ABAQUS拓扑优化例题计算指导
基于 ABAQUS 的多载荷工况结构拓扑优化设计研究
基于 ABAQUS 的多载荷工况结构拓扑优化设计研究贺志峰;荣见华;张利安;廖银玲【摘要】如何高效、准确的对拓扑优化问题进行求解是结构优化领域发展的重点。
本文提出了一种以体积为约束的多载荷工况下柔顺度最小的优化方法。
在优化迭代过程中，为使优化拓扑有较好的0-1分布特征，确保优化迭代中的结构非奇异及快速收敛，采用改变体积约束限和调整设计空间策略。
基于导重法给出了结构拓扑求解算法，给出的算例证明该方法不仅迭代次数少而且求解效率高，具有清晰的0-1分布。
%Efficiently and accurately solving the problem of structural topological optimization is a key point for the development of the field of structural optimization. A new structural topological optimization methodis proposed to obtain the optimum topology with the minimum weighting compliance under the multi-load cases and with volume constraints. In the optimum iterative process, the evolutionary optimization way and space designing adjust strategy with variable volume constraints are adopted to make the optimized topology be of a better 0/1 distribution topology, be non-singular and Fast convergence. Finally, based on the guide-weight method, a structural topology algorithm is provided to show that proposed method has the advantage of less number of iterations, high solving efficiency and easily getting the clear distribution of 0/1.【期刊名称】《湖南理工学院学报（自然科学版）》【年(卷),期】2015(000)002【总页数】8页(P56-63)【关键词】多工况;柔顺度;拓扑优化;体积约束;导重法【作者】贺志峰;荣见华;张利安;廖银玲【作者单位】长沙理工大学汽车与机械工程学院，长沙 410004; 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室，长沙 410004;长沙理工大学汽车与机械工程学院，长沙 410004; 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室，长沙 410004;长沙理工大学汽车与机械工程学院，长沙410004; 长沙理工大学工程车辆轻量化与可靠性技术湖南省高校重点实验室，长沙 410004;长沙理工大学外国语学院，长沙 410004【正文语种】中文【中图分类】U462随着科学技术的不断向前推进, 结构拓扑优化方法也在不断发展. 目前应用比较广泛的方法有: 变密度法、均匀化法和水平集法等. 如何寻找到一种快速、高效的求解方法, 一直以来都是结构优化研究的难点和重点. 传统的优化求解方法具有各自的优缺点: ①优化准则法物理意义明确、收敛速度快、计算效率高, 但是由于其对设计变量的增加不敏感性, 构造出的准则也不相同, 所以不具有良好的通用性; ②数学规划法不仅理论严谨而且具有适用面广和收敛性好等特点, 但是其计算量大, 收敛慢, 对于处理多个变量优化问题时更是如此. 将数学规划法与准则法两者的优势相结合的求解新方法—导重法, 具有迭代次数少易收敛、求解效率高等优点.本文以体积为约束, 求解结构柔顺度总和最小的多载荷工况问题, 将RAMP法和导重法进行联合求解, 形成了一种新的求解拓扑优化的多载荷工况结构拓扑优化设计方法.同ICM方法类似[1～3], 设第i号单元的拓扑变量用xi表示, 当xi=0时, 表示该单元不存在; 当0＜xi ＜1时, 表示该单元从无到有的过渡状态; 当xi=1时, 表示该单元存在.本文用fk(xi )识别单元刚度; fv(xi)识别单元体积. 