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 应力和位移约束下连续体结构拓扑优化 引用本文： 杨德庆,隋允康,刘正兴,孙焕纯.应力和位移约束下连续体结构拓扑优化[J].应用数学和力学,2000,21(1):17-24. 作者姓名： 杨德庆  隋允康  刘正兴  孙焕纯 作者单位： 1. 上海交通大学,工程力学系,上海,2000302. 北京工业大学,机械学院,北京,1000103. 大连理工大学,工程力学系,大连,116024 摘    要： 同时考滤应力和位移约束的连续体结构拓扑优化问题，很难用现有的均匀方法或变密度方法等求解。主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式；即使建立了这种关系，也由于优化问题规模过大，利用常规的数学规划方法难以求解。隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换（ＩＣＭ）的桁架结构拓扑优化模型。本文在此基础上，建立了以重量为目标，考虑应力和位移约束的连续体结构拓扑优化模型，并推导出 关 键 词： 拓扑优化  对偶规划  连续体结构  应力  位移 修稿时间： 1998-11-27 Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints Yang Deqing,Sui Yunkang,Liu Zhengxing,Sun Huanchun.Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints[J].Applied Mathematics and Mechanics,2000,21(1):17-24. Authors: Yang Deqing  Sui Yunkang  Liu Zhengxing  Sun Huanchun Abstract: Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressions between topological variables and stress or displacement constraints can't be obtained using homogenization method or variable density method. Furthermore, large quantities of design variables in the problem makes it hard to deal with by the formal mathematical programming approach. In this paper, a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing. Moreover, the approximate explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solved by using dual programming approach, and the proposed element deletion criterion implement the inversions of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method. Keywords: structure  optimization  topology optimization  modeling  dual programming 本文献已被 CNKI 维普 万方数据 等数据库收录！