最新Abaqus6.13拓扑优化 atom-book超全学习资料-05

Abaqus中优化有拓扑优化、形状优化和尺寸优化。

（本文尺寸优化只用于abaqus6.13版本以上（包括6.13版本），因为在6.13版本abaqus才加入尺寸优化这个模块）前两种优化目前可以参考江丙云的那本书书中对前两种优化讲的很详细。

而尺寸优化目前所有abaqus书籍中都没有写关于尺寸优化的内容，但是在6.13版本以上的abaqus官方英文帮助手册里有尺寸优化的相关理论，英文好的可以自学，很简单，在帮助手册中只有两个尺寸优化的例子，一个是控制臂，另一个是车门，如下面两张图所示，你们可以自己在帮助手册里找到这两个例子的inp文件，下载下来自己在abaqus中分析一下。

尺寸优化只对壳单元进行优化，而其他单元例如实体单元会被忽视掉不优化，尺寸优化就是变化壳单元的厚度。

下图是自带的两个例子图（1）控制臂图（2）车门下面是尺寸优化的流程1.创建尺寸优化job （即点击sizing optimization，各选项参数参考《Abaqus中Topology和Shape 优化指南》说明）2.创建设计响应（设计响应就是接下来的目标函数和约束条件需要用到的所有变量都需要在这里进行创建，这些创建好的设计响应全都是用于接下来的目标函数和约束条件）3创建目标函数（选择2中的某个响应作为目标函数，注意目标函数不是随意定的，是有限制的4.创建约束条件（选择2中的某些响应作为约束，同样不是所有对象都能作为约束，参考江丙云的书中优化模块）5.创建尺寸约束（这里是最重要的地方，thickness control 是用于定义优化区域的壳单元厚度变化范围，例如定义set-1集合的壳单元厚度为1-3mm，若模型中有多个优化区域就需要分别使用thickness control功能对不同优化区域定义壳的厚度；下面的那个cluster area 功能是让优化区域优化后厚度保持一致，例如例如对set-2区域定义cluster area ，假设它原先厚度为3mm，优化后厚度为1mm，那么整个set-,2区域优化后所有单元的厚度都是1mm，若不设置cluster area 则该区域的单元厚度是不相同的，可能有的单元1mm，有的单元是2mm或者其他厚度，而实际中我们都希望某块板的厚度优化后，厚度保持一致，这样好加工，所以这个功能的价值就体现在这里，这个功能非常重要。

ABAQUS入门使用手册一、前言ABAQUS是国际上最先进的大型通用有限元计算分析软件之一，具有惊人的广泛的模拟能力.它拥有大量不同种类的单元模型、材料模型、分析过程等。

可以进行结构的静态与动态分析，如：应力、变形、振动、冲击、热传递与对流、质量扩散、声波、力电耦合分析等；它具有丰富的单元模型，如杆、梁、钢架、板壳、实体、无限体元等;可以模拟广泛的材料性能，如金属、橡胶、聚合物、复合材料、塑料、钢筋混凝土、弹性泡沫，岩石与土壤等.对于多部件问题,可以通过对每个部件定义合适的材料模型，然后将它们组合成几何构形。

对于大多数模拟，包括高度非线性问题，用户仅需要提供结构的几何形状、材料性能、边界条件、荷载工况等工程数据。

在非线性分析中，ABAQUS能自动选择合适的荷载增量和收敛准则,它不仅能自动选择这些参数的值，而且在分析过程中也能不断调整这些参数值,以确保获得精确的解答。

用户几乎不必去定义任何参数就能控制问题的数值求解过程.1.1 ABAQUS产品ABAQUS由两个主要的分析模块组成,ABAQUS/Standard和ABAQUS/Explicit。

前者是一个通用分析模块，它能够求解广泛领域的线性和非线性问题，包括静力、动力、构件的热和电响应的问题。

后者是一个具有专门用途的分析模块,采用显式动力学有限元格式，它适用于模拟短暂、瞬时的动态事件，如冲击和爆炸问题，此外,它对处理改变接触条件的高度非线性问题也非常有效，例如模拟成型问题。

ABAQUS/CAE(Complete ABAQUS Environment）它是ABAQUS的交互式图形环境。

通过生成或输入将要分析结构的几何形状，并将其分解为便于网格划分的若干区域,应用它可以方便而快捷地构造模型,然后对生成的几何体赋予物理和材料特性、荷载以及边界条件。

