基于Ordered-RAMP模型的热固耦合结构多材料拓扑优化方法

针对传统单材料热固耦合拓扑优化设计难以实现结构材料与性能综合最优的问题,提出一种基于变密度理论有序材料属性有理近似模型的多材料拓扑优化方法.该方法通过搭建比例系数与平移系数,将多种材料属性采用0,1]连续分布的单设计变量进行描述,并研究和比较与有序固体各向同行惩罚微结构模型的优缺点;其次借助归一化加权方法定义以结构柔度最小化和散热弱度最小化为目标函数的数学模型.结合设计变量敏度分析,详细推导多材料、多目标条件下热固耦合结构拓扑优化的迭代公式.通过数值算例分析对比了不同权系数以及不同材料属性组合对优化结果的影响;结果表明,所提出的优化方法在热固耦合结构多材料多目标拓扑优化设计中具有可行性和有效性.

Multi-material Topology Optimization for Thermo-elastic Coupling Structure Based on Ordered-RAMP Method

In general,it is difficult for single material thermo-elastic coupling topology optimization to obtain the comprehensive optimum of structural materials and properties.In this study,a multi-material topology optimization approach based on the ordered rational approximation of material properties(Ordered-RAMP)is proposed.In this method,the proportional and translation coefficients are established and the associated materials properties are described by a single design variable with0,1]continuous distribution.The pros and cons of the proposed method were investigated and compared with the ordered solid isotropic microstructures with penalization(Ordered-SIMP).The normalized weighting method is introduced to construct the multi-objective function with minimization of structural compliance and heat dissipation,followed by sensitivity analysis of design variables.The iterative formation of thermo-elastic coupling topology optimization is derived under the multi-material and multi-objective conditions.The effects of weight coefficients and materials combination on the optimal results were analyzed through numerical examples.The results are shown that the proposed method is feasible and efficient to the multi-thermo-elastic coupling topology optimization problems.