其参数识别采用的函数为其中Ki表示xi对应的单元刚度矩阵; Vi表示xi对应的单元体积; 表示单元的固有刚度矩阵; 表示单元的固有体积.类似于SIMP方法, 采用Stolpe[4]等提出的近似有理分式材料模型(RAMP)的过滤方法, 选取. 体积的过滤函数为fv(xi)=xi.在优化过程中, 为了更加方便的进行求解, 将拓扑单元人为的分为可设计部分和不可设计部分两个部分. 用P表示可进行设计部分的单元个数, 第p个单元的编号设为ip (p=1,2,…,P), 拓扑变量用表示. 用Q表示不可设计部分的单元个数, 第q个单元的编号为nq (q=1,2,…,Q), 拓扑变量用表示.在优化迭代计算过程中, 在(0,1]之间变化, =1表示该单元始终保持不变. 因此, 以体积为约束的总的柔顺度最小的结构多工况优化问题可表示为其中Csum为所有工况下结构柔顺度加权之和; Cj和wj分别表示结构在第j载荷工况下的柔顺度和权重因子, 其中; L为总工况数, V为结构体积; 为可设计部分的初始体积; 为不可设计部分的初始体积; V0为整个设计区域的初始体积; θ（0＜θ＜1）为体积约束因子. xip为第p号单元的拓扑变量值,取.在有限元中, 静平衡方程可表示为结构柔顺度为其中N是有限单元的数量; K是总体刚度矩阵; Uj是在Fj载荷作用下结构的位移向量; ui,j是在Fj载荷作用下第i个单元的位移向量; Ki第i个单元的刚度矩阵. 对方程(4)中的设计变量xi求导, 得为了结构在优化过程获得较好的 0-1分布, 通过改变体积约束限来改变相邻迭代步的拓扑量变化的大小, 使迭代过程平稳. 将模型(2)转变为模型(9)形式进行求解.5.1 设计空间的调整为了使获得的拓扑结构有良好的0-1分布结果, 确保在优化过程中的结构不会出现奇异性, 同时对大规模、复杂有限元网格模型的结构优化问题能够有效的进行求解. 本文采用类似于文[9]提出的设计空间减缩和扩展策略.设计空间减缩和扩展的准则是:其中为最潜在删除的候选单元集; 为最大删除单元阀值;为最潜在增添的候选单元集; 为最小增添单元阀值, η*为经验参数值.如果式(23)成立, 则按照(25)和(26)式进行:当完成对式(25)和式(26)的操作时, 其中非零的对应的单元材料特性参数编号就自动的转变成为保留单元的特性参数编号; 而那些为零的对应的单元材料特性参数编号就会自动的转变为无材料单元所对应的特性参数编号.当求解结果开始接近最优结构, 能够符合的可设计单元已经不多了, 这时则可以适当提高的值, 能够满足要求的单元则按照式(27)和式(28)进行操作:5.2 优化终止条件在迭代过程中, 如果能符合式(29)给出的要求, 则表示优化求解收敛; 如果不能满足要求, 继续执行以上操作直到收敛为止.其中kd代表循环迭代步的编号.6.1 两组载荷工况下板结构优化设计如图1所示为一个在平面左右两端固定的基结构. 最大设计域为2 m× 1.0m×0.1m . 作用于结构的两组载荷工况为: 一个均布静载荷τ=19.84× 103 N/m 作用于上界面铅垂方向以中心点为中心的宽0.0625m的区域上; 另一个均布静载荷τ=19.84× 103 N/m 作用于下界面铅垂方向以中心点为中心的宽0.0625m的区域上. 弹性模量E=210Mpa , 泊松比ν=0.3, 密度ρ=7800kg/m3. 初始设计结构体积为0.2m3, 目标体积比θ=0.1. 初始结构区域划分为200× 100×2个六面体有限元单元网格.参数设置如下: 体积约束限值β=0.1; 步长因子α=0.45; s过滤函数“惩罚因子”取值, 借鉴文献[10]的取值, 本文取s=25; 拓扑变量下限值为xip =0.001(p=1,2,…,P ); 拓扑变量变化阀值η*=0.1.图1 为两组不同载荷工况下的结构模型和选定的初始优化区域. 应用所提的方法对其进行优化设计,图2显示了该方法获得的结构的优化过程图. 图3和图4分别显示了结构体积和柔顺度变化历程.利用本文提出的方法得到最优结果, 总共经历了60迭代步用时19min, 而文[11]中提出的方法用时41 min迭代90步达到最优拓扑. 说明了本文方法的高效性与快速性.6.2 多工况圆柱弧体结构优化设计图5所示为长1.5m、厚25mm的圆柱弧体, θ=57.3°, 四个角固支, 其弹性模量E=210GPa , 泊松比v=0.3, 密度ρ=7800kg/m3. 结构受两组载荷工况作用: 工况1. 在沿母线处施加集中载荷P1=1.0× 105 KN ; 工况2. 在沿母线处施加集中载荷P2=1.0× 105 KN . 目标体积比=0.65. 整个结构一共划分为4500个六面体有限单元网格.参数设置如下: 步长因子α=0.45, 其它参数的设置与上例相同.应用本文的方法对其进行拓扑优化设计, 图6显示的是采用本文的方法获得的圆柱弧体结构的优化历程图. 