnsure that the optimization constraints have been satisfied within toleranceOptimization_report.csv is created in the working directoryITERATION OBJECTIVE-1 OBJ_FUNC_DRESP:COMPLIANCE OBJ_FUNC_TERM:COMPLIANCE OPT-CONSTRAINT-1:EQ:VOL Norm-Values: 0.6456477 0.6456477 0.6456477 0.8000001 0 0.6456477 0.6456477 0.6456477 1 1 0.6497207 0.6497207 0.6497207 0.948712 2 0.6501995 0.6501995 0.6501995 0.9437472 3 0.6512569 0.6512569 0.6512569 0.93827784 0.6520502 0.6520502 0.6520502 0.9331822 0.6916615 0.6916615 0.6916615 0.831561823 0.6954725 0.6954725 0.6954725 0.8268944 24 0.7028578 0.7028578 0.7028578 0.8217635 25 0.8512989 0.8512989 0.8512989 0.8169149 26 0.7232164 0.7232164 0.7232164 0.8110763 27 0.7404507 0.7404507 0.7404507 0.8057563 28 0.7356095 0.7356095 0.7356095 0.8024307w w w .3d s .c o m | © D a s s a u l t S y s t èm e sHistory outputOptimization_report.csv should not be accessed while the optimization is running.Use the history output variables in Abaqus/CAE to monitor constraints and objectivesL3.34w w w .3d s .c o m | © D a s s a u l t S y s t èm e s1.In this workshop you will:a.become familiar with setting up, submitting and postprocessing a topology optimization problem with astamping geometric restrictionWorkshop 2a: Topology Optimization of a Cantilever Beam With Stamping Geometric RestrictionsL3.35w w w .3d s .c o m | © D a s s a u l t S y s t èm e s1.In this workshop you will:a.further explore demold control geometric restrictions, specifically with the central plane technique whichensures that the final design proposal is moldableWorkshop 2b: Topology Optimization of a Cantilever Beam With Demold Control Using the Central Plane Technique30 minutesL3.36w w w .3d s .c o m | © D a s s a u l t S y s t èm e s1.In this workshop you will:a.explore various symmetry restrictions available in the topology optimization modulee symmetry restrictions to create specific patterns in the design area as required for ease ofmanufacturing a particular componentWorkshop 2c: Topology Optimization of a Cantilever Beam With Symmetry Geometric Restrictions。
基于ABAQUS的多载荷工况结构拓扑优化设计研究
Ｖ０ １ ． ２ ８ ＮＯ ． ２ Ｊ ｕ ｎ ． ２ ０ １ ５
基于 Ａ Ｂ ＡＱ ＵＳ的 多载荷 工况结构
拓 扑优 化 设 计 研 究
贺志峰 ，荣见 华 １ ， ２ ７张利 安 ，廖银玲
（ １ ． 长沙理工大学 汽车与机械 工程学 院， 长沙 ４ １ ０ ０ ０ ４ ；
２ ． Ｋｅ ｙ Ｌ ａ ｂ ｏ ｒ ａ ｔ ｏ ｒ ｙ ｏ ｆ Ｌｉ ｇ ｈ ｔ ｗｅ ｉ ｇ ｈ ｔ ａ ｎ ｄ Ｒｅ ｌ ｉ ａ ｂ ｉ ｌ ｉ ｔ ｙ Ｔ ｅ ｃ ｈ ｎｏ ｌ ｏ ｇ ｙ ｆ ｏ ｒ Ｅ ｎ ｇ ｉ ｎ ｅ ｅ ｒ ｉ ｎ ｇ Ｖ ｅ ｈ ｉ ｃ ｌ ｅ Ｃｏ ｌ ｌ ｅ ｇ ｅ ｏ ｆ Ｈｕ ｎ ａ ｎ Ｐ ｒ ｏ ｖ ｉ ｎ ｃ ｅ ， Ｃｈ ａ ｎ ｇ ｓ ｈ ａ Ｕｎ ｉ ｖ ｅ ｒ ｓ ｉ ｔ ｙ ｏ ｆ Ｓ ｃ ｉ ｅ ｎ ｃ ｅ ａ ｎ ｄ Ｔ ｅ ｃ ｈ ｎ ｏ ｌ ｏ ｇ ｙ ， Ｃｈ ａ ｎ ｇ ｓ ｈ ａ ４ １ｃ ｈ ｏ ｏ ｌ ｏ ｆ Ｆ ｏ ｒ ｅ ｉ ｇ ｎ Ｌａ ｎ ｇ ｕ ａ ｇ ｅ ｓ ， Ｃｈ ａ ｎ ｇ ｓ ｈ ａ Ｕｎ ｉ ｖ ｅ ｒ ｓ ｉ ｔ ｙ ｏ ｆ Ｓ ｃ ｉ ｅ ｎ ｃ ｅ
第２ ８卷 第 ２期
２ ０ １ ５年 ６月
湖南理 １ ： 学院学报（ 自然科学版）
Ｊ ｏ ｕ ｒ ｎ ａ ｌ ｏ ｆ Ｈ ｕ ｎ ａ ｎ Ｉ ｎ ｓ ｔ ｉ ｔ ｕ ｔ ｅ ｏ ｆ Ｓ ｃ ｉ ｅ ｎ ｃ ｅ ａ ｎ ｄ Ｔ ｅ ｃ ｈ ｎ ｏ ｌ ｏ ｇ ｙ（ Ｎａ ｕｒ ｔ ａ ｌ Ｓ ｃ ｉ ｅ ｎ ｃ ｅ ｓ ）
关 键 词 ：多工 况 ；柔 顺度 ； 拓 扑优 化 ； 体 积 约 束：导 重 法 中图分类号： ［ ３ ４ ６ ２ 文 献标 识码 ： Ａ 文章编号： １ ６ ７ ２ ． ５ ２ ９ ８ （ ２ ０ １ ５ ） ０ ２ ． ０ ０ ５ ６ — ０ ８
Abaqus中Topology和Shape优化指南
Abaqus中Topology和Shape优化指南目录1. 优化模块界面......................................................................................................- 1 -2. 专业术语..............................................................................................................- 1 -3.定义拓扑优化Task(general optimization和condition-based optimization).......- 2 -3.1 General Optimization 参数设置.................................................................- 3 -3.1.1 Basic选项参数..................................................................................- 3 -3.1.2 Density选项参数..............................................................................- 4 -3.1.3 Perturbation选项参数.......................................................................- 5 -3.1.4 Advanced选项参数...........................................................................- 5 -3.2 Condition-based topology Optimization 参数设置....................................- 6 -3.2.1 Basic选项参数..................................................................................- 7 -3.2.2 Advanced选项参数...........................................................................- 7 -4 定义Shape Optimization Task方法....................................................................- 8 -4.1 Basic选项参数............................................................................................- 8 -4.2 Mesh Smoothing Quality选项参数............................................................- 9 -4.3 Mesh Smoothing Quality选项参数..........................................................- 11 -5 定义design response变量方法.........................................................................- 13 -5.1 单个design response定义方法...............................................................