| 罗阳军,亢战,蔡坤.考虑非概率可靠性的结构柔顺度拓扑优化设计[J].计算力学学报,2011,28(6):821~826 |
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| 考虑非概率可靠性的结构柔顺度拓扑优化设计 |
| A compliance based topology optimization design of structures considering non-probabilistic reliability |
| 投稿时间：2010-09-28 修订日期：2011-03-15 |
| DOI：10.7511/jslx20116002 |
| 中文关键词: 凸模型 非概率可靠性 柔顺度 拓扑优化 Minimax问题 |
| 英文关键词:convex model non-probabilistic reliability compliance topology optimization minimax problem |
| 基金项目:国家自然科学基金(51008248);陕西省自然科学基金(2010JQ1008);西北工业大学基础研究基金(JC200936)资助项目. |
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| 中文摘要: |
| 实际工程中广泛存在的不确定性可能对结构拓扑设计产生重要影响。基于不确定性的多椭球凸模型描述及非概率可靠性指标的定义,建立了材料体积约束和不确定参数范围约束下、结构柔顺度极小极大化为目标的非概率可靠性拓扑优化数学模型。结合移动渐进线方法,基于单循环策略实现该连续Minimax优化问题的求解。经典算例尺寸优化设计结果说明了进行非概率可靠性拓扑优化设计的实际意义,即相对于确定性优化而言,在相同的可靠性要求下,非概率可靠性拓扑优化能够达到更为经济有效的设计要求。数值算例验证了本文优化模型及数值算法。 |
| 英文摘要: |
| 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. |
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