ABAQUS/CAE具有对几何体划分网格的强大功能，并可检验所形成的分析模型.模型生成后，ABAQUS/CAE可以提交、监视和控制分析作业。

基于ＡＢＡＱＵＳ的喷雾机喷杆结构拓扑优化乔白羽ꎬ丁素明ꎬ薛新宇ꎬ崔龙飞ꎬ顾㊀伟ꎬ陈㊀晨(农业部南京农业机械化研究所ꎬ南京㊀２１００１４)摘㊀要:喷杆喷雾机在田间正常作业时ꎬ由于地面不平产生的激励会传递到喷杆上ꎬ导致喷杆的振动问题ꎮ为此ꎬ对一种喷杆结构进行了拓扑优化ꎬ从喷杆的内部材料布局出发ꎬ得到最合理的喷杆材料分布ꎬ通过优化喷杆自身的结构来改变喷杆的固有频率ꎬ使喷杆的固有频率远离激振源的共振频率区间ꎮ以材料的畸变能密度为优化目标ꎬ在ＡＢＡＱＵＳ软件中采用变密度法对初始喷杆结构进行了结构拓扑优化设计ꎬ并对优化前后喷杆结构的动力学特性进行了比较ꎬ验证了此次拓扑优化的合理性ꎮ结果表明:在该喷雾机喷杆的质量减少１６.３％的情况下ꎬ喷杆的１阶固有频率增加了９.５６Ｈｚꎬ有效避开了激振源的频率区间ꎬ减轻了喷杆的振动ꎮ本文可为喷雾机喷杆的动力学特性研究与结构优化提供理论依据ꎮ关键词:喷杆喷雾机ꎻ喷杆ꎻ拓扑优化中图分类号:Ｓ４９１㊀㊀㊀㊀㊀㊀㊀文献标识码:Ａ文章编号:１００３－１８８Ｘ(２０１９)０５－００３９－０５０㊀引言近年来ꎬ随着中国农业机械化进程的加速推进ꎬ大型植保机械得到了快速的发展ꎬ地面植保机具中ꎬ大型喷杆喷雾机应用最为广泛ꎬ主要使用在大田作业中[１－５]ꎮ大型喷杆喷雾机的优点是作业效率高㊁施药面积大ꎬ能够极大程度地减小作业过程中对农作物的损害ꎬ因此具有较大的使用价值ꎮ但是ꎬ大型喷杆喷雾机在田间施药的过程中ꎬ由于地面不平所产生的外部激励会通过机架传递到喷杆ꎬ导致喷杆发生振动ꎬ进而影响到喷雾效率ꎬ降低药液的分布均匀性ꎬ严重时还会引起喷杆的断裂ꎬ从而降低喷雾效率ꎬ缩短喷杆喷雾机的使用寿命[６－９]ꎮ为了减轻喷雾机喷杆的振动ꎬ提高喷杆喷雾机在田间作业过程中的喷洒效率ꎬ国内外学者在机械结构抑振方面进行了大量的研究ꎮ其中ꎬＲｏｎｇＪ.Ｈ.等人基于约束频率和约束响应之间的函数关系式ꎬ利用结构拓扑优化方法ꎬ对机械结构进行了拓扑优化研究ꎬ证明了拓扑优化对机械结构的抑振性能[１０]ꎻＮｉｏｒｄｓｏｎ等人对梁结构进行了结构优化设计ꎬ结果显示优化后梁结构的抗振性能极大的提高[１１]ꎻ李艳辉等以钢架结构收稿日期:２０１７－１２－０７基金项目:江苏省农业科技自主创新资金项目(ＣＸ[１６]１０４３)ꎻ国家重点研发计划项目(２０１７ＹＦＤ０７００９０５)ꎻ中国农业科学院基本科研业务费专项(Ｓ２０１６１４)作者简介:乔白羽(１９９４－)ꎬ女ꎬ山西吕梁人ꎬ硕士研究生ꎬ(Ｅ－ｍａｉｌ)９９２６７０３７４＠ｑｑ.ｃｏｍꎮ通讯作者:丁素明(１９７７－)ꎬ男ꎬ江苏姜堰人ꎬ研究员ꎬ硕士生导师ꎬ(Ｅ－ｍａｉｌ)４６５８９０５５１＠ｑｑ.ｃｏｍꎮ作为研究对象ꎬ将钢架结构的固有频率作为目标函数ꎬ利用结构节点渐进法对其进行了动力学性能优化[１２]ꎻ陈晨等人研究了喷杆的动力学特性以及结构尺寸优化ꎬ结果表明构成喷杆的钢管壁厚和截面尺寸均与喷杆的１阶固有频率成正比ꎬ为喷杆的进一步动力学性能研究以及结构优化做准备[１３]ꎻ茅志颖等人对结构优化设计的渐进优化理论进行了研究ꎬ提出了基于渐近理论的结构性能优化方法ꎬ并通过试验验证了多目标多约束优化方法的合理性[１４]ꎻ扶原放等基于变密度法对某微型电动车的车架结构进行了拓扑优化设计ꎬ优化结果显示优化后车架结构的动力学性能得到很大提升ꎬ并且实现了车架结构的轻量化设计[１５]ꎻ陈达等以等腰梯形的喷杆悬架结构为研究对象对其进行了优化设计ꎬ采用动态测试分析㊁有限元模态分析及整机路谱模拟等方法ꎬ优化了悬架结构的动力学性能ꎬ减轻了悬架结构的振动[１６]ꎮ上述将拓扑优化方法应用到其他机械结构中已经实现了部分机械结构的动力学性能优化ꎬ但并没有从机械结构的原始设计方面考虑ꎬ也没有将拓扑优化方法应用到喷杆结构的优化设计中ꎮ为此ꎬ基于计算机辅助优化设计的设计理论与方法ꎬ从喷杆原始设计出发ꎬ通过改变喷杆结构的内部材料布局ꎬ对喷杆进行最优拓扑优化ꎬ从而实现减振的目的ꎮ１㊀喷杆的结构设计本文利用三维建模软件Ｐｒｏ/Ｅ建立了喷杆喷雾机的几何模型ꎬ如图１所示ꎮ此次研究的喷杆主要由方２０１９年５月㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀农机化研究㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第５期形钢管和圆柱形钢管焊接而成的５段式喷杆ꎬ整个喷杆总长为１２ｍꎮ其中ꎬ每侧喷杆的两段喷杆之间以回转关节的方式折叠放置ꎬ机架与喷杆直接相连ꎬ是振动传递的主要来源ꎮ整个机身主要包括４根方形钢管㊁６根圆柱形钢管㊁药箱㊁连接部件ꎬ以及其他辅助构件ꎮ此次拓扑优化不考虑药箱和喷头的作用ꎬ在优化过程中只对喷杆和机架部分进行拓扑优化ꎮ由图１可以看到ꎬ目前喷杆的内部分布多为四边形ꎬ此种结构形状不稳定ꎬ不利于减轻喷杆作业过程中所产生的振动ꎬ所以需要对喷杆的内部材料分布进行优化ꎬ以达到最好的材料布局ꎬ从而提高喷杆的动力学性能ꎮ１.