- 14 -5.2 combined design response定义方法........................................................- 15 -5.3 design response使用注意事项.................................................................- 17 -5.3.1 定义design response的操作.........................................................- 17 -5.3.2 condition-based topology optimization的design response............- 18 -5.3.3 general topology optimization的design response..........................- 18 -5.3.4 design response for shape optimization...........................................- 21 -6 定义objective function方法..............................................................................- 22 -6.1 目标函数定义...........................................................................................- 23 -6.2 目标函数的运算.......................................................................................- 23 -6.2.1 min运算..........................................................................................- 23 -6.2.2 max运算..........................................................................................- 24 -6.2.3 minimizing the maximum design response......................................- 24 -7 定义Constraints方法........................................................................................- 24 -8 定义Geometric restrictions方法.......................................................................- 25 -8.1 Defining a frozen area................................................................................- 26 -8.2 Specifying minimum and maximum member size....................................- 26 -8.3 maintaining a moldable structure(可拔模结构)........................................- 27 -8.4 maintaining a stampable structure(冲压成型结构)...................................- 28 -8.5 Specifying a symmetric structure...............................................................- 29 -8.6 Applying additional restrictions during a shape optimization...................- 31 -8.7 Combining geometric constraints..............................................................- 31 -9 定义Stop conditions方法..................................................................................- 32 -9.1 Global stop conditions...............................................................................- 32 -9.2 Local stop conditions.................................................................................- 33 -10 Abaqus优化模块支持.......................................................................................- 34 -10.1 Support for analysis types........................................................................- 34 -10.2 Support for geometric nonlinearities.......................................................- 34 -10.3 Support for multiple load cases................................................................- 34 -10.4 Support for acceleration loading..............................................................- 35 -10.5 Support for contact during the optimization............................................- 35 -10.6 Restrictions on an Abaqus model used for topology optimization..........- 35 -10.7 Restrictions on an Abaqus model used for shape optimization...............- 35 -10.8 Support materials in the design area........................................................- 36 -10.8.1 Materials supported by condition-based topology optimization....- 36 -10.8.2 Materials supported by general topology optimization.................- 36 -10.8.3 Material support in shape optimization..........................................- 37 -10.9 支持的单元类型.....................................................................................- 37 -10.9.1 支持的二维实体单元...................................................................- 37 -10.9.2 支持的三维实体单元...................................................................- 38 -10.9.3 支持的对称实体单元...................................................................- 39 -10.9.4 额外支持的单元...........................................................................- 39 -11. Job模块中优化过程的设置............................................................................- 40 -11.1 优化过程的理解.....................................................................................- 40 -11.2 Optimization Process Manager................................................................- 42 -12 拓扑优化理论...................................................................................................- 42 -12.1 General Topology Optimization理论......................................................- 43 -12.1．1 SIMP(Solid Isotropic Material With Penalization Method).......- 43 -12.1.2 RAMP(Rational Approximation of Material Properties)...............- 43 -12.1.3 Gradient-based methods.................................................................