A compliance based topology optimization design of structures considering non-probabilistic reliability
Received:September 28, 2010  Revised:March 15, 2011
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KeyWord:convex model  non-probabilistic reliability  compliance  topology optimization  minimax problem
罗阳军 西北工业大学力学与土木建筑学院, 西安
亢战 大连理工大学工业装备结构分析国家重点实验室, 大连
蔡坤 西北农林科技大学水利与建筑工程学院, 杨凌
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      In practical engineering, existing uncertainties may play an important role in structural topology optimization. Based on the multi-ellipsoid convex model for uncertainties and the definition of the non-probabilistic reliability index, a mathematical model for non-probabilistic reliability based topology optimization is proposed. The optimization objective is to minimax the structural compliance with the constraints on the material volume and the bounds of uncertainties. The single loop strategy combining with the method of moving asymptotes is adopted for the solution of the optimization problem. Then the meanings of the proposed topology optimization is revealed by a classical example of size optimization design, namely, the non-probabilistic topology optimization could yield more economical material layout than the deterministic optimization under equal reliability requirements. Numerical investigations illustrate the validity of the present model as well as the proposed numerical techniques.