Full-scale 3D structural topology optimization using adaptive mesh refinement based on the level-set method

摘要

We propose a parallel distributed and open-source framework for full-scale 3D structural topology optimization (TO). This can be achieved by properly combining parallel computing and mesh adaption techniques by adopting a reaction-diffusion equation (RDE) based level-set method. Mesh adaptivity which discretizes and optimizes an implicitly defined surface (level-set interface) can allow us to reach an optimal solution with high-resolution and clear boundaries. Our framework can be easily extended to design real world engineering products which have complex geometries, and optimized structures represented by body-fitted tetrahedral meshes can be efficiently post-processed. Furthermore, the proposed optimization algorithm can mitigate dependency to initial guess and mesh resolution to some extent. Our numerical implementation uses FreeFEM for finite element analysis (FEA), PETSc for distributed linear algebra, and Mmg for mesh adaption. Several numerical examples and 3D printed prototypes support these remarkable features.