- 43 -12.2 General与Condition-based Topology Optimization对比.....................- 44 -13 拓扑优化结果后处理.......................................................................................- 44 -13.1 单元相对密度值.....................................................................................- 44 -13.2 Isosurfaces................................................................................................- 45 -13.3 Extraction.................................................................................................- 47 -14 形貌优化后处理...............................................................................................- 48 -14.1 向量DISP_OPT.....................................................................................- 48 -14.2 场变量DISP_OPT_V AL........................................................................- 48 -14.3 正常分析步中的优化迭代过程中的应力和位移等场变量.................- 49 -14.4 Extracting a surface mesh........................................................................- 49 -15 几何非线性的开与闭对拓扑优化结果的影响...............................................- 50 -16. 形貌优化中的几何约束..................................................................................- 53 -16.1 Demold control(脱模控制)......................................................................- 53 -16.2 Turn control(车床加工控制)...................................................................- 55 -16.3 Drill control(钻孔控制)...........................................................................- 56 -16.4 Planar symmetry(平面对称约束)............................................................- 57 -16.5 Stamp control(锻造控制)........................................................................- 58 -16.6 Growth约束............................................................................................- 58 -16.7 Design direction约束..............................................................................- 59 -16.8 Penetration check(穿越检查)..................................................................- 60 -1. 优化模块界面2. 专业术语① optimization task：对优化任务的一个定义，即定义一个优化Job；② design responses：一个设计响应可以直接从输出数据库中提取，例如模型的体积，另外，对于拓扑优化模块的设计响应不仅可以直接从输出数据库中提取，而且可以计算设计响应，如模型的应变能；③ objective function：目标函数指的是设计响应的函数值或者是一组设计响应的组合，如整个模型的应变能的最小值；④ constraints：约束是一个设计响应的函数值，但不能是多个设计响应组合的函数值；⑤ geometric restriction：A geometric restriction places restrictions on the changes that the Abaqus Topology Optimization Module can make to the topology of the model. Geometrical restrictions include frozen regions from which material cannot be removed and manufacturing constraints, such as restrictions on cavities and undercuts, that would prevent the optimized model from being removed from a mold⑥ stop condition：停止条件是对优化计算收敛的一个指示器，如当在一个指定数量的迭代后一个优化被认为完成了；global stop condition定义了优化迭代的最大数目，local stop condition指定了优化迭代达到所需最小或最大数目；⑦ optimization processes：需要在job模块中创建；⑧ design varible：对于topo优化，优化区域的每个单元的密度即为设计变量；而shape优化，优化区域表面单元的节点的位移即为设计变量；⑨ design cycle：优化过程中的每个迭代成为design cycle；【提示】：I、优化算法总是在满足了约束的基础上才开始最大或最小化目标函数；II、一个优化任务中最多只能包含一个体积约束；【附英文原版】3.定义拓扑优化Task(general optimization和condition-based optimization)3.1 General Optimization 参数设置 3.1.1 Basic选项参数3.1.2 Density选项参数3.1.3 Perturbation选项参数3.1.4 Advanced选项参数在优化计算过程中，拓扑优化模块会自动给优化区域分配一个指定的质量来满足约束和目标函数，在优化结束时，整个优化区域的结构包含了硬单元(hard elements)和软单元(soft elements)，其中软单元对结构的刚度没有任何影响，但是影响着结构的自由度，因此会影响优化计算的速度。
基于ABAQUS的位移约束结构拓扑优化方法研究
第二章 基于有限元分析软件 Abaqus 的二次开发 .......................................... 7
2.1 引言.............................................................................................................................. 7 2.2 Abaqus 软件总体介绍.................................................................................................. 7
Abaqus作习题讲解3
话框，输入边界条件名称 BC-bottom，分析步选择 Step-1,边界条件类型 选择 Mechanianl：Displacement/Rotation，单击 Continue 按钮，选择 Y 坐标为 0 的边，即筒体底部的横边，单击提示区中的 Done 按钮，进入 Edit Boundary Condition 对话框，选中 U2 前面的复选框，并接受其默认 值 0，其他均为默认单击 Ok 完成对筒体底部边界条件的施加。 12.单击工具箱中 （Create Boundary Condition） ， 在弹出的 Create
Manager） ，点击弹出的对话 框下部的 Create，在新的对 话框 Create Job 中定义作业 名称为 Pressure-vessel， 单击 Continue， 进入 Edit Job 对话 框，输入作业描述 Description： Static analysis of a pressure vessel，其他为默 认设置，单击 OK，在 Job Manager 中出现作业 Pressure-vessel，单击对话框 右部的 Write Input 可以输出 与作业同名的.inp 文件，单 击 Submit 提交作业， 进行计 算；单击 Monitor 弹出 Link Monitors 对话框， 可以对作业运行 情况进行监视。 18.执行 PlotContoursOn Both Shapes， 显示模型变形前后的 云图。 19.执行 OpinionsCommon， 在弹出的 Common Plot Opinions 对 话框，切换到 Basic 选项卡，选中 Deformation Scale Factor 栏中，默 认的时 Auto-compute， 即程序自动 选择变形放大系数，本例默认为放大 385.206 倍的结果。选择 Uniform 前面的单选按钮，在出现的 Value 后面自定义均匀放大系数为 150，单击 Apply 按钮即可；也可通过 Nonuniform 分别定义 X、Y、Z 方向的放 大系数。 20.执行 ReportField Output，在弹出的 Report Field Output 对话框输出变量 Output Variable 栏中 Position 下选择 Unique Nodal 然后在下拉列表中选择 U: Spatial displacement 下面的 U1，单击 Apply 按钮，