喷头㊀２.药箱㊀３.机架㊀４.喷杆图１㊀喷杆喷雾机整机结构图Ｆｉｇ.１㊀Ｔｈｅｗｈｏｌｅｓｔｒｕｃｔｕｒｅｏｆｂｏｏｍｓｐｒａｙｅｒ２㊀喷杆结构的拓扑优化２.１㊀拓扑优化理论基础拓扑优化技术已经广泛应用于机械结构的优化设计中ꎬ这种方法的优点就是可以在结构的初始设计过程中ꎬ使得材料得到合理分配ꎬ从而减轻机械结构的重量[１７－１９]ꎮ将拓扑优化技术应用于喷杆的结构设计中ꎬ不仅可以缩短喷杆的制造时间ꎬ还可以提高喷杆的结构性能ꎮ拓扑优化的基本思想是在指定的区域内寻求材料的最佳布局ꎮ通过设置目标函数和约束条件ꎬ对设计域内的单元进行取舍ꎬ实现结构在指定约束条件下的最优设计ꎮ目前ꎬ机械结构拓扑优化的方法主要有均匀化法㊁变密度法㊁渐进结构优化法以及变厚度法[２０]ꎮ本文采用的是变密度法对喷杆结构进行拓扑优化求解ꎮ变密度法的基本原理:假想一种密度可变的材料ꎬ人为的去设定材料的物理参数特性与密度之间的关系ꎬ在拓扑优化过程中将材料的密度定义为拓扑优化的设计变量ꎬ从而将拓扑优化的问题转变成材料最优分布的问题ꎬ实现材料的最合理分布ꎬ从而实现最优拓扑结构[２１]ꎮ拓扑优化的数学模型为Ｍｉｎｆ(ｘ)ｓ.ｔ.ｇｊ(ｘ)ɤ０㊀ｊ＝１ꎬ ꎬｍｈｋ(ｘ)＝０㊀ｋ＝１ꎬ ꎬｎＸ＝(ｘ１ꎬｘ２ꎬ ꎬｘｎ)０ɤｘｉɤ１㊀ｉ＝１ꎬ ꎬｒ式中㊀ｘ 单元密度ꎻ㊀ｆ(ｘ) 目标函数ꎻ㊀ｇ(ｘ) 不等式约束函数ꎻ㊀ｈ(ｘ) 等式约束函数ꎮ结构拓扑优化的３个重要因素就是设计变量㊁约束函数以及目标函数ꎬ拓扑优化的具体过程是:在设置好设计变量和约束函数后ꎬ通过对其进行迭代ꎬ实现目标函数最优的过程ꎮ拓扑优化的本质就是材料最优分布问题ꎬ也就是通过拓扑优化去除不必要的材料ꎬ将材料添加到结构性能需要加强的区域ꎬ通过寻找合理的载荷传递路径ꎬ提高材料的使用效率ꎬ提升结构的刚度和模态性能[２２－２３]ꎮ２.２㊀拓扑优化模型的建立在进行结构拓扑优化之前ꎬ首先需要根据实际要求建立结构的初始拓扑优化模型ꎬ初始结构模型可以分为实体单元或者壳单元ꎬ通过简化结构的设计域和非设计域来控制结构的拓扑优化设计ꎮ由于此次研究的喷杆结构具有对称结构ꎬ因此只需要对喷杆的右侧进行拓扑优化即可ꎮ优化之前ꎬ所建立的喷杆结构模型为２２６０ˑ５００的长方形模型ꎬ单元类型为壳单元ꎬ如图２所示ꎮ图２㊀拓扑分析模型的初始结构Ｆｉｇ.２㊀Ｔｈｅｉｎｉｔｉａｌｓｔｒｕｃｔｕｒｅｏｆｔｈｅｔｏｐｏｌｏｇｙａｎａｌｙｓｉｓｍｏｄｅｌ上述的拓扑优化初始模型采用一阶四面体单元建立ꎬ设计域是整个拓扑优化分析模型ꎮ拓扑优化的单元尺寸为２０ｍｍꎬ壳单元数量为２８５０个ꎬ材料的特性定义如表１所示ꎮ表１㊀初始模型的材料特性Ｔａｂｌｅ１㊀Ｍａｔｅｒｉａｌｐｒｏｐｅｒｔｙｐａｒａｍｅｔｅｒｓｏｆｔｈｅｉｎｉｔｉａｌｍｏｄｅｌ材料弹性模量/ＧＰａ泊松比密度/ｋｇ ｍ－３结构钢２.０ｅ５０.３７.９ｅ－９２.３㊀拓扑优化的过程２.３.１㊀确定设计变量㊁约束条件和目标函数本次拓扑优化采用变密度法ꎬ思想和前提是:①将离散单元的相对密度定义为拓扑优化的设计变量ꎬ单元内部的其他材料属性均为常数ꎻ②在拓扑优化过２０１９年５月㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀农机化研究㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第５期程中ꎬ单元相对密度一直在变化ꎬ由此使得单元材料属性也在变化ꎮ基于上述两个前提和假设ꎬ材料的属性可以理解为初始材料的属性和单元相对密度之间的指数关系ꎬ且每一个单元只将密度作为唯一的设计变量ꎬ这样可以大大地简化拓扑优化的过程[２４]ꎮ根据上述分析ꎬ以调整喷杆的固有频率避开外界激励力的频率为主要目标ꎬ在不会大幅影响喷杆整体结构重量的前提下建立喷杆的优化模型ꎮ一般的喷杆喷雾机在田间作业时ꎬ会受到田间路面凹凸不平和喷雾机轮胎弹性的影响ꎬ导致喷雾机的机架受到激励ꎬ从而传递到喷杆ꎬ引起喷杆的振动ꎬ激励频率为０~１０Ｈｚ[２５－２６]ꎮ因此ꎬ在定义拓扑优化的设计变量时ꎬ需要考虑喷雾机动态性能的要求ꎬ并结合优化设计理论来进行确定ꎮ此次优化的边界条件是在初始模型的末端施加１００Ｎ的力ꎬ力的大小是由右侧喷杆的质量所决定的ꎬ这样可以模拟喷杆的实际受力情况ꎮ本次拓扑优化的设计目标是畸变能密度最小ꎬ约束条件是体积减小初始体积的５０％ꎬ位移约束等于或者小于０.