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Indexed by:期刊论文

Date of Publication:2017-01-01

Journal:ENGINEERING COMPUTATIONS

Included Journals:SCIE、EI

Volume:34

Issue:8

Page Number:2731-2751

ISSN No.:0264-4401

Key Words:Finite element method; Fundamental analytical solutions; Quasi-conforming

Abstract:Purpose - Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conformingmethod and fundamental analytical solutions to overcome the difficulties.
   Design/methodology/approach - First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration.
   Findings - The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy.
   Originality/value - New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.