应力约束下三维连续体结构拓扑优化分析

Topological Optimization Analysis of Three Dimensional Continuum Structure with Stress Constraints

本文基于ICM(独立、连续、映射)方法,建立了以连续体结构重量为目标的应力约束下多工况的三维连续体结构拓扑优化模型。利用von Mises强度理论,提出了应力约束全局化方法,从而将局部的应力约束转化为全局的应变能约束,由此减少了约束数目,降低了问题的规模,避免了敏度分析。另外,利用对偶理论,将建立的优化模型转化为对偶模型,用序列二次规划法进行了求解,从而减少了设计变量的数目,提高了求解效率。借助MSC．Patran和MSC．Nastran提供的软件平台,利用PCL语言实现了本文的优化算法。数值算例验证了方法的可行性与有效性。

The optimal topology model of three dimensional continuum structure was established based on Independent Continuous Mapping （ICM） method, which refers to the weight as objective and subjected to the stress constraints with multi-load-cases. A globalization of stress constraints was proposed by virtue of yon Mises＇ yield criterion in machanics of materials. Thus, the transformation of local stress constraints of element into the global stain energy constraints of structure was achieved. As a result, the numbers of constraints was reduced, the computational complexity of both optimization algorithm and sensitivity analysis was decreased. Furthermore, the dual model corresponding to the optimal model of continuum structure was solved by serial quadratic programming. As a result, the number of design variables is dramatically cut down, the efficiency of computation is improved. In addition, the present optimal model and its algorithm have been implemented by means of MSC/Patran software platform using Patran Command Language （PCL）. Numerical examples indicate that the method is effective and efficient.