Affiliation:
1. Institute of Continuum Mechanics Leibniz Universität Hannover Garbsen Germany
2. State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian China
Abstract
AbstractIn this article, a novel weak‐form zonal Petrov–Galerkin free element method is proposed for two‐ and three‐dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong‐form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two‐ and three‐dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.
Funder
Alexander von Humboldt-Stiftung
Subject
Applied Mathematics,General Engineering,Numerical Analysis