三维弹塑性自然单元法算法实现

自然单元法是一种新兴的无网格数值计算方法,其实质是基于自然相邻插值(C∞)的伽辽金法。该方法计算精度与四边形或六面体单元有限元法相当,自然相邻插值函数比其他无网格法插值函数的计算速度快。由于自然相邻插值在凸域的边界上的相邻点之间是严格线性的,所以自然单元法在边界面的处理也相当简单。本文研究了在自然单元法中采用Von.Mises,Mohr-Coulomb和Drucker-Prager屈服准则解决三维弹塑性问题,并编制了相应计算程序,最后通过算例验证算法的正确性。

The computational methods of natural element method in three dimensional elasto-plastic analysis

The Natural Element Method(NEM) is a recently developed meshless method and is the Galerkin Method based on the Natural Neighbour Interpolation essentially.The numerical results are almost equal to the results of the quadrangular or hexahedral finite element method,and the time cost involved in evaluating natural neighbour shape functions is less than that of other meshless methods.The Natural Neighbour Interpolation is strictly linear between adjacent nodes on the bound of the convex hull,which facilitates imposition of essential boundary condition.The algorithm for three dimensional elasto-plastic analysis based on the yield criteria of Von.Mises,Mohr-Coulomb and Drucker-Prager are presented.Each of them has an example to check its veracity.