最新Abaqus6.13拓扑优化atom-book超全学习资料-11
Workshop 3Shape Optimization of a Plate with a Hole© Dassault Systèmes, 2012Topology and Shape Optimization in AbaqusIntroductionIn this workshop you will become familiar with the process of setting up, submitting, monitoring and postprocessing a shape optimization problem using Abaqus/CAE.A finite element model of a plate with a hole is provided (see Figure W3–1). You will import this model into Abaqus/CAE and then perform a shape optimization on it.Preliminaries1. Enter the working directory for this workshop:../atom/plate2. Start a new session of Abaqus/CAE using the following command:abaqus caewhere abaqus is the command used to run Abaqus.3. In the Start Session dialog box, underneath Create Model Database , click With Standard/Explicit Model .4. From the main menu bar, select File →Run Script .5. In the Run Script dialog box, select ws_atom_plate.py and click OK .6. A model named hole-plate-quarter will be created.Figure W3– 1 Quarter symmetry model of a plate with a hole.171Examining the finite element modelIn this finite element model we are interested in the static response of a plate with a hole tomultiple load cases. Taking advantage of symmetry, we construct only a quarter symmetrymodel. The model consists of the following:1.Parts: The model consists of a single part named PART–1.2.Mesh: The plate is meshed with CPS4 elements.3.Materials: Material properties of steel have been assigned to the plate.4.Steps: Two steps, one for each load case are specified. Nonlinear geometric effects areconsidered.5.Loads: Two loads of magnitude 200 and 100 are specified in the X- and Y-directions, inSteps 1 and 2, respectively. The loads are not propagated from one step to another; thus,they represent independent load cases.6.Boundary conditions: Symmetry boundary conditions are applied to appropriate edges.Before proceeding with the optimization analysis, examine the finite element model.To examine the finite element model:1. In the Model Tree, click to expand the model hole–plate–quarter as shown in FigureW3–2.2.Expand the following containers: Parts, Materials, Assembly, Steps, Loads and BCs.3.Right-click on each of the items in the containers and choose Edit from the menu thatappears.4.Click Cancel in order to avoid making changes to the analysis.Figure W3–2 Model Tree for quarter plate model.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 172© Dassault Systèmes, 2012 Topology and Shape Optimization in AbaqusCreating and submitting an analysis job Once you have examined the model, you will submit an analysis job to ensure that the model runs without error and produces meaningful results.To create and submit an analysis job:1. Switch to the Job module.2. From the main menu bar, select Job →Manager .3. From the buttons on the bottom of the Job Manager , click Create to create a job.4. In the Create Job dialog box that appears:a. Name the job hole –plate –quarter and select the model hole –plate –quarteras the source; click Continue .5. In the Edit Job dialog box that appears, click OK to accept all defaults.6. From the buttons on the right side of the Job Manager , click Submit to submit your job for analysis. The status field will show Running . When the job completes successfully, the Status field will change to Completed as shown in Figure W3–3.Figure W3–3 Job Manager.7. In the Job Manager , click Results to postprocess the analysis results.8. In the Visualization toolbox, plot the Mises stress distribution for each of the load cases as shown in Figure W3–4.Figure W3–4 Contour plots of Mises stress.9. Return to the Job module and dismiss the Job Manager.173Defining a shape optimizationIn shape optimization, typically the goal is to homogenize the stress on the surface of acomponent by adjusting the surface nodes. Thus, the minimization is achieved byhomogenization. Shape optimization is not limited to minimizing stresses; it may be extended to plastic strains, natural frequencies, etc.In this workshop you will homogenize the Mises stress on the periphery of a hole in a plate. You will consider two load cases simultaneously, ensuring that the plate is equally stressed in bothload cases and therefore equally likely to fail (or survive) either load case.The workflow for shape optimization is exactly the same as that for topology optimization.Creating an optimization task:1.Switch to the Optimization module (Figure W3–5).Figure W3–5 Switching to the Optimization module.2.From the main menu bar, select Task→Create.3.In the Create Optimization Task dialog box that appears: the optimization task optimize-shape.b.Select Shape optimization as the type and click Continue.c.You will be prompted to select an optimization region.d.Select the set DESIGN_NODES, as shown in Figure W3–6.