基于参数化水平集的三维多相材料拓扑优化方法

3D topology optimization of multiphase materials using parametric level set method

参数化水平集拓扑优化解决了传统水平集方法数值计算复杂的问题,由于水平集拓扑优化需要引入更高级别的函数来构建拓扑模型,大部分关于参数化水平集拓扑优化的研究止于二维。文章在二维参数化水平集拓扑优化的基础上拓展到三维,结合点云的思想解决了三维拓扑构型的表达问题,并通过悬臂梁、简支梁等典型数值算例验证了算法能解决三维水平集无法引入更高维度函数等问题,亦讨论了引入SIMP(Solid Isotropic Material with Penalization)多材料插值模型的多相材料拓扑优化方法,以供多相材料拓扑优化方面研究进行参考。

Parametric level set topology optimization addresses numerical complexities associated with traditional level set methods.Since topological optimization using level sets requires introducing more advanced functions to construct topological models,most research on parametric level set topology optimization has been limited to two dimensions.This article extends the foundation of two-dimensional parametric level set topology optimization to three dimensions.By incorporating the concept of point clouds,it tackles the representation challenges of three-dimensional topological configurations.The algorithm is validated through typical numerical examples involving cantilever beams and simply supported beams,demonstrating its ability to address issues that arise when introducing higher-dimensional functions in three-dimensional level sets.Additionally,the article discusses the application of the SIMP(Solid Isotropic Material with Penalization)multi-material interpolation model for multi-material topology optimization,providing valuable insights for further research in this field.