A NORMED G SPACE AND WEAKENED WEAK (W²) FORMULATION OF A CELL-BASED SMOOTHED POINT INTERPOLATION METHOD

Abstract

This paper presents a normed G 1 space and a weakened weak (W 2 ) formulation of a cell-based smoothed point interpolation method (CS-PIM) for 2D solid mechanics problems using three-node triangular cells. Displacement fields in the CS-PIM are constructed using the point interpolation method (polynomial PIM or radial PIM) and hence the shape functions possess the Kronecker delta property facilitating the easy enforcement of Dirichlet boundary conditions. The edge-based T-schemes are introduced for selecting supporting nodes for creating the PIM shape functions and an adaptive coordinate transformation (CT) technique is proposed to solve the singularity problem for the moment matrix. Smoothed strains are obtained by performing the generalized smoothing operation over each triangular background cell. Because the nodal PIM shape functions can be discontinuous, a W 2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is then used to create the discretized system equations. Numerical examples including static, free and forced vibration problems have been studied to examine the present method in terms of accuracy, convergence, efficiency and temporal stability.