无单元伽辽金法新形函数技术

针对目前以移动最小二乘技术构造的无单元形函数需要大量的求逆运算,且在边界处无过点插值性质而给计算带来了困难的问题,以泰勒展开理论为基础,继承最小移动二乘法的高阶连续性,用Shepard插值实现"移动最小二乘法的由局部到整体区域的移动性"及"有限元法形函数过点插值性",旨在使无单元伽辽金法的形函数在满足高阶连续性的同时具有过点插值的性质,并避免了现有无单元伽辽金法形函数求解繁琐的缺点.

A new technique of shape function construction with element-free Galerkin method

The moving least-square technique is used to construct element-free shape function at present,so that a large amount of inverse matrix computation is necessary and,besides,there is no such property as point-passing interpolation at the boundary,so the a great difficulty happens with the computation.In this paper the Taylor expansion is taken as a theoretical basis,high-order continuity of moving least-square method is further inherited,and Shepard interpolation is adopted to obtain the mobility from local region to global one,which is characteristic with the method of moving least-square,and the property of point-passing interpolation of shape function,which is characteristic with the finite element method,in order to make the element-free Galerkin shape function to satisfy the requirement of high-order continuity and,at the same time,to have the property of point-passing interpolation and to avoid the tediousness with the solution by means of recent element-free Galerkin shape function.