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Indexed by:Journal Papers

Date of Publication:2019-12-01

Journal:COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals:EI、SCIE

Volume:78

Issue:11

Page Number:3563-3585

ISSN No.:0898-1221

Key Words:Element differential method (EDM); Element collocation method; Triangular and tetrahedral element; Strong formulation; New shape functions

Abstract:A novel strong form numerical method, Element Differential Method (EDM), is developed to solve geometrically complex mechanics problems based on triangular or tetrahedral meshes. The discretization of the structure under investigation has been based on Lagrange isoparametric quadrilateral or hexahedral elements while applying EDM. In this paper, a new family of isoparametric triangular and tetrahedral elements with a central node is proposed for EDM. A set of shape functions with analytical expressions for their first and second order partial derivatives is constructed for these triangular and tetrahedral elements, respectively. Moreover, a new element collocation scheme is proposed to establish a system of equations directly from the governing differential equations for internal nodes and traction-equilibrium equations for nodes on edges of an element. In this collocation scheme, no variational principles or virtual energy principles are required to set up the solution scheme, while no integration is needed when forming the coefficients of the system of equations. Numerical examples including standard patch tests and more practical problems are given to demonstrate the correctness of the constructed elements and the efficiency of the proposed element collocation method. (C) 2019 Elsevier Ltd. All rights reserved.