Geometrically Non-linear Analysis of Elastic Structures by Petrov-Galerkin Natural Element Method

Abstract

This paper is concerned with the geometrically non-linear analysis of elastic structures using the natural element method, particularly a Petrov-Galerkin Natural Element Method (PG-NEM). The geometrically non-linear problem is linearized and formulated by the Taylor series expansion and the Total Lagrangian (TL) method. The Voronoi polygon-based Laplace Interpolation (LI) functions are used to approximate the displacement increments, while the Delaunay triangle-supported Constant-Strain (CS) basis functions are adopted for the expansion of the virtual displacement. The iterative computation is performed by the Newton-Raphson method, and a set of Delaunay triangles serves as a background cell for the traditional Gauss integration rule-based numerical integration. The proposed PG-NEM is illustrated through the numerical experiments, and its numerical accuracy is compared with MSC/Marc, CS-FEM and BG-NEM.