基于无网格法的热力耦合周期性结构多目标拓扑优化

Multiobjective Topology Optimization of Thermo-mechanical Coupling Periodic Structure Based on Meshless Method

基于网格类方法的结构拓扑优化易出现网格依赖性和棋盘格等数值不稳定现象。采用无网格伽辽金(Element-free galerkin,EFG)法建立了正交各向异性材料热力耦合周期性结构的多目标拓扑优化模型,以结构柔度和散热弱度的加权函数为目标函数,并通过重新分配不同子域内对应节点处的目标函数灵敏度保证结构的周期性。研究了权系数、设计子域数、泊松比因子、热导率因子及材料方向角对EFG最优多目标周期性拓扑结构和目标函数的影响,并得到了上述参数值的合理范围。与有限元拓扑优化结果对比验证了模型的正确性,结果表明该模型不使用敏度过滤技术也能获得清晰的结构轮廓边界,并利用3D打印技术加工了最优周期性结构。最后,选取了一组最优参数对正交各向异性材料结构进行了EFG多目标周期性拓扑优化设计,并与各向同性材料结构对比发现,正交各向异性材料最优周期性拓扑结构的温度场、位移场和应力场均有明显改善,加权目标函数、结构柔度和散热弱度分别降低了6.5%、32.6%和48.6%,体现了正交各向异性材料多目标周期性结构的性能优势。建立的无网格法拓扑优化模型,为复合材料周期性结构的轻量化设计提供了重要的理论指导。

Structural topology optimization based on mesh method is prone to numerical instability such as mesh dependence and checkerboard.The multiobjective topology optimization model of thermo-mechanical coupling periodic structure for orthotropic material is established using the Element-free Galerkin(EFG) method.The weighted function of compliance and heat dissipation is defined as the objective function,and then the periodicity of the structure is ensured by readjusting the objective function sensitivity of corresponding nodes in the different subdomains.The effects of the weight coefficient,number of design subdomains,Poisson’s ratio factor,thermal conductivity factor,and off-angle on the EFG optimal multiobjective periodic topological structure and objective function are studied,and the reasonable ranges of the above parameter values are obtained.The correctness of the proposed model is verified by the topological results based on the finite element method,and the results show that the present model can generate a clearer structure boundary profile without using sensitivity filtering technique,then the EFG optimal multiobjective periodic structures are manufactured by 3D printing technology.Finally,a group of optimal parameters is selected to carry out the EFG multiobjective periodic topology optimization design of orthotropic structure,and the optimal result is compared with isotropic structure.It is found that the temperature,displacement and stress field of the optimal periodic topological structure with orthotropic material are significantly improved,and the value of the weighted objective function,compliance and heat dissipation are reduced by 6.5%,32.6%and 48.6% respectively,which reflects the performance advantages of the multiobjective periodic structure with orthotropic material.The proposed topology optimization model based on meshfree method provides an important theoretical guidance for the lightweight design of composite periodic structure.