图7和图8分别显示了圆柱弧体结构体积和柔顺度变化历程.本算例从开始优化到最终的优化结果, 总共经历19个迭代步, 历时4min, 且优化迭代过程平稳.1) 本文提出了一种以体积为约束柔度最小的多载荷工况结构拓扑优化方法.2) 对多载荷工况的算例进行了拓扑优化计算, 得到了清晰、正确的优化结果, 提出的方法具有高效、稳定和迭代次数少等特点.【相关文献】[1] Sui YUNKANG,Yang DEQING. A New Method for Structural Topological Optimization Based on the Concept of Independent Continuous Variables and Smooth Model[J].Acta Mech Sinica,1998,14(2):179～185[2] 隋允康, 彭细荣. 结构拓扑优化ICM方法的改善[J]. 力学学报, 2005(2): 190～198[3] 荣见华, 邢晓娟, 邓果. 一种变位移约束限的结构拓扑优化方法[J]. 力学学报, 2009(3): 431～439[4] M. STOLPE,K. SVANBERG.An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization[J]. Struct Multidisc Optim, 2001, 22(2): 116～124[5] 陈树勋. 工程结构系统的分析、综合与优化设计[M]. 香港: 中国科学文化出版社, 2008[6] 叶尚辉, 陈树勋. 天线结构优化设计的最佳准则法[J]. 西北电讯工程学院学报, 1982(1): 17～34[7] 陈树勋. 精密复杂结构的几种现代设计方法[M]. 北京: 北京航空航天大学出版社, 1992[8] LIU Xin-jun, LI Zhi-dong, CHEN Xiang. A New Solution for Topology Optimization Problems with Multiple Loads:the Guide-weight Method[J].Science China (technological Sciences), 2011(6): 1505～1514[9] 荣见华, 张强, 葛森, 等. 基于设计空间调整的结构拓扑优化方法[J]. 力学学报, 2010(2): 109～120[10] 陈祥, 刘辛军. 基于RAMP插值模型结合导重法求解拓扑优化问题[J]. 机械工程学报, 2012(1): 135～140[11] 张新超. 基于ABAQUS的位移约束结构拓扑优化方法研究[D]. 长沙: 长沙理工大学硕士学位论文, 2012。
abaqus形貌优化计算案例
【导言】1. 介绍abaqus形貌优化计算的背景和意义2. 简要说明本文将以某个具体案例为例，详细介绍abaqus形貌优化计算的过程和结果【背景】1. 说明abaqus是什么软件，以及形貌优化计算的概念和应用范围2. 引出本文将要介绍的案例，即某个特定工程问题的形貌优化计算过程【案例描述】1. 详细描述这个工程问题的背景和需求2. 介绍该工程问题的初始设计和现有方案的缺陷或不足之处3. 阐述需要进行形貌优化计算的原因和目的【abaqus形貌优化计算过程】1. 罗列出进行形貌优化计算所需要的前期准备工作，包括材料性质的参数设定、加载条件的给定等2. 详细说明具体的abaqus形貌优化计算流程，包括模型建立、加载应力场、设定拓扑优化目标等步骤3. 在每个步骤中加入相关的截图、图表或计算结果，以便读者能够清晰地理解每个步骤的操作和计算原理4. 可适当引入一些相关的数学推导或理论解释，加深读者对形貌优化计算方法的理解【结果分析】1. 展示并解释形貌优化计算的最终结果2. 对比形貌优化前后的模型参数和性能指标，分析优化后的模型设计在性能上的改善和优势3. 可参考文献和实验数据，从理论和实际角度论证形貌优化计算的有效性和可行性【结论】1. 总结本文介绍的abaqus形貌优化计算案例，强调其在工程设计中的重要性和应用价值2. 可以展望未来形貌优化计算在相关领域的发展前景，以及可能的拓展方向和研究重点【致谢】1. 感谢相关机构或个人在该案例研究中提供的支持和帮助2. 致敬相关领域的专家学者和工程师们的努力和贡献【参考文献】1. 列出本文中涉及的相关文献和资料来源2. 参考文献的格式要符合要求的标准，包括作者、篇名、来源、出版年份等信息【附录】1. 如果有需要，可以在文章末尾附上一些相关的补充资料，如模型文件、数据表格、程序代码等以上就是整篇文章的大致结构和内容安排。
在撰写时，要注意语言通顺、表述清晰、严谨客观，以达到高质量、易读、结构合理的文章要求。
abaqus拓扑优化例题计算指导