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 174Figure W3–6 Selecting the optimization region.In shape optimization the design variables are the positions of the surface nodes; thus, the optimization region is always a set of nodes.Next, you will select and configure the optimization algorithm.In the Edit Optimization Task dialog box (Figure W3–7):1.In the Basic tabbed page, select Freeze boundary condition regions.2.Select Specify smoothing region, and select the whole model.3.Select Fix all as the Number of node layers adjoining the task region to remain free.4.In the Mesh Smoothing Quality tabbed page, set the Target mesh quality to Medium.5.Accept all defaults in the Advanced tabbed page.6.Click OK.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus175© Dassault Systèmes, 2012 Topology and Shape Optimization in AbaqusFigure W3–7 Optimization task editor.You have now configured the shape optimization algorithm. Next, you will define design responses.Creating design responses:1. From the main menu bar, select Design Response →Create .2. In the Create Design Response dialog box that appears:a. Name the design response Mises –Stress –step1.b. Accept Single-term as the type, and click Continue .c. You will be prompted to select the design response region type.d. In the prompt area, select Whole Model as the design response region.3. In the Edit Design Response dialog box that appears (Figure W3–8):a. In the Variable tabbed page, select Stress and Mises hypothesis .b. Note that the field Operator on values in region is set to Maximum value bydefault.c. Switch to the Steps tabbed page, select Specify and click to add a step.d. Select Step-1 from the Step and Load Case drop-down list.e. Click OKto create the design response.176© Dassault Systèmes, 2012 Topology and Shape Optimization in AbaqusFigure W3–8 Design response for the strain energy.4. Similarly, define a design response for Step –2.a. Name the design response Mises –Stress –step2.5. Similarly, define a design response for the volume (see Figure W3–9).a. Name the design response Volume .Figure W3–9 Design response for the volume.177© Dassault Systèmes, 2012 Topology and Shape Optimization in AbaqusNext, you will create an objective function. Creating an objective function:1. From the main menu bar, select Objective Function→Create .2. In the Create Objective Function dialog box that appears:a. Name the objective function optimize-shape and click Continue .3. In the Edit Objective Function dialog box that appears (Figure W3–10):a. Click to add all design responses eligible to participate in an objectivefunction.b. Leave the Reference Target field at the Default setting.c. Change the Target to Minimize the maximum design response values .d. Click OK .Figure W3–10 Objective function optimize-shape .Next, you will create a volume constraint.The purpose of creating volume constraints in a shape optimization is to ensure that the overall volume of the component remains the same. In most cases it is undesirable to simply addmaterial to reduce stress. Rather, material is redistributed to minimize stress. Volume constraints ensure that either no material is added or very little material is added as a result of the shape optimization.Creating a constraint:1. From the main menu bar, select Constraint →Creat e .2. In the Create Constraint dialog box that appears:a. Name the constraint volume-constraint and click Continue .3. In the Edit Optimization Constraint dialog that appears (Figure W3–11):a. Click the drop-down menu for the Design Response , and select Volume .b. Toggle on A fraction of the initial value and enter 1.c. Click OKto create the optimization constraint for volume.178Figure W3–11 Optimization constraint on volume.The setup of the optimization task is now complete. Next, you will create and submit an optimization process.Creating an optimization process:1.Switch to the Job module.2.From the main menu bar, select Optimization→Create.3.In the Edit Optimization Process dialog box that appears (Figure W3–12): the optimization process optimize-shape.b.In the Description field of the dialog box, enter shape optimization.c.Note the Maximum cycles field is set to 10 by default for shape optimization.d.Click OK.Figure W3–12 Edit optimization process.