００１ꎬ这样可以保证拓扑优化的材料分布实现最佳布局ꎮ因此ꎬ拓扑优化的目标函数是在满足结构约束的条件下ꎬ最小化整个喷杆结构的畸变能ꎬ约束函数是在给定载荷约束和满足最小畸变能的条件下ꎬ实现喷杆结构的整体体积比ꎮ拓扑优化的数学模型为ｍｉｎＦ(ηｉ)ｓ.ｔʏΩηｉｄΩɤａＶ０式中㊀Ｆ 结构的畸变能密度ꎻ㊀ηｉ 第ｉ个单元的伪密度ꎻ㊀ａ 体积减小的百分比ꎻ㊀Ｖ０ 喷杆的初始体积ꎮ２.３.２㊀优化结果分析完成上述步骤后ꎬ就可以进行迭代优化ꎮ本次拓扑优化在ＡＢＡＱＵＳ中进行ꎬ将喷杆初始模型的壳单元导入ＡＢＡＱＵＳ后ꎬ定义各个参数化变量ꎬ随后进入优化过程ꎮ本次优化一共进行３１次迭代ꎬ优化后的密度和位移云图如图３和图４所示ꎮ图３㊀拓扑优化后的密度云图Ｆｉｇ.３㊀Ｄｅｎｓｉｔｙｐｌｏｔａｆｔｅｒｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎ图４㊀拓扑优化后的位移云图Ｆｉｇ.４㊀Ｄｉｓｐｌａｃｅｍｅｎｔｐｌｏｔａｆｔｅｒｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎ本次优化采用变密度法ꎬ可以看出ꎬ拓扑优化后的材料分布用单元密度值(０~１)来表示ꎬ图中的空洞部分表示密度值为０的部分ꎬ也就是拓扑优化后需要移除的材料ꎮ从图３㊁图４中可以看出:喷杆结构的最大变形量减少１０.９％ꎬ最大应力减小２７.６％ꎬ拓扑优化取得了很好的效果ꎮ优化过程中的目标函数变化曲线如图５所示ꎮ它反映了在迭代过程中喷杆结构变形量的变化情况ꎬ随着迭代次数的增加ꎬ结构变形量在不断减小ꎮ约束函数变化曲线如图６所示ꎮ由图６可看出:随着迭代过程的进行ꎬ体积在不断减小ꎬ当体积减小到０.２９７ｍ３时ꎬ总体积减小到初始体积的７０％ꎮ图５㊀结构变形量变化图Ｆｉｇ.５㊀Ｃｈａｎｇｅｏｆｔｈｅｓｔｒｕｃｔｕｒａｌｄｅｆｏｒｍａｔｉｏｎｅｎｅｒｇｙ图６㊀体积变化图Ｆｉｇ.６㊀Ｃｈａｎｇｅｏｆｔｈｅｖｏｌｕｍｅ３㊀优化后多段式喷杆的动态特性分析根据上述分析ꎬ本次优化的主要目标是调整喷杆的固有频率使其避开外界的激励频率ꎬ同时在不大幅度改变喷杆质量的前提下建立喷杆的优化模型ꎮ优化后的动力学特性分析就是为了比较喷杆在优化前后动力学特性的变化ꎮ通过将优化后的模型导入ＡＢＡＱＵＳ中ꎬ可以计算出优化后喷杆的前８阶固有频率和动力学性能ꎮ优化后喷杆材料的内部布局如图７所示ꎮ图７㊀优化后喷杆内部材料分布Ｆｉｇ.７㊀Ｔｈｅｉｎｔｅｒｎａｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆｔｈｅｍａｔｅｒｉａｌａｆｔｅｒｏｐｔｉｍｉｚｉｎｇ对优化后的整机喷杆进行动力学特性分析ꎬ获得优化前后前８阶多段式喷杆的阵型位移对比图ꎬ如图８所示ꎮ从图８可以看出:优化后喷杆的第１阶模态位移变形量由７.６ｍｍ下降到５.１ｍｍꎻ第２阶阶模态位移变形量由７ｍｍ下降到４.９ｍｍꎬ实现了低阶模态振动的有效控制ꎬ显著的减轻了喷杆的振动ꎬ进而改善了整个喷杆喷雾机的振动特性ꎮ图８㊀优化前后模态阵型位移对比图Ｆｉｇ.８㊀Ｃｏｍｐａｒｉｓｏｎｏｆｔｈｅｍｏｄｅｄｅｆｏｒｍａｔｉｏｎｄｉｓｐｌａｃｅｍｅｎｔｂｅｆｏｒｅａｎｄａｆｔｅｒｏｐｔｉｍｉｚａｔｉｏｎ优化前后喷雾机喷杆的前８阶固有频率和阵型描述如表２及图９所示ꎮ表２㊀优化前后各变量值对比Ｔａｂｌｅ２㊀Ｃｏｍｐａｒｉｓｏｎｏｆｖａｒｉａｂｌｅｓｂｅｆｏｒｅａｎｄａｆｔｅｒｏｐｔｉｍｉｚａｔｉｏｎ优化变量优化前优化后增加量１阶频率/Ｈｚ２.３１１.８６９.５６２阶频率/Ｈｚ３.１１４.９７１１.８７３阶频率/Ｈｚ３.６１５.６２１２.０２４阶频率/Ｈｚ５.９１７.４８１１.５８５阶频率/Ｈｚ７.９１９.６９１１.７９６阶频率/Ｈｚ８.６２０.５３１１.９３７阶频率/Ｈｚ１０.４８２７.５４１７.０６续表２优化变量优化前优化后增加量８阶频率/Ｈｚ１１.４３２９.６５１８.２２总质量/ｋｇ１００.８８４.３４１６.４６图９㊀优化前后前８阶固有频率对比图Ｆｉｇ.９㊀Ｃｏｍｐａｒｉｓｏｎｏｆｔｈｅｎａｔｕｒａｌｆｒｅｑｕｅｎｃｉｅｓｏｆｆｉｒｓｔｅｉｇｈｔｍｏｄｅｓ优化结果表明:在喷杆的质量减少１６.３％的情况下ꎬ喷杆的１阶固有频率增加９.