Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints
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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.Abstract: Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present.The main obstacle lies in that,the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method.Furthermore,large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach.In this paper,a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing.Moreover,the approximate explicit expressions are given between topological variables and stress or displacement constraints.The problem is well solved by using dual programming approach,and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous.Numerical examples verify the validity of proposed method.
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Key words:
- structure /
- optimization /
- topology optimization /
- modeling /
- dual programming
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