基于等几何分析的参数多孔结构拓扑优化

Topology Optimization for Parametric PorousStructure Based on Iso-Geometric Analysis

利用等几何分析方法求解薄板多孔结构最小柔度拓扑优化问题,在材料均匀分布的设计域中实现最佳的特征参数分布,以提高薄板多孔结构的力学性能.通过三向周期极小曲面(TPMS)设计多孔单元,并分析多孔单元特征参数与材料分布间的关系.该方法以多孔单元特征参数为优化变量求解优化问题,保证了静力平衡分析过程中应力函数的连续性,提高了计算精度.同时基于优化结果设计多孔结构可调控多孔单元数,且多孔单元间光滑连接.

We used iso-geometric analysis method to solve the minimum compliance topology optimization for the thin plate porous str ucture,and the optimal characteristic parameter distribution was realized in the design domain of uniformly distributed materials,which improved the mechanical perfor mance of the thin plate porous structure.The triply periodic minimal surface(TPMS)was presented to design the porous element,and the relationship between the porous element characteristic parameter and the material distribution was analyzed.The porous element characteristic parameters were taken as optimization v ariables to solve the optimization problem in the proposed method,which ensured the continuity of stress function in the process of static equilibrium analysis and improved the calculation accuracy.Meanwhile,the number of porous elements could be controlled by designing porous structure based on optimization results,and the porous elements were connected smoothly.