５６Ｈｚꎬ２阶固有频率增加１１.８７Ｈｚꎬ有效避开了喷杆的共振区间ꎬ减轻了喷杆整机的振动ꎮ同时ꎬ对比优化前后喷杆的分析结果可以看出:优化后喷杆的频率集中在１０~５０Ｈｚꎬ优化后喷杆的低阶固有频率远离了路面激励以及容易引起共振的频率区间ꎬ实现了固有频率的提升ꎬ从而优化了喷杆的动力学特性ꎮ此次拓扑优化的使得喷杆结构在田间作业时运行会更加平稳ꎬ极大地减小了发生共振的概率ꎬ在材料最佳分布的情况下ꎬ实现了喷杆最优的动力学性能ꎮ４㊀结论１)采用变密度法对喷杆进行拓扑优化ꎬ分析比较优化前后喷杆的动力学特性ꎮ结果表明:优化后的第１阶模态位移变形从７.６ｍｍ减小为５.１ｍｍꎬ第２阶模态位移变形量从７ｍｍ减小到４.９ｍｍꎬ极大地改善了喷杆整机的振动ꎮ２)在喷杆整机质量减小１６.３％的情况下ꎬ喷杆的１阶固有频率提高９.５６Ｈｚꎬ可以有效避免激励源的共振区间ꎬ减轻喷杆的振动ꎮ参考文献:[１]㊀王怀敏ꎬ刘加平.我国植保机械及施药技术现状与发展趋势[Ｊ].中国机械ꎬ２０１５(１７):６９－７０.[２]㊀ＣａｔｔａｎｉＭꎬＣｅｎａＫꎬＥｄｗａｒｄｓＪꎬｅｔａｌ.ＰｏｔｅｎｔｉａｌｄｅｒｍａｌａｎｄｉｎｈａｌａｔｉｏｎｅｘｐｏｓｕｒｅｔｏｃｈｌｏｒｐｙｒｉｆｏｓｉｎＡｕｓｔｒａｌｉａｎｐｅｓｔｉｃｉｄｅｗｏｒｋｅｒｓ[Ｊ].ＡｎｎａｌｓｏｆＯｃｃｕｐａｔｉｏｎａｌＨｙｇｉｅｎｅꎬ２００１ꎬ４５(４):２９９－３０８.[３]㊀周海燕ꎬ杨炳南ꎬ严荷荣ꎬ等.我国高效植保机械应用现状及发展展望[Ｊ].农业工程ꎬ２０１４ꎬ４(６):４－６. [４]㊀ＺａｍａｎＱＵꎬＥｓａｕＴＪꎬＳｃｈｕｍａｎｎＡＷꎬｅｔａｌ.Ｄｅｖｅｌｏｐｍｅｎｔｏｆｐｒｏｔｏｔｙｐｅａｕｔｏｍａｔｅｄｖａｒｉａｂｌｅｒａｔｅｓｐｒａｙｅｒｆｏｒｒｅａｌ－ｔｉｍｅｓｐｏｔ－ａｐｐｌｉｃａｔｉｏｎｏｆａｇｒｏｃｈｅｍｉｃａｌｓｉｎｗｉｌｄｂｌｕｅｂｅｒｒｙｆｉｅｌｄｓ[Ｊ].ＣｏｍｐｕｔｅｒｓａｎｄＥｌｅｃｔｒｏｎｉｃｓｉｎＡｇｒｉｃｕｌｔｕｒｅꎬ２０１１ꎬ７６(２):１７５－１８２.[５]㊀王帅.国内植保机械发展探析[Ｊ].农业科技与装备ꎬ２０１２(９):４２－４３.[６]㊀刘丰乐ꎬ张晓辉ꎬ马伟伟ꎬ等.国外大型植保机械及施药技术发展现状[Ｊ].农机化研究ꎬ２０１０ꎬ３２(３):２４６－２４８. [７]㊀贾卫东ꎬ张磊江ꎬ燕明德ꎬ等.喷杆喷雾机研究现状及发展趋势[Ｊ].中国农机化学报ꎬ２０１３(４):１９－２２. [８]㊀陈晨ꎬ薛新宇ꎬ顾伟ꎬ等.喷雾机喷杆悬架系统的研究现状及发展[Ｊ].中国农机化学报ꎬ２０１５ꎬ３６(３):９８－１０１. [９]㊀乔白羽ꎬ丁素明ꎬ薛新宇ꎬ等.喷雾机喷杆结构的研究现状及展望[Ｊ].农机化研究ꎬ２０１７ꎬ３９(１１):２４６－２５０. [１０]㊀ＲｏｎｇＪＨꎬＸｉｅＹＭꎬＹａｎｇＸＹꎬｅｔａｌ.Ｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａ￣ｔｉｏｎｏｆｓｔｒｕｃｔｕｒｅｓｕｎｄｅｒｄｙｎａｍｉｃｒｅｓｐｏｎｓｅｃｏｎｓｔｒａｉｎｔｓ[Ｊ].ＪｏｕｒｎａｌｏｆＳｏｕｎｄａｎｄＶｉｂｒａｔｉｏｎꎬ２０００ꎬ２３４(２):１７７－１８９. [１１]㊀ＮｉｏｄｓｏｎＦＩ.Ｔｈｅｏｐｔｉｍｕｍｄｅｓｉｇｎｏｆｖｉｂｒａｔｉｎｇｂｅａｍｓ[Ｊ].ＱｕａｒｔｅｒｌｙｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓꎬ１９６５ꎬ２３(１):４７－５３. [１２]㊀李艳辉.刚架结构动力学形状优化[Ｄ].西安:西北工业大学ꎬ２００５.[１３]㊀陈晨ꎬ薛新宇ꎬ顾伟ꎬ等.喷雾机喷杆结构形状及截面尺寸优化与试验[Ｊ].农业工程学报ꎬ２０１５ꎬ３１(９):５０－５６.[１４]㊀茅志颖.结构动力学设计渐进优化方法研究[Ｄ].南京:南京航空航天大学ꎬ２０１０.[１５]㊀扶原放ꎬ金达锋ꎬ乔蔚炜.微型电动车车架结构优化设计方法[Ｊ].机械工程学报ꎬ２００９ꎬ４５(９):２１０－２１３. [１６]㊀陈达ꎬ陈志ꎬ周丽萍ꎬ等.喷杆喷雾机等腰梯形悬架改进与验证[Ｊ].农机化研究ꎬ２０１４ꎬ３６(４):１７１－１７４. [１７]㊀张学亮.齿轮箱模态分析和结构优化方法研究[Ｄ].太原:太原理工大学ꎬ２０１０.[１８]㊀许华旸ꎬ关立文ꎬ王立平ꎬ等.惯性载荷下飞行模拟器大臂结构的拓扑优化[Ｊ].机械工程学报ꎬ２０１４ꎬ５０(９):１４－２３.[１９]㊀范文杰ꎬ范子杰ꎬ苏瑞意.汽车车架结构多目标拓扑优化方法研究[Ｊ].