• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (19): 116-122.

• 论文 • 上一篇    下一篇

双材料结构非概率可靠性拓扑优化设计

罗阳军;王彦飞;岳珠峰   

  1. 西北工业大学力学与土木建筑学院
  • 发布日期:2011-10-05

Non-probabilistic Reliability Based Topology Optimization Design of Two-material Structures

LUO Yangjun;WANG Yanfei;YUE Zhufeng   

  1. School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University
  • Published:2011-10-05

摘要: 利用凸模型描述和非概率可靠性的量化定义,研究存在材料属性、几何及荷载不确定性的双材料结构拓扑优化问题。基于扩展的相对密度惩罚方法,建立优化模型为给定材料体积约束下,同时满足可靠性要求的连续型极小极大优化问题,以寻找两种不同实心材料的最优联合材料分布布局。采用序列近似规划策略,结合不确定参数直接迭代公式和移动渐近线方法来求解该极小极大优化问题。该方法可把原问题转化为一系列近似的确定性优化问题,从而极大减少了计算量。数值研究表明,存在的不确定性可能对双材料结构的最优联合布局产生较大影响,优化模型和数值算法为双材料结构拓扑设计提供了一个有效途径。

关键词: 非概率, 双材料结构, 拓扑优化, 序列近似规划

Abstract: Using the convex model description and the quantified definition of the non-probabilistic reliability, topology optimization of two-material structures considering uncertainties in material properties, geometry and loads is studied. Based on the extended penalization scheme of relative density, a continuous minimax optimization problem, which satisfies the material volume constraint and the reliability requirement, is presented for finding the united distribution of two candidate materials. The minimax problem is solved in the sequential approximate programming manner by embedding a direct iterative formula and the method of moving asymptotes (MMA). The computation cost is thus greatly decreased since the original problem is transformed into a series of deterministic ones. Numerical examples show that system uncertainties may have considerable effects on the optimal united layout of two-material structures. The results prove that a powerful approach for the topology design of two-material structures is furnished by the proposed numerical technique.

Key words: Non-probabilistic, Sequential approximate programming, Topology optimization, Two-material structure

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