追究根基的结构拓扑优化方法  

A STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON EXPLORING CONCEPTUAL ROOT

作　　者：隋允康[1] 叶红玲[1] 刘建信[1] 陈实[1] 宇慧平[1] 

机构地区：[1]北京工业大学工程数值模拟中心,北京100124

出　　处：《工程力学》2008年第A02期7-19,共13页Engineering Mechanics

基　　金：国家自然科学基金项目(10472003);汽车车身先进设计制造国家重点实验室开放基金项目(30715002);高校博士点基金项目(20060005010)

摘　　要：结合作者在结构拓扑优化方面的研究工作,围绕了ICM(独立、连续、映射)方法涉及的基本概念上的突破,叙述了将本质上为0-1离散变量的拓扑优化问题转化为连续变量优化问题的具体做法,其中介绍了若干要点:以阶跃函数把离散问题化为连续问题即完成关键的等价性转换是第一步;定义磨光函数逼近阶跃函数的可操作的近似是第二步;引入作为磨光函数反函数的过滤函数实现映射性建模是第三步;采用某些光滑算法求解连续变量模型则是第四步。通过连续体结构的典型数值算例说明了将结构拓扑优化的模型转化为独立层次的拓扑优化过程。该方法对于纯数学的0-1离散变量优化的求解也适用,方法与数值都表明了这一点。This paper introduces the transformation of the 0-1 discrete variables into continuous variables in topological optimization problem by ICM （Independence, continuous and Mapping） method. The first step is to convert equivalently the discrete problem into continuous problem taking advantages of the step-up function; The second step is to define the polish function to approach the step-up function; The third step is to establish the mapping model by introducing the filter function which is the inverse function of the polish function; The fourth step is to solve the model with continuous variables by some smooth algorithms. Some representative numerical examples of continuous structures have illustrated the process of transforming the topological optimization model into independent level one. This method and the numerical solutions show that the method is also suitable for pure mathematical optimization problems with 0-1 discrete variables.

关 键 词：结构拓扑优化 ICM方法 0-1离散变量数学规划 优化模型的建立 磨光函数 过滤函数 

分 类 号：O34[理学—固体力学]