中国机械工程ꎬ２００８ꎬ１９(１２):１５０５－１５０８.[２０]㊀沈伟ꎬ廖敏ꎬ王强ꎬ等.基于拓扑优化的变速箱壳体轻量化设计[Ｊ].农机化研究ꎬ２０１８ꎬ４０(４):２３４－２４１. [２１]㊀焦洪宇ꎬ周奇才ꎬ李文军ꎬ等.基于变密度法的周期性拓扑优化[Ｊ].机械工程学报ꎬ２０１３ꎬ４９(１３):１３２－１３８. [２２]㊀王书贤ꎬ向立明ꎬ刘鹏ꎬ等.基于拓扑优化的某汽车悬架控制臂轻量化设计[Ｊ].轻工科技ꎬ２０１７(１０):３０－３１. [２３]㊀姜缪文ꎬ闫健卓ꎬ陈继民ꎬ等.基于拓扑优化技术的军用头盔内胆结构三维打印[Ｊ].兵工学报ꎬ２０１７ꎬ３８(９):１８４５－１８５３.[２４]㊀昌俊康ꎬ段宝岩.连续体结构拓扑优化的一种改进变密度法及其应用[Ｊ].计算力学学报ꎬ２００９ꎬ２６(２):１８８－１９２.[２５]㊀姚艳春ꎬ杜岳峰ꎬ朱忠祥ꎬ等.基于模态的玉米收获机车架振动特性分析与优化[Ｊ].农业工程学报ꎬ２０１５ꎬ３１(１９):４６－５３.[２６]㊀邹春江ꎬ左孔天ꎬ向宇ꎬ等.基于ＳＩＭＰ方法微电容加速度计结构固有频率拓扑优化[Ｊ].科学技术与工程ꎬ２０１１ꎬ２９(１１):７０８６－７０９１.ＴｏｐｏｌｏｇｙＯｐｔｉｍｉｚａｔｉｏｎｏｆＳｐｒａｙｅｒＢｏｏｍＳｔｒｕｃｔｕｒｅＢａｓｅｄｏｎＡＢＡＱＵＳＱｉａｏＢａｉｙｕꎬＤｉｎｇＳｕｍｉｎｇꎬＸｕｅＸｉｎｙｕꎬＣｕｉＬｏｎｇｆｅｉꎬＧｕＷｅｉꎬＣｈｅｎＣｈｅｎ(ＮａｎｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＡｇｒｉｃｕｌｔｕｒａｌＭｅｃｈａｎｉｚａｔｉｏｎꎬＭｉｎｉｓｔｒｙｏｆＡｇｒｉｃｕｌｔｕｒｅꎬＮａｎｊｉｎｇ２１００１４ꎬＣｈｉｎａ)Ａｂｓｔｒａｃｔ:Ｉｎｖｉｅｗｏｆｔｈｅｐｒｏｂｌｅｍｏｆｂｏｏｍｖｉｂｒａｔｉｏｎｃａｕｓｅｄｂｙｕｎｅｖｅｎｐａｖｅｍｅｎｔꎬｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎｏｆａｂｏｏｍｓｔｒｕｃ￣ｔｕｒｅｗａｓｃａｒｒｉｅｄｏｕｔ.Ａｃｃｏｒｄｉｎｇｔｏｔｈｅｌａｙｏｕｔｏｆｔｈｅｉｎｔｅｒｎａｌｍａｔｅｒｉａｌｏｆｔｈｅｂｏｏｍꎬｔｈｅｍｏｓｔｒｅａｓｏｎａｂｌｅｉｎｔｅｒｎａｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆｔｈｅｂｏｏｍｍａｔｅｒｉａｌｗａｓｏｂｔａｉｎｅｄ.Ｂｙｃｈａｎｇｉｎｇｔｈｅｓｔｒｕｃｔｕｒｅｏｆｔｈｅｂｏｏｍｉｔｓｅｌｆꎬｔｈｅｎａｔｕｒａｌｆｒｅｑｕｅｎｃｙｏｆｔｈｅｂｏｏｍｗａｓｃｈａｎｇｅｄꎬｓｏｔｈａｔｔｈｅｎａｔｕｒａｌｆｒｅｑｕｅｎｃｙｏｆｔｈｅｓｐｒａｙｂｏｏｍｃｏｕｌｄｂｅｆａｒａｗａｙｆｒｏｍｔｈｅｒｅｓｏｎａｎｃｅｆｒｅｑｕｅｎｃｙｒａｎｇｅｏｆｔｈｅｅｘ￣ｃｉｔａｔｉｏｎｓｏｕｒｃｅ.ＴａｋｉｎｇｔｈｅｄｉｓｔｏｒｔｉｏｎｅｎｅｒｇｙｄｅｎｓｉｔｙｏｆｍａｔｅｒｉａｌａｓｔｈｅｏｐｔｉｍｉｚａｔｉｏｎｏｂｊｅｃｔｉｖｅａｎｄｔｈｅｖａｒｉａｂｌｅｄｅｎｓｉｔｙｍｅｔｈｏｄｗａｓａｐｐｌｉｅｄｔｏｔｈｅｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎｄｅｓｉｇｎｉｎｔｈｅＡＢＡＱＵＳｓｏｆｔｗａｒｅꎬａｎｄｔｈｅｄｙｎａｍｉｃｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｔｈｅｏｐｔｉｍｉｚｅｄｂｏｏｍｓｔｒｕｃｔｕｒｅｗｅｒｅａｎａｌｙｚｅｄꎬｗｈｉｃｈｖｅｒｉｆｉｅｄｔｈｅａｃｃｕｒａｃｙｏｆｔｈｅｏｐｔｉｍｉｚａｔｉｏｎｒｅｓｕｌｔｓ.Ｔｈｅｒｅｓｕｌｔｓｓｈｏｗｅｄｔｈａｔｗｈｅｎｔｈｅｍａｓｓｏｆｔｈｅｓｐｒａｙｅｒｗａｓｒｅｄｕｃｅｄｂｙ１６.３％ꎬｔｈｅｆｉｒｓｔｎａｔｕｒａｌｆｒｅｑｕｅｎｃｙｏｆｔｈｅｂｏｏｍｉｎｃｒｅａｓｅｄｂｙ９.５６Ｈｚꎬｗｈｉｃｈｅｆｆｅｃｔｉｖｅｌｙａｖｏｉｄｅｄｔｈｅｆｒｅｑｕｅｎｃｙｒａｎｇｅｏｆｔｈｅｅｘｃｉｔａｔｉｏｎｓｏｕｒｃｅａｎｄｒｅｄｕｃｅｄｔｈｅｖｉｂｒａｔｉｏｎｏｆｔｈｅｂｏｏｍ.Ｔｈｉｓｐａｐｅｒｐｒｏｖｉｄｅｓａｔｈｅｏｒｅｔｉｃａｌｂａｓｉｓｆｏｒｔｈｅｓｔｕｄｙｏｆｔｈｅｄｙｎａｍｉｃｃｈａｒａｃｔｅｒｉｓｔｉｃｓａｎｄｓｔｒｕｃｔｕｒａｌｏｐｔｉｍｉｚａｔｉｏｎｏｆｔｈｅｓｐｒａｙｅｒｂｏｏｍ.Ｋｅｙｗｏｒｄｓ:ｂｏｏｍｓｐｒａｙｅｒꎻｂｏｏｍꎻｔｏｐｏｌｏｇｙｏｐｔｉｍｉｚａｔｉｏｎ。