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus179Submitting an optimization process:1.From the main menu bar, select Optimization→Manager.2.From the buttons on the right side of the Optimization Process Manager, click Validateto validate the optimization process.a.When the validation process completes successfully, the Status field will changeto Check Completed.3.Click Submit in the Optimization Process Manager.4.Once the Status changes to Running,click Monitor if you wish to monitor the progressof the optimization process.Postprocessing shape optimization resultsYou may postprocess the solution when the optimization process is complete.Opening the Abaqus output database file:1.Click Results in the Optimization Process Manager.Note that the Abaqus output database file is stored in the folder named ATOM_POST. Allsolution folders generated by ATOM have the structure shown in Figure W3–13.The .odb file stored in the folder ATOM_POST contains the optimization results. Note thatthe history data available for optimization are also available inoptimization_report.csv. You may access this file after the optimization is completebut not during it. Abaqus will stop writing to the file if it is opened during the run. Thefolders SAVE.dat, SAVE.inp, etc. are archives of the Abaqus runs that were performed bythe optimizer. The file atom.out contains the output log from the optimizer.Figure W3–13 File structure from an optimization run.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 180Contour plotting the shape change:1.From the main menu bar, select Result→Step/Frame.a.From the Step/Frame dialog box, select the ATOM OPTIMIZATION step.b.Select Frame10 (or the highest iteration available to you) from the list ofavailable frames.c.Click OK to close the Step/Frame dialog box.d.In the Visualization toolbox, click and set the Deformation Scale Factor to1.e.In the Field Output toolbar:i. Set the Primary variable to DISP_OPT _VAL.ii.Set the Deformed variable to DISP_OPT.f.In the Visualization toolbox, click and hold .g.Select the last icon to plot contours on both the deformed and undeformedshapes.The contour plot of the deformed shape overlaid on the undeformed shape after 10iterations appears as shown in Figure W3–14. The figure shows the displacementsapplied by the optimizer (shape change) as a scalar. Growth is visualized in red whileshrinkage is visualized in blue. This plot provides an understanding of where themodel is shrinking and where it is growing. Recall that the volume was constrained toremain constant; thus, the growth and shrinkage balance each other. The plot alsoshows that the mesh in the interior moves as a result of the smoothing that wasapplied.Figure W3–14 Contour plot of DISP_OPT_VAL at 10 cycles.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus181Figure W3–15 shows the results after 150 iterations. As seen in the two figures, the difference in the peak values of DISP_OPT_VAL between the two jobs is not large. This implies that theshape optimization only made minor corrections to the shape between iterations 10 and 150.Figure W3–15 Contour plot of DISP_OPT_VAL at 150 cycles.While creating the objective function we had chosen to minimize the maximum design response values. The formulation finds the maximum objective function term and seeks to minimize itduring each design iteration. Given that the optimizer employs a large number of iterations, it is expected that the objective function terms will be more or less equal in magnitude at end of theoptimization. In this example, the stress due to the load in steps 1 and 2 is more or less equalafter the shape optimization. Thus, the plate is not more likely to fail in one load case versus the other.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 182Plot the Mises stress and compare the peak stress from each of the load cases.Plotting the Mises stress:1.From the main menu bar, select Result→Step/Frame.a.From the Step/Frame dialog box, select step Step-1_Optimization.b.Select Frame10 from the list of available frames.c.Click OK to close the Step/Frame dialog box.d.In the Visualization toolbox, click and set the Deformation Scale Factor to300.e.In the Field Output toolbar:i. Set the Primary variable to S (Int Pt) and select Mises as the component.ii.Set the Deformed variable to U.f.In the Visualization toolbox, click to plot contours on both the deformed andundeformed shapes.g.Repeat steps a-f for Step-2_Optimization.The results are shown in Figure W3–16 (a and b). Note the significant differencebetween the peak values of Mises stress after 10 iterations. This is a strong indicationthat the MIN_MAX formulation needs more iterations to achieve its goal.Figure W3–16 (c and d) shows the results from a solution that was allowed to run for150 iterations. The difference in the peak stresses is now significantly reduced.