导重法求解单工况的拓扑优化问题  

Guide-weight Method on Solving Topology Optimization Problems under Single Load Case

作　　者：李枝东[1] 刘辛军[1] 

机构地区：[1]清华大学精密仪器与机械学系,北京100084

出　　处：《机械工程学报》2011年第15期107-114,共8页Journal of Mechanical Engineering

基　　金：摩擦学国家重点实验室自主研究课题(SKLT10C02);国家高技术研究发展计划(863计划;2010AA101404);国家科技重大专项(2010ZX04004-116)资助项目

摘　　要：在拓扑优化中,因为设计变量多并且目标函数和约束函数都是设计变量的隐函数,求解难度较大,所以寻找更快更好的求解方法一直都是拓扑优化问题的研究重点。为此,将导重法引入到拓扑优化的求解中,介绍质量约束下求结构最优性能问题和性能约束下求结构最小质量问题的导重法迭代准则,采用密度惩罚(Solid isotropic material with penalization,SIMP)方法建立单工况下求最小柔度和最小质量这两类拓扑优化问题的优化模型,推导出用导重法求解这两类问题的迭代公式并计算了相应的算例,与ANSYS中采用的优化准则法(Optimality criteria,OC)和序列凸规划法(Sequential convex programming,SCP)进行对比分析。通过计算和对比分析显示出用导重法求解拓扑优化问题具有迭代公式简单、适用范围广、收敛速度快、求解效果好的优点。导重法为拓扑优化问题的求解提供了一条新的途径。About topology optimization,finding a good solution method for topology optimization problems is always paid attention to by the research field because they are subjected to the large number of the design variables and to the complexity that occurs because the objective and constraint functions are usually implicit with respect to design variables.Thus the guide-weight method is introduced into topology optimization.The iteration algorithms of the guide-weight method for solving problems seeking best structural performance under weight constraint and problems seeking least weight under structural performance constraint are described.Two kinds of topology optimization problems under single load case are constructed by solid isotropic material with penalization（SIMP） method and solved by the guide-weight method.Corresponding numerical examples are presented and comparison with the optimality criteria（OC） and sequential convex programming（SCP） methods employed in ANSYS is made.The examples and comparison demonstrate that the Guide-Weight method can solve topology optimization problems with simple iteration algorithm,wide availability,high efficiency and accuracy.This method provides alternative for solving topology optimization problems.

关 键 词：拓扑优化 导重法 单工况 

分 类 号：TP31[自动化与计算机技术—计算机软件与理论] TH11[自动化与计算机技术—计算机科学与技术]