第12章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。

Abaqus6.13最新更正版详细图文安装过程本次采用的安装文件为ABAQUS 6.13（包括Crack破解文件）总大小1.7G左右。

Crack文件可能是另外下载的。

（本教程并非作者原创，是在原文件的基础上修改而来，此次特意写为word文档，希望大家有新的体会可以下载修改后上传，供大家交流，谢谢，在此也是感谢原作者，但是这是第二次安装记不得作者名字了，还是感谢）详细安装过程如下：一、安装许可证文件1、运行Autorun.exe文件，出现如下界面，点击第一个“Install Abaqus Product & Licensing”，如果运行Autorun.exe文件没反应则可以直接运行setup.exe即可，后面步骤相同。

（亲测有效）2、选择Next；3、提示安装C++2005和2008，点击OK，根据提示安装4、弹出提示窗口，点击continue；5、点击next6、不用勾选，点击next7、默认选择第一个，点击next8、自动生成计算机名，记住自己的Hostname，点击Next9、默认选择第一个，这里要点选第二个，然后next10、选择许可证安装位置，默认C:\SIMULIA，这里改成你想要安装的位置，本人安装在D:\SIMULIA，点击next11、弹出提示窗口，点击yes，之后进行安装，很快安装完成出现如下界面，点击done，完成安装12、出现如下界面提示安装products，先不要点yes，先进行许可证文件的修改。

