用于金属切削的粒子有限元方法、ALE方法和SPH方法比较以及求解器开发

A Comparison among PFEM,ALE and SPH Methods with the Numerical Solver Development for Machining Simulation

基于粒子有限元方法(Probabilistic Finite Element Method,PFEM)开发了金属切削粒子有限元求解器,用于测试二维和三维垂直切削算例。三维切削可以直接用于复杂结构,并和ALE方法和SPH方法做了原理性比较。PFEM方法目前尚无公开的商业和开源软件,但表现出了良好的自由边界跟踪效果,可以直接使用有限元方法的边界条件和接触算法。目前,计算机算力很强,弥补了PFEM方法作为无网格方法存在的计算效率缺陷。PFEM同时兼具无网格方法和有网格方法的优点。作为无网格方法,它避免了ALE方法在紊乱网格和规则网格之间区域重分算法和守恒算法的复杂性;作为有网格方法,它避免了SPH方法在邻近点和边界条件上的缺陷。后续工作会针对非均匀网格边界重构、网格自适应、并行计算和三维复杂切削展开进一步研究。

We compare the principles among the Particle Finite Element Method(PFEM),ALE and SPH,and use the PFEM to develop a numerical solver for machining simulation.We test 2D and 3D orthogonal cutting problems and the 3D numerical solver could be used for more complex problems.According our knowledge,there is no commercial or open source software which uses the PFEM.The PFEM shows very good advantages for solving free boundary problems,and the boundary conditions and contact algorithm from finite element methods could be used directly.Because of the strong power and cheap cost of computers,this improves the computational efficiency of the PFEM as a meshless method.The PFEM has the advantages from mesh and meshless methods.As a meshless method,the PFEM avoid the very complex algorithm of the ALE from distoration meshes to regular meshes with conversation laws.As a mesh method,the PFEM avoid the disadvantages of the SPC from neighbour particles and boundary conditions.In the future,we will continue to improve the PFEM solver for the surface reconstruction of uniform point clouds,mesh adaptive algorithms,parallel computing and complex 3D machining problem.