Inelastic analysis of 2D solids using a weak-form RPIM based on deformation theory Original Research Article

A radial point interpolation method (RPIM) is presented for inelastic analysis of 2D problems. In this method, the problem domain is represented by a set of scattered nodes and the field variable is interpolated using the field values of local supporting nodes. Radial basis function (RBF) augmented with polynomials is used to construct the shape functions. These shape functions possess delta function property that makes the numerical procedure very efficient and many techniques used in the finite element method can be adopted easily. Galerkin weak-form formulation is applied to derive the discrete governing equations and integration is performed using Gauss quadrature and stabilized nodal integration. The pseudo-elastic method proposed by H. Jahed et al. is employed for the determination of stress field and Hencky’s total deformation theory is used to define the effective material parameters. Treated as field variables, these parameters are functions of the final state of stress fields that can be obtained in an iterative manner based on pseudo-linear elastic analysis from one-dimensional uniaxial material curve. A very long thick-walled cylinder and a V-notched tension specimen are analyzed and their stress distributions match well with those obtained by finite element commercial software ANSYS or the available literature.