三维弹性力学改进的插值型维数分裂无单元Galerkin方法权函数研究

Study on weight function of the improved interpolating dimension splitting element-free Galerkin method for 3D elasticity problems

三维弹性力学改进的插值型维数分裂无单元Galerkin方法的关键是将三维问题转化为二维问题.二维问题采用改进的插值型无单元Galerkin法进行求解,分裂方向上采用有限差分法.在构造形函数时,权函数对其具有较大影响.研究三次样条函数、四次样条函数、指数函数和正定紧支径向基函数为权函数时,三维弹性力学改进的插值型维数分裂无单元Galerkin方法数值计算结果的计算精度和计算效率.并与改进的无单元Galerkin方法计算结果进行比较,说明该方法的优越性及权函数的重要性.

The key of the improved interpolation dimension splitting element-free Galerkin(IIDSEFG)method for three-dimensional(3 D)elasticity problems is to transform the 3 D problem into a series of related 2 D problems.The improved interpolation element-free Galerkin method is used to solve these 2 D problems,and the finite difference method(FDM)is used in the splitting direction.In the course of constructing the shape function,weight function has great influence on it.In this paper,the calculation accuracy and efficiency of numerical results of 3 D elasticity examples are studied when cubic spline function,quartic spline function,exponential function and compactly supported basis radial function are selected as weight function.Compared with the improved element-free Galerkin(IEFG)method,the superiority of the IIDSEFG method and the importance of weight function research are illustrated.