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 引用本文: 杨德庆, 隋允康, 刘正兴, 孙焕纯. 应力和位移约束下连续体结构拓扑优化[J]. 应用数学和力学, 2000, (1): 17-24.
Yang Deqing, Sui Yunkang, Liu Zhengxing, Sun Huanchun. Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints[J]. Applied Mathematics and Mechanics, 2000, (1): 17-24.
 Citation: Yang Deqing, Sui Yunkang, Liu Zhengxing, Sun Huanchun. Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints[J]. Applied Mathematics and Mechanics, 2000, (1): 17-24.

应力和位移约束下连续体结构拓扑优化

作者简介:杨德庆(1968~ ),男,博士后.
• 中图分类号: O223;TU323

Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints

• 摘要: 同时考虑应力和位移约束的连续体结构拓扑优化问题,很难用现有的均匀化方法或变密度方法等求解.主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式;即使建立了这种关系,也由于优化问题规模过大,利用常规的数学规划方法难以求解.隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换(ICM)的桁架结构拓扑优化模型.本文在此基础上,建立了以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型,并推导出应力及位移约束与拓扑设计变量间显式关系式.利用对偶规划简化模型,通过对应力拓扑解和位移-应力拓扑解的综合协调,进而对于拓扑协调解采用阈值完成从离散到连续的反演.数值算例验证了本文模型及算法的有效性.
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出版历程
• 收稿日期:  1998-11-27
• 修回日期:  1999-05-18
• 刊出日期:  2000-01-15

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