基于热固耦合问题的多尺度拓扑优化设计

Multi-scale topology optimization design based on thermo-mechanical coupling problem

基于均质材料的拓扑优化逐渐难以适应现代化生产对工业产品高品质、轻量化的需求,同时很多工业设备经常面临着高温和高负载的工作环境。为了提高结构在温度载荷和机械载荷共同作用下的力学性能,本文提出了一种在稳态热源作用下的热固耦合连续体结构并行化拓扑优化方法。以结构刚度作为目标函数,材料的体分比为约束,利用能量均匀化方法预测微结构的等效属性,建立热固耦合结构并行化拓扑优化数学模型。为便于数值计算,利用直接法进行灵敏度分析,同时采用Heaviside非线性密度过滤技术抑制数值不稳定性,将OC准则算法用于求解优化问题。数值算例表明,本文方法能够有效地进行优化设计且能显著地提高结构的刚度性能和散热性能。

Topological optimization based on homogeneous materials is difficult to meet the demand of modern production for high quality and light weight of industrial products,and many industrial equipment are often faced with high temperature and high load working environment.In order to improve the mechanical properties of a structure under temperature load and mechanical load,a concurrent topological optimization method for the thermo-mechanical coupled continuum structure under the action of a steady-state heat source is proposed in this paper.Taking the structural stiffness as the objective function and volume fraction ratio of the material as the constraint,the equivalent properties of the microstructure are predicted by using the energy homogenization method,and the mathematical model of topology optimization of the thermo-mechanical coupled structure is established.In order to facilitate numerical calculation,sensitivity analysis was carried out by direct method,meanwhile,Heaviside nonlinear density filtering technology was used to suppress numerical instability and OC criterion algorithm is used to solve the optimization problem.Numerical examples show that the proposed method can effectively optimize the design and significantly improve the stiffness and heat dissipation performance of the structure.