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论文类型：期刊论文

发表时间：2018-01-06

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：SCIE、EI

卷号：113

期号：1

页面范围：82-108

ISSN号：0029-5981

关键字：BEM; element differential method (EDM); FEM; Lagrange isoparametric elements; shape functions; thermal-mechanical problems

摘要：In this paper, a new numerical method, element differential method (EDM), is proposed for solving general thermal-mechanical problems. The key point of the method is the direct differentiation of the shape functions of Lagrange isoparametric elements used to characterize the geometry and physical variables. A set of analytical expressions for computing the first- and second-order partial derivatives of the shape functions with respect to global coordinates are derived. Based on these expressions, a new collocation method is proposed for establishing the system of equations, in which the equilibrium equations are collocated at nodes inside elements, and the traction equilibrium equations are collocated at interface nodes between elements and outer surface nodes of the problem. Attributed to the use of the Lagrange elements that can guarantee the variation of physical variables consistent through all elemental nodes, EDM has higher stability than the traditional collocation method. The other main features of EDM are that no mathematical or mechanical principles are required to set up the system of equations and no integrals are involved to form the coefficients of the system. A number of numerical examples of 2- and 3-dimensional problems are given to demonstrate the correctness and efficiency of the proposed method.