二维无网格伽辽金-有限元耦合方法的研究

论述无网格伽辽金方法（element-free Galerkin method,EFG）的基本原理－－移动最小二乘原理（moving leastsquare,MLS）和EFG方法的位移近似函数，给出变分方程及离散方程。对无网格伽辽金－有限元耦合（EFG－FE coupling）方法进行详细阐述。编制相应程序，通过算例表明拉格朗日乘子对强制边界条件的作用及无网格伽辽金方法在权函数参数变化时的收敛特性，论证无网格伽辽金－有限元耦合的有效性。

STUDIES ON TWO-DIMENSIONAL ELEMENT-FREE GALERKIN-FINITE ELEMENT COUPLING METHOD

The element free Galerkin (EFG) method which is based on the moving least square interpolant is studied. The approximation and the selection of the weight function are described. In order to implement EFG method through computer program, the discrete equation from the variational principle (weak form) are carried out. The Lagrange multipliers are used to make the weak form of the equilibrium equation satisfied the boundary conditions. A cell structure which is independent to the nodes is used to evaluate the integrals of EFG method. An element free Galerkin finite element coupling (EFG FE coupling) method is then presented and implemented. Two numerical examples are carried out using the EFG method. The first is apparent that the imposition of essential boundary conditions by Lagrange multipliers is imperative. The second shows the rate of convergence when changing the data of weight function and how to select the data. Finally, the validity and effectivity of the presented EFG FE coupling method is also verified through comparing the numerical solutions with the theoretical ones.