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。
设计变量（Design variables）：设计变量即优化设计中需要改变的参数。拓扑优化中，
设计区域中单元密度是设计变量，ABAQUS/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。
最优化方法（Optimization）是一个通过自动化程序增加设计者在经验和直觉从而缩短 研发过程的工具。想要优化模型，必须知道如何去优化，仅仅说要减小应力或者增大特征值 是不够，做优化必须有更专门的描述。比方说，想要降低在两种不同载荷工况下的最大节点 力，类似的还有，想要最大化前五阶特征值之和。这种最优化的目标称之为目标函数（Object Function） 。另外，在优化过程中可以同时强制限定某些状态参量。例如，可以指定某节 点的位移不超过一定的数值。这些强制性的指定措施叫做约束（Constraint）。
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
【免费下载】例题ABAQUS
五 载荷
1 施加位移边界条件：Module，Load，Create Boundary Condition，
命名为 BC-1，在分析步 Step-1 中，性质：力学，针对位移和转角，Continue。选中梁左端，Done，约
束 u1、u2、u3、uR1、uR2 各自由度。 命名为 BC-2，在分析步 Step-1 中，性质：力学，针对位移和转角，Continue。选中梁右端，Done，约
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=2.239×105m4，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，bl=0.1，b2=0.1，tl=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。 4 将截面的几何、力学性质附加到部件上：Module，Property，Assign Section， 选中两段线段，将 Section-1 信息注入 Part-1。
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。
Abaqus优化设计和敏感性分析教程
优化设计和敏感性分析本章主要讲解应用Abaqus进行结构优化设计和敏感性分析。
目前的产品结构设计，大多靠经验，规划几种设计方案，结合CAE分析择优选取，但规划的设计方案并不一定是最优方案，故本章前半部分讲解优化设计中的拓扑优化和形状优化，并制定操作SOP，辅以工程实例详解。
工程实际中，加工制造、装配误差等造成的设计参数变异，会对设计目标造成影响，因此寻找出参数的影响大小即敏感性，变得尤为重要，故本章后半部分着重讲解敏感性分析，并制定操作SOP，辅以工程实例求出设计参数敏感度，详解产品的深层次研究。
知识要点：结构优化设计基础拓扑、形状优化理论拓扑、形状优化SOP及实例敏感性分析理论敏感性分析SOP及实例12.1 优化设计基础优化设计以数学中的最优化理论为基础，以计算机为手段，根据设计所追求的性能目标，建立目标函数，在满足给定的各种约束条件下，优化设计使结构更轻、更强、更耐用。
在Abaqus 6.11之前，需要借用第三方软件（比如Isight、TOSCA）实现优化设计及敏感性分析，远不如Hyperworks及Ansys等模块化集成程度高。
从Abaqus 6.11新增Optimization module后，借助于其强大的非线性分析能力，结构优化设计变得更具可行性和准确性。
12.1.1 结构优化概述结构优化是一种对有限元模型进行多次修改的迭代求解过程，此迭代基于一系列约束条件向设定目标逼近，Abaqus优化程序就是基于约束条件，通过更新设计变量修改有限元模型，应用Abaqus进行结构分析，读取特定求解结果并判定优化方向。
Abaqus提供了两种基于不同优化方法的用于自动修改有限元模型的优化程序：拓扑优化（Topology optimization）和形状优化（Shape optimization）。
两种方法均遵从一系列优化目标和约束。
12.1.2 拓扑优化拓扑优化是在优化迭代循环中，以最初模型为基础，在满足优化约束（比如最小体积或最大位移）的前提下，不断修改指定优化区域单元的材料属性（单元密度和刚度），有效地从分析模型中移走单元从而获得最优设计。
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
基于ABAQUSCAE的某乘用车后下控制臂拓扑优化设计