二、修改许可证文件13、将crack文件夹复制到桌面打开，里面有三个文件14、以文本文件打开abaqus.lic文件将this_host改成自己的计算机名15、之后进行保存关闭16、将'abaqus.lic'，将复制到安装目录中，本机是在D:\SIMULIA\License，新建abaqus.txt文档将扩张名.txt改成.log。

17、打开D:\SIMULIA\License中的lmtool.exe，打开Config Services，进行如图设置，后点击Save Services。

Abaqus拓扑优化分析手册13.优化技术13.1 结构优化：概述13.1.1 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——拓扑优化和形貌优化。

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单元而获得最优的设计目标。

形貌优化（Shape optimization）则是在分析中对指定的优化区域不断移动其表面节点从而达到减小局部应力集中的优化目标。

拓扑优化和形貌优化均遵从一系列优化目标和约束。

最优化方法（Optimization）是一个通过自动化程序增加设计者的经验和直觉，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的，做优化必须有更具体的描述。

比方说，想要降低在两种不同载荷工况下（Load Step）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）。

可以使用Abaqus/CAE创建待优化的模型，然后定义、配置和执行结构优化。

更多信息请参考Abaqus/CAE User’s Guide的第十八章“The Optimization module”。

13.1.1.1术语（Terminology）结构优化拥有它自己的一套术语。

以下术语适用于整个Abaqus帮助文档以及Abaqus/CAE用户界面。

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。

一定的边界条件、载荷及人为约束下：●拓扑优化通过增加/删除区域中的材料达到最优化设计●形貌优化通过移动区域内的节点来达到优化的目的。

ABAQUS学习总结1.ABAQUS中常用的单位制。

-（有用到密度的时候要特别注意）单位制错误会造成分析结果错误，甚至不收敛。

2.ABAQUS中的时间对于静力分析，时间没有实际意义（静力分析是长期累积的结果）。

对于动力分析，时间是有意义的，跟作用的时间相关。

3.更改工作路径4.对于ABAQUS/Standard分析，增大内存磁盘空间会大大缩短计算时间;对于ABAQUS/Explicit分析，生成的临时数据大部分是存储在内存中的关键数据，不写入磁盘，加快分析速度的主要方法是提高CPU的速度。

临时文件一般存储在磁盘比较大的盘符下提高虚拟内存5.壳单元被赋予厚度后，如何查看是否正确。

梁单元被赋予截面属性后，如休查看是否正确。

可以在VIEW的DISPLAY OPTION里面查看。

6.参考点对于离散刚体和解析刚体部件，参考点必须在PART模块里面定义。

而对于刚体约束，显示休约束，耦合约束可以在PART ,ASSEMBLY,INTERRACTION,LOAD等定义参考点.PART模块里面只能定义一个参考点，而其它的模块里面可以定义很多个参考点。

7.刚体部件（离散刚体和解析刚体），刚体约束，显示体约束离散刚体：可以是任意的形状，无需定义材料属性，要定义参考点，要划分网格。

解析刚体：只能是简单形状，无需定义材料属性，要定义参考点，不需要划分网格。

刚体约束的部件：要定义材料属性，要定义参考点，要划分网格。

显示体约束的部件:要定义材料属性，要定义参考点，不需要要划分网格(ABAQUS/CAE会自动为其要划分网格)。

刚体与变形体比较:刚体最大的优点是计算效率高，因为它在分析作业过程中不参与所在基于单元的计算，此外，在接触分析，如果主面是刚体的话，分析更容易收敛。

刚体约束和显示体约束与刚体部件的比较：刚体约束和显示体约束的优点是去除约束后，就可以立即变为变形体。

刚体约束与显示体约束的比较:刚体约束的部件会参与计算，而显示约束的部件不会参与计算，只是用于显示作用。

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。

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。

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。

配置拓扑优化任务优化模块提供了各种设置，允许您配置拓扑优化任务。

配置设置取决于您是为一般拓扑优化配置优化任务，还是为基于条件的拓扑优化配置优化任务。

包括以下主题:“配置一般拓扑优化任务”“配置基于条件的拓扑优化任务”配置一般拓扑优化任务一般拓扑优化是一种灵活的、基于敏感性的优化，允许您将一系列约束和目标函数应用于模型。

您可以使用优化任务编辑器自定义一般拓扑优化的各个方面。

要定位编辑器，请从主菜单栏中选择Task-Edit-optimization任务名称。

要指定一般拓扑优化，请选择Advanced选项卡并选择general optimization(基于灵敏度)。

包括以下主题:“配置基本设置”“配置密度设置”“配置扰动设置”收敛“配置选项”“配置高级选项”配置基本设置配置基本设置:1.在优化任务编辑器中，单击Basic选项卡。

2.选择是冻结荷载还是边界条件区域。

建议您冻结应用指定条件的区域，因为您不希望在优化过程中删除这些区域。

冻结这些区域可以稳定优化，并常常导致迭代次数显著减少。

配置密度设置配置密度设置:在优化任务编辑器中，单击Density选项卡。

选择密度更新策略。

此设置控制优化模块在优化期间更新设计元素的相对材料密度的速度。

在大多数情况下，您应该接受默认设置(正常)。

然而，如果设计响应非常敏感，并且在满足约束方面存在问题，则可能需要更保守的速率，这需要更多的优化迭代。

在初始优化迭代过程中，指定每个元素的相对密度:选择优化产品默认值，允许优化模块确定初始密度。

如果选择材料体积作为约束，优化模块计算初始密度，使体积约束得到准确的满足。

如果选择材料体积作为目标函数，每个元素的初始相对密度为50%。

选择指定并输入一个值(0.0 <初始密度≤1.0)。

只有在选择体积作为目标函数而不是约束时，才应该使用此选项;如果您知道，在优化之前，将初始密度设置为较大或较小的值将满足其他约束;例如，位移约束。