基于应变能的自适应EFG方法关键技术研究

Research on key technology of adaptive element-free Galerkin method based on strain energy

本文研究了基于应变能的自适应无网格伽辽金方法。给出自适应无网格伽辽金方法的原理、算法流程和程序实现,并对该方法中的关键技术进行了讨论,包括提出基于背景网格的误差估计方法、由结点组成的四边形或三角形局部结点加密技术和EFG-FE耦合方法及自适应搜索半径算法,计算了带小圆孔平板拉伸和圆柱体与刚性平面的弹性接触的算例。计算表明,该方法能在较少的计算规模下得到较正确的计算结果。

This paper mainly analyzes an adaptive Element-Free Galerkin Method （EFGM） procedure based on the gradient of swain energy.The schemes,including principle explanation,arithmetic analysis and programming realization,based on the gradient of strain energy are introduced.Key technology,including a cell error estimate based on background cells,a local domain refinement technique using quadrilateral or triangle composed of nodes,Element-Free Galerkin-Finite Element coupling method and adaptive algorithm which can change the size of influence domain with difference local nodal density are discussed.Through analysis an infinite plate with a circular hole problem and an elastic cylinder contacting with a rigid plane problem,the adaptive EFGM procedure correctness is verified.These numerical examples are shown that the automatic adaptive EFGM procedure is effective and valid.