A cell-based smoothed radial point interpolation method using condensed shape functions for free and forced vibration analysis of solids

Abstract

In this work, a novel cell-based smoothed radial point interpolation method (CS-RPIM) has been developed for free and forced vibration analysis of solids by using condensed radial point interpolation method (RPIM) shape functions with virtual points. In the scheme of the present method, the generalized gradient smoothing technique (GST) is used for constructing smoothed strains and the ingenious six virtual nodes are selected together with real nodes for creating condensed RPIM shape functions, which helps the proposed method avoid not only the overly-stiff problem existing in traditional finite element method (FEM) but also the overly-soft issue of original CS-RPIM models. Thanks to the well-constructed system stiffness, the proposed method has shown very good performance in terms of accuracy, efficiency and stability for the examples studied. As three-nodes triangular elements, that can be automatically generated for complex problem domains, are used as background mesh, the proposed method is supposed to possess good potential for solving practical engineering problems.