10.16638/ki.1671-7988.2021.04.015基于ABAQUS/CAE的某乘用车后下控制臂拓扑优化设计王振东1，李德淯2，伍初东1（1.湖南湖大艾盛汽车技术开发有限公司，湖南长沙410205；2.上汽通用五菱汽车股份有限公司，广西柳州545006）摘要：文章介绍了利用ABAQUS/CAE对某乘用车后下控制臂进行拓扑优化设计。
在通过模拟整车实际恶劣工况对其进行加载及约束，并结合ABAQUS/CAE中的优化模块下对控制臂进行拓扑优化参数设计，计算求解得出最优的减重方案，并提供给设计工程师对控制臂逆向建模。
最后对设计的新结构进行应力分析校核，校核结果显示优化后的新结构满足刚强度设计要求。
关键词：ABAQUS；控制臂；拓扑优化；轻量化；刚度中图分类号：U463 文献标识码：A 文章编号：1671-7988(2021)04-47-03Topology optimization design of a passenger vehicle rear lower controlarm based on ABAQUS/CAEWang Zhendong1, Li Deyu2, Wu Chudong1( 1.Hunan Huda Aisheng Automobile Technology Development Co., Ltd., Hunan Changsha 410205;2.SAIC-GM-Wuling Automobile Co., Ltd., Guangxi Liuzhou 545006 )Abstract: In this paper, ABAQUS/CAE will be used to optimize the topology design of the rear and lower control arm of a passenger car.In by simulating actual condition of the vehicle to load and constraints, combined with the optimization module of ABAQUS/CAE topology optimization parameter design for control arm, calculated to solve the optimal weight loss plan, and provide design engineers to control arm reverse modeling, and finally to design a new structure of the stress analysis and checking, to check whether meet the requirements of structural strength stiffness design.Keywords: ABAQUS; Control arm; Topology optimization; Lightweight; StiffnessCLC NO.: U463 Document Code: A Article ID: 1671-7988(2021)04-47-03引言拓扑优化技术作为以提高结构性能或减轻结构质量为目标的一种新型结构设计方法，目前已广泛在国内外汽车企业得到成功应用[1]。
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
例题ABAQUS
ABAQUS计算指导0：应用梁单元计算简支梁的挠度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-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。
ABAQUS算例2
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。
abaqus算例
abaqus算例ABAQUS实例操作一、型钢梁建模分析1.1 问题描述一型钢梁，尺寸如图所示，利用软件分析其内力。
材料特性：弹性模量E=2.1e11N/m2,泊松比μ=0.3，屈服强度ƒ=3.45e8N/m2。
y1.2创建部件点击创建部件按钮，在对话框中设置参量如右图：模型空间设置为三维的，类型为可变性的，基本特征为实体，可拉伸，比例设为1.1.2生成三维模型首先，在二维的环境下，输入横截面的各点坐标，然后再输入深度6m，便可生成如下图型：1.3创建材料和截面属性创建材料先输入弹性模量，泊松比，以及屈服应力，塑性应变，点击确认即可。
名字命名为section-beam，种类为实体，类型为均质，其他值保持默认，点击确认，接着选择整个部件，将截面性质赋予之。
1.4 定义装配件点击装配功能模块，选择部件为非独立实体其他保持为默认值点解确认即可。
