DIRECT FORMULATION OF QUADRILATERAL PLANE ELEMENT WITH QUASI-CONFORMING METHOD——INTO THE FORBIDDEN ZONE OF FEM

