具有增强计算效率和收敛性的多分辨率非线性拓扑优化

Multi-resolution nonlinear topology optimization with enhanced computational efficiency and convergence

高昂的计算成本和算法收敛困难是非线性拓扑优化的两大核心难题.为此,基于多分辨率设计策略和附加超弹性技术,提出了一种考虑几何非线性和材料非线性的多分辨率非线性拓扑优化方法.在固体各向同性材料惩罚方法框架中建立多分辨率非线性拓扑优化策略,并采用Neo-Hookean超弹性材料本构模型表征材料非线性.利用粗糙的分析网格用于有限元计算,而精细的材料网格用于描述材料构型.为了解决算法非线性收敛问题和降低灵敏度计算复杂度,联合ANSYS软件与附加超弹性技术进行非线性有限元计算.在灵敏度分析过程中,提出了一种应变能重分配策略,将Neo-Hooken和二阶Yeoh超弹性分析单元的应变能转换为对应的材料单元应变能.数值算例表明了所提出方法的三个显著优点:(1)可显著提高计算效率;(2)进一步弥补了基于附加超弹性技术的非线性拓扑优化方法在解决非线性拓扑优化问题时所遇到的收敛困难,该效果在三维问题中更为显著;(3)可在个人计算机上成功处理高分辨率三维复杂非线性拓扑优化问题.

Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.