1.5 设置分析步选择分析步模块，点击create instance 在对话框里面，输入名字为step,procedure type 设置为general ，在下拉菜单中选择static general 项，保持其他参数不变，点击确认。
1.6 定义荷载和边界条件选择荷载模块：①施加荷载在 create load对话框中，名字设置为load,step项中选择为step,将荷载设置为pressure，其他值保持不变，点击继续，在荷载的大小后面输入3.5e5，其他参数不变，完成荷载的定义。
②定义便捷条件在对话框中将step 设置为initial,将施加边界条件的方式设置为位移/转角，保持其余参数不变，点击确认。
在弹出的对话框中选择U1=U2=UR2=UR3=0，即对选中面施加铰接约束，点击ok。
同样的方式在另一边同样设置。
1.7 划分网格在列表中选择功能模块，对模型进行网格划分，将环境栏中的object项设为part，即为部件划分网格。
分割下翼缘和腹板，用点和垂线的方法进行分割，先选中下翼缘和腹板的交点，再选中腹板上一条垂线，点击确认，同样的方法分割上翼缘和腹板。
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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 – Volume; Operator: Sum of values. OK。
设计变量（Design variables）：设计变量即优化设计中需要改变的参数。拓扑优化中，
设计区域中单元密度是设计变量，ABAQUS/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。
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。
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。
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。
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。
最优化方法（Optimization）是一个通过自动化程序增加设计者在经验和直觉从而缩短 研发过程的工具。想要优化模型，必须知道如何去优化，仅仅说要减小应力或者增大特征值 是不够，做优化必须有更专门的描述。比方说，想要降低在两种不同载荷工况下的最大节点 力，类似的还有，想要最大化前五阶特征值之和。这种最优化的目标称之为目标函数（Object Function） 。另外，在优化过程中可以同时强制限定某些状态参量。例如，可以指定某节 点的位移不超过一定的数值。这些强制性的指定措施叫做约束（Constraint）。
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。
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.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。
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。
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）
本例的优化目的是在保留总体积的 57%的条件下，达到结构的刚度最大（应变能最小） 另外本例并非通常的密度法拓扑优化，而是刚度法的拓扑优化，刚度法的优化速度快些，但 适用范围较小。密度法的操作类似。 一 部件 此处部件比较复杂，且也不是 ATOM 中的主要操作，就不再自己建模，而直接导入 inp 的 mesh part。导入方式：菜单 File – import – model（inp），选择之前提到的 control_arm.inp， 得到 Part 名为：Part-1。如下图，单位（mm）
这些迭代或者设计循环不会停止，除非： 1） 最大迭代数达到 2） 指定的停止条件达到。
4.拓扑优化
拓扑优化开始于包含指定条件（例如边界条件和载荷）的初始设计开始。优化分析过程 在符合优化约束（比如最小体积或者最大位移）的前提下改变初始设计区域的单元密度和刚 度从而确定结构新的材料分布方式。 ABAQUS 可以应用如下目标到拓扑优化过程中：
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)
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：