Hybrid boundary point interpolation methods and their coupling with the element free Galerkin method

Hybrid boundary point interpolation methods (HBPIM and HBRPIM) are presented for solving boundary value problems of two-dimensional solids. In HBPIM and HBRPIM, the boundary of a problem domain is represented by properly scattered nodes. The point interpolation methods are used to construct shape functions with Kronecker delta function properties based on arbitrary distributed boundary nodes. Boundary conditions can be implemented with ease as in the conventional boundary element method. In HBPIM and HBRPIM, the,stiffness' matrices so obtained are symmetric. This property of symmetry can be an added advantage in coupling the HBPIM and HBRPIM with other established meshfree methods. A novel coupled element free Galerkin (EFG)/HBPIM (or HBRPIM) method for 2D solids is then developed. The compatibility condition on the interface boundary is introduced into the variational formulations of HBPIM, HBRPIM and EFG using the Lagrange multiplier method. Coupled system equations are derived based on the variational formulation. The validity and efficiency of the present HBPIM, HBRPIM and coupled methods are demonstrated through the numerical examples. It is found that presented methods are very efficient for solving problems of computational mechanics. (C) 2003 Elsevier Ltd. All rights reserved.