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus183a.Mises stress Step-1 at 10 cycles.b. Mises stress Step-2 at 10 cycles.c.Mises stress Step-1 at 150 cycles.d. Mises stress Step-2 at 150 cycles.Figure W3–16 Contour plots of Mises stress.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 184Plot the history output for variables OBJ_FUNCTION_DRESP: MISES-STRESS-STEP1 andOBJ_FUNCTION_DRESP:MISES-STRESS-STEP2. Compare the magnitudes, as shown inFigure W3–17.To plot history output:1.From the main menu bar, select Result→History Output.2.From the History Output dialog box that appears, select the ATOM OptimizationHistory variables.3.Click Plot to plot the selected variables.4.Click Dismiss to dismiss the dialog box.The red arrow in Figure W3–17 indicates the results obtained in 10 iterations. Clearly 10iterations were not sufficient for the optimization process to converge.Figure W3–17 History plots.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus185Finally, it is important to clarify that the MIN_MAX formulation may result in the increase insome objective function terms as it operates on others, even though a minimization wasspecified. In Figure W3–17 we see that during the first 60 iterations the peak Mises stress forStep-1 reduces while the peak Mises stress for Step-2 increases. The increase in peak Misesstress for Step-2 is nothing more than an unavoidable side effect of the shape change that wasdriven by Step-1 (the Mises stress in Step-1 was greater during the first 60 iterations). Atapproximately the 60th iteration, Step-2 begins to dominate the shape change and the Mises stress for Step-2 begins to reduce. Fortunately, the subsequent shape changes do not adversely affectthe Mises stress in Step-1.Note: A script that creates the model described in these instructions is availablefor your convenience. Run this script if you encounter difficulties following theinstructions outlined here or if you wish to check your work. The script is named ws_atom_plate_answer.pyand is available using the Abaqus fetch utility.© Dassault Systèmes, 2012 Topology and Shape Optimization in Abaqus 186。
有限元基础教程Abaqus软件例题详解2
弹出的对话框中定义载荷名称为 Force-left， 分析 步选择定义类型步 Apply-PF，载荷类型选择 Mechanical：Concentrated force（集中力） ，单击 Continue，用鼠标在图 形区域选择右上角点， 单击鼠标中键，引入 Edit Load 对话框，在 CF1、CF2、CF3 后面分 别输入 3000、0、0，,， 单击 OK 完成在点 3 上 集中力的施加。 17.类似上步操 作， 选择均布荷载 Line force 对水平梁施加竖 直向下大小为 4167N 的集中力。 18.网格的划分： 在环境栏 Module 后面选择 Mesh， 进入后 Object 选 择 Part 选项。在工具箱中单击 （Seed Edge：By
Number） ，在图形中框选整个模型，单击鼠标中键， 在提示区中 Number of elements along the edges 后 面输入每条边划线单元的数目为 1。按下 Enter 键， 单击鼠标中键完成种子设置。 19.在工具箱中单击 （Assign Element Type） ，
用鼠标在图形区域框选整个模型，单击鼠标中键， 在弹出的 Element Type 对话框中选择单元 B31，单 击 Ok 完成单元类型的选择。 20.在工具箱中单击 （Mash Part） ，单击提
称 verleft，Modeling Space 栏选择 3D 。Type 栏选择 Deformable，Base Feature 栏 选择 Wire:Planar，Approximate Size 输入 400，然后单击 Continue,进入草图环境。 3.单击 （Create Lines） ，依次输入点坐标值“0,0” “0，96” “144,96” “144,0”
拓扑优化算法及其实现111详解
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n T e p T min C U F ( ) ue k o ue e 1 KU F s.t. V ( ) V0 0 1 min
密度变量的引入： 在工程中，材料的刚度线性依赖材 料的密度，即刚度大的材料，密度也大。 比如，钢的密度比铝的密度大，因此钢 的刚度比铝的刚度大。按照这个朴素的 逻辑，就可用单元的密度来代替材料的 有无，如下式 Ke p Ke
拓扑优化建模方法
变密度法
SIMP（ Solid Isotropic Microstructures with Penalization ） (固体各向同性惩罚函数法）
RAMP（ Rational Approximation of Material Properties ） （材料属性的理性近似模型）
T C U T F ( e ) pue k e ue e 1
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优化结果：各单元密度组成的矩阵——X >Imagesc(-x)
目的：消除棋盘格效应及网格依赖性 方法：1、高阶单元法（计算量大） 2、周长约束法（周长约束的上限值需要依靠经验来确定，因为局部 尺寸和周长边界间没有直接的关系。如果周长约束边界定得太紧，则可能 导致没有计算结果，如果定的太松又达不到预期的效果。因此约束边界很 难确定，这种情况在三维问题下特别明显） 3、局部梯度约束方法（局部斜率约束属于局部约束，可防止局部细 条的形成，从而降低结构拓扑பைடு நூலகம்几何复杂性，但优化结果难以满足全局最 佳，并且，这种方法在优化问题中引入了2N(二维)或3N(三维)个额外约束， 使计算效率大大降低） 4 、网格过滤法（网格过滤方法只需定义一个局部长度尺寸，相对 较为容易，在约束尺度下的结构变量都被过滤掉。网格过滤方法的优点是 不需要在优化问题中加入额外约束，且容易实施。缺点是过滤方法为一种 基于启发式求解规则的方法）
有限元基础教程Abaqus软件例题详解2
示区 OK to mesh the part 后面的 Yes 完成网格划分并保存模型。
21.提交分析作业： 在环境栏 Module 后面选择 Job， 进入该模块后，单击工具箱中的 （Job Manager） ，
点击弹出的对话框下部的 Create， 在新的对话框 Create Job 中定义作业名称为 link4，单击 Continue，进入 Edit Job 对话框， 输入作业描述 Description： Analysis of a four link mechanism，切换到 Memory 选项卡，设置用于输 入文件处理和 ABAQUS/Standard 分析时能够使用的内 存（据计算机配置情况而定，默认为 256MB） ，单击 OK，在 Job Manager 中出现 beam3，单击对话框右部 的 Write Input 可以输出与作业同名的输入文件，单击 Submit 提交作业，进行计算；单击 Monitor 弹出 Link Monitors 对话框，可以对作业运行情况进行监视。在 该对话框中可以显示作业提交的时间、运行状态、结 束时间、运行过程中出现的警告、错误信息、输出结 果等。 22.后期处理： 打开结果输出文件 link4.odb： 方式一： 在 Job Manager 对话框中单击 Results； 方式二： 进入 Visualization 模块的 Open 按钮，在弹出的 Open Datebase 对话框 中， ；方式三：在模型树中把 Model 切换到 Results 选 项，双击 Output Datebase，在弹出的对话框中点选 link4.odb。 显示节点和单元编号：OpinionsCommon，在弹 出的 Common Plot Opinions 对话框，切换到 Labels 选 项卡， 选中 Show element labels 和 Show node labels 并 选择字体颜色，单击 Ok 完成设置。 执行 PlotContoursOn both shapes，显示变形 前后的结构云图。 生成各个节点位移的结果报告：ReportField Output， 在弹出的 Report Field Output 对话框输出位置 Position 后面选择 Unique Nodal。输出选项中取消默认 的 S：Stress components，选择 U：Spatial displacement 下面的 U1、U2,；切换到 Setup 选项卡，设定输出文件 的名称为 link-nodal-U.rpt，取消下部 Column totals（列 汇总）选项，单击 Ok。在软件工作目录 temp 下找到该文件，选择记事本打开即可。 若输出位置 Position 选择 Integration Point（积分点） ，输出选项选择 S:Stress components 中的 S11，报 告文件名为 link-nodal-S.rpt，可得各单元应力值。 若输出位置 Position 选择 Unique Nodal，输出选项选择 RF:Reaction force 中的 RF1、RF2，报告文件名 为 link-nodal-RF.rpt，可得各节点处支反力的值。 王学兵 2012 年 3 月 21 日
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1） 应变能（结构刚度的度量值） 2） 特征频率 3） 内力和支反力 4） 重量和体积 5） 重心 6） 惯性矩。 可以应用其他相同约束变量到拓扑优化分析中。另外，拓扑优化同样可以考虑标准产品 制造过程。例如铸造和冲压。可以冻结指定区域、应用数量尺寸、对称性及耦合约束。拓扑 优化的例子在 ABAQUS Example Problems Manual 的 Section11.1.1 中。(本文的算例就是来自 于此)
ABAQUS 中 ATOM 模 块的拓扑优化功能
By 姜琛（BravoWa） HNU
QQ：490135416
ABAQUS 中 ATOM 模块的拓扑优化功能
从 Abaqus6.11 开始，ABAQUS/CAE 新增加了拓扑优化模块，简称 ATOM（Abaqus Topology Optimization Module），这标志着 Abaqus 开始从分析向设计进军。虽然 ABA 非线 性能力十分强大，CAE 的操作也比较人性化，但由于拓扑优化的需要，而转而采用 ANSYS 和 Hyperworks/Optistruct。ATOM 采用了专业拓扑优化软件 TOSCA 的核心，在 ABA 没有拓 扑优化模块的时候，该软件已经能通过像 FE-SAFE 那样，调用 odb 文件进行拓扑优化，但 是显然不如 ANSYS 等模块化的集成度高和操作便捷。如果将 ABA 强大非线性分析能力和 越来越完善的 ATOM 结合起来，非线性问题的拓扑优化难题应该可以得到很好的解决。
1.建立约束 couplingn, Name: Constraint-1;。如下图左选择 inp 中设置好的 set。 2.建立约束 couplingn, Name: Constraint-2;。如下图右选择 inp 中设置好的 set。
六 载荷 1 施加位移边界条件： inp 中已经施加，无需自己设定。 2 创建载荷：Name: Load-1,Step-1; Type: Concentrated force; Region: Set-CONTROLPT; Uniform, CF1=70000, CF2=-70000, CF3=0; 关闭 七 网格 inp 就是网格，略过。 八 ATOM（Module: Optimization）
设计变量（Design variables）：设计变量即优化设计中需要改变的参数。拓BAQUS/CAE 优化分析模块在其优化迭代过程中改变单 元密度并将其耦合到刚度矩阵之中。实际上，拓扑优化将模型中单元移除的方法是将单元的 质量和刚度充分变小从而使其不再参与整体结构响应。对于形状优化而言，设计变量是指设 计区域内表面节点位移。优化时，ABAQUS 或者将节点位置向外移动或者向内移动，抑或 不移动。在此过程中，约束会影响表面节点移动的多少及其方向。优化仅仅直接修改边缘处 的节点，而边缘内侧的节点位移通过边缘处节点插值得到。
二 性质 1 创建材料： 将材料命名，Name: Elasti_Material；弹性，E=210000Mpa，ν=0.3；关闭。 2 创建截面： Name: Solid_Section，Solid 实体，各向同性，选上材料名 Elasti_Material，关闭。
3 将截面的性质附加到部件上： 选中 Part: Part-1，将 Section: Solid_Section 赋给 Part- Part-1。 三 组装 创建计算实体，以 Part: Part-1，用 Independent 方式生成实体。 四 分析步 分析步在 inp 文件中已经建立，命名为 Step-1，Static,Linear perturbation,静态，线性摄动步， 几何非线性 OFF。 五 接触
1.创建优化任务（Optimization Task）。从 ATOM 开始，多加入一些图； Creat：Name: controlArmTopologyOptimization; Type: Topology optimization; Continue。 然后弹出选择框，选择 Set-Design Element。 在 新 弹 出 的 （ Optimization Task Manager ） 中 ， 选 择 Advanced – algorithm: Stiffness_Optimization. 关闭。
3） 弹性、塑性、全应变和应变能密度 形状优化只能应用体积约束，另外，可以使用一定数量的制造几何限制条件使提出的设计能 够继续铸造或者冲压过程。也可以冻结某特定区域、应用数量尺寸、对称性及耦合限制等。
ATOM 拓扑优化算例
本算例直接采用 ABAQUS Example Problems Manual 的 Section11.1.1 中的例子，相应的 inp 和 py 文件可在 x（x 为 ABAQUS 的安装盘）:\simulia\Abaqus\6.11-1\samples\job_archive\ samples.zip 中找到，分别为 control_arm.inp 和 control_arm_topology_optimization.py。当然这 样直接使用脚本，对我们熟悉 ATOM 的操作不是很有帮助，将 py 文件逆向分析一下找到对 应的 CAE 操作。
约束（Constraints）: 约束亦是从设计变量中萃取的一定范围的数值。然而，一个约束 不能由设计响应集合而来。约束限定了设计响应 ，比如可以指定体积必须降低 45%或者某 个区域的位移不能超过 1mm。约束也可以指定制造跟优化无关的制造或者几何约束，比如 轴承面的直径不能改变。
停止条件（Stop conditions）: 全局停止条件决定了优化的最大迭代次数。 局部停止条 件在局部最大/最小达成之后指定优化应该停止。
2. 术语（Terminology）
设计区域（Design area）: 设计区域即模型需要优化的区域。这个区域可以是整个模型， 也可以是模型的一部分或者数部分。一定的边界条件、载荷及人为约束下，拓扑优化通过增 加/删除区域中单元的材料达到最优化设计，而形状优化通过移动区域内节点来达到优化的 目的。
ATOM 中拓扑优化技术概述
1. 结构优化：概述
ABAQUS 结构优化是一个帮助用户精细化设计的迭代模块。结构优化设计能够使得结 构组件轻量化，并满足刚度和耐久性要求。ABAQUS 提供了两种优化方法——拓扑优化和 形状优化。拓扑优化（Topology optimization）通过分析过程中不断修改最初模型中指定优 化区域的单元材料性质，有效地从分析的模型中移走/增加单元而获得最优的设计目标。形 状优化（Shape optimization）则是在分析中对指定的优化区域不断移动表面节点从而达到减 小局部应力集中的优化目标。拓扑优化和形状优化均遵从一系列优化目标和约束。
3. ABAQUS/CAE 结构优化步骤
下面的步骤需要合并到 ABAQUS/CAE 模型结构优化设计中： 1） 创建需要优化的 ABAQUS 模型。 2） 创建一个优化任务。 3） 创建设计响应。 4） 利用设计响应创建目标函数和约束。 5） 创建优化进程，提交分析。
基于优化任务的定义及优化程序，ABAQUS/CAE 拓扑优化模块进行迭代运算： 1） 准备设计变量（单元密度或者表面节点位置）。 2） 更新 ABAQUS 有限元模型。 3） 执行 ABAQUS/Standard 分析。
本文目的即熟悉 ATOM 的 CAE 中的操作。首先将 ABAQUS ANALYSIS USER MANUAL 的 Topology Optimization 章节的概论部分翻译成中文，权当本文的概述（取自 SIMWE 的 Songyer 的翻译）。然后将官方提供的算例，做成 Step-by-step 以便操作。也算对本人近几天 对 ATOM 学习的总结。
设计响应（Design responses）: 优化分析的输入量称之为设计响应。设计响应可以直接 从 ABAQUS 的结果输出文件.odb 中读取，比如刚度、应力、特征频率及位移等。或者 ABAQUS 从结果文件中计算得到模型的设计响应，例如质心、重量、相对位移等。一个设计响应与模 型紧密相关，然而，设计响应存在一定的范围，例如区域内的最大应力或者模型体积。另外， 设计响应也与特点的分析步和载荷状况有关。
2. 创建设计响应（Design response） 设计响应 1（Design Response 1）
Create Design Response – Name: strainEnergy; Type: Single-term; Continue. Edit Design Response – Region: Whole Model; Variable: Strain Energy; Operator: Sum of values. OK。 设计响应 2（Design Response 2） Create Design Response – Name: volume; Type: Single-term; Continue. Edit Design Response – Region: Whole Model; Variable: Volume; Operator: Sum of values. OK。
6. 形状优化
形状优化采用了跟基于刚度的拓扑优化算法类似的算法。形状优化一般是对表面节点进 行较小的调整以减小局部应力集中。形状优化用于产品外形需要微调的情况。
形状优化试图重置既定区域的表面节点位置直到此区域的应力成为常数（应力均匀）。 下图是连杆形状优化以减小局部应力集中的例子：