隋允康, 王西旺, 杜家政. 位移约束刚架拓扑优化的非线性有无复合体方法[J]. 工程力学, 2014, 31(5): 15-19. DOI: 10.6052/j.issn.1000-4750.2013.04.ST09
引用本文: 隋允康, 王西旺, 杜家政. 位移约束刚架拓扑优化的非线性有无复合体方法[J]. 工程力学, 2014, 31(5): 15-19. DOI: 10.6052/j.issn.1000-4750.2013.04.ST09
SUI Yun-kang, WANG Xi-wang, DU Jia-zheng. NONLINEAR EXIST-NULL COMBINED BODIES METHOD FOR FRAME TOPOLOGICAL OPTIMIZATION WITH DISPLACEMENTS CONSTRAINTS[J]. Engineering Mechanics, 2014, 31(5): 15-19. DOI: 10.6052/j.issn.1000-4750.2013.04.ST09
Citation: SUI Yun-kang, WANG Xi-wang, DU Jia-zheng. NONLINEAR EXIST-NULL COMBINED BODIES METHOD FOR FRAME TOPOLOGICAL OPTIMIZATION WITH DISPLACEMENTS CONSTRAINTS[J]. Engineering Mechanics, 2014, 31(5): 15-19. DOI: 10.6052/j.issn.1000-4750.2013.04.ST09

位移约束刚架拓扑优化的非线性有无复合体方法

NONLINEAR EXIST-NULL COMBINED BODIES METHOD FOR FRAME TOPOLOGICAL OPTIMIZATION WITH DISPLACEMENTS CONSTRAINTS

  • 摘要: 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

     

    Abstract: A nonlinear exist-null combined body is proposed to raise the efficiency of the searching optimum solution of structural topology optimization based on a physical model. As an example of topology optimization for a frame structure, a mathematical model for the minimization of structural weight is implemented to realize in procedure coding. In different with the linear exist-null combined body, the nonlinear one is a combination with infinite numbers of infinitesimal exist cells and nulls cells according to their nonlinear lengths. Owing to invariance property in sum of lengths between exist cells and nulls cells for each beam element, its topological variable can be expressed by total lengths of its exist cells. Structural weight and displacements constraints are deduced to build an optimization model. The model is solved by the algorithm of the linear programming to show the increasing efficiency of an optimizing point. The comparison of ICM (Independent, Continuous and Mapping) as a mathematical transformation method, the physical model presented has also different approaches but equally satisfactory results. A nonlinear relationship in length of the latter replaces the filter functions of element weight and displacements constraints of the former. Similarities and differences between the mathematical transformation method and the physical model method are an interesting problem affording for thought.

     

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