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多工况应力和位移约束下连续体结构拓扑优化
引用本文:隋允康,杨德庆,王备.多工况应力和位移约束下连续体结构拓扑优化[J].力学学报,2000,32(2):171-179.
作者姓名:隋允康  杨德庆  王备
作者单位:1. 北京工业大学机电学院力学部,北京,100022
2. 大连理工大学工程力学系,大连,116023
摘    要:将文「1」所提出的对拓扑变量的独立连续映射(IGM)的拓扑估化方法应用于连续体结构,从而建立了统一的以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型。通过对位移-应力拓扑解和各工况下应力拓扑解的综合协调,进而对于协调拓扑解按照阈值完成从离散到连续的反演,并且采用分层与加权策略克服了“荷载病态”困难。给出的经典的二维平面问题和三维连续体结构拓扑优化算例表明,这种统一的模型由骨架结构发展到连续

关 键 词:连续体  结构拓扑优化  多工况  应力约束  位移约束
收稿时间:1999-5-7

TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE WITH STRESS AND DISPLACEMENT CONSTRAINTS UNDER MULTIPLE LOADING CASES
Sui Yunkang,Yang Deqing,Wang Bei.TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE WITH STRESS AND DISPLACEMENT CONSTRAINTS UNDER MULTIPLE LOADING CASES[J].chinese journal of theoretical and applied mechanics,2000,32(2):171-179.
Authors:Sui Yunkang  Yang Deqing  Wang Bei
Abstract:ICM (Independent Continuous Mapping) methodology is used to establish an optimization model for continuum structure in which the formulation is identical to skeleton structure's. The model minimizes the structural weight with stress and displacement constraints for multiple loading cases. The topological variable is independent so that it doesn't attach to the sectional or shape variable any longer. Moreover, the topological variable is continuous instead of discrete because of the use of a filter function. The filter function can also recognize element weight, stiffness and allowable stress and it is the key to construct ICM model. Inverse mapping from the continuous variable to the discrete variable is implemented using an adaptive threshold. In each iteration, stress topology variables and displacement topology variables are obtained using the zero order and the first order approximate models respectively and the later is the solution of a quadratic programming that is a second order approximation of the dual programming corresponding to the primal problem with displacement constraints under multiple loading cases. A multiple--level strategy and a weight factor are used when the loads are of different order of magnitude whose state is called as ill loading case in the paper. Typical topology optimization examples of both two and three dimension show that the method is successfully extended from the skeleton structure to the continuum structure.
Keywords:structural topological optimization  independent and continuous topological variable  filter function  mapping method  continuum structure  
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