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工程力学  2014 

位移约束刚架拓扑优化的非线性有无复合体方法

DOI: 10.6052/j.issn.1000-4750.2013.04.ST09, PP. 15-19

Keywords: 结构拓扑优化,非线性有无复合体,刚架结构,重量极小化,位移约束

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Abstract:

为了提高基于物理模型的结构拓扑优化的寻优效率,该文提出了非线性有无复合体,以刚架结构在位移约束下的拓扑优化为例,进行了结构重量目标函数极小化的数学模型建立和程序实现。与线性有无复合体不同,非线性有无复合体是无限多个无穷小的“有单元”和“无单元”各自长度的非线性组合。由于每个梁单元“有”单元长度和“无”单元长度之和的不变性,其拓扑变量可以用“有”单元的总长度予以表达。推导了结构重量、位移约束同结构拓扑变量的显式函数,建立了优化模型。使用线性规划算法求解了相应的优化模型,算例表明,该文方法的寻优效率得到了提高。同作为数学变换的ICM(独立、连续和映射)方法比较,该文提出的作为物理模型的方法,二者在解决结构拓扑优化上具有异曲同工之效:后者的“有”单元长度的非线性关系替代了前者的单元重量、位移约束中的过滤函数。数学变换方法与物理模型方法的异同点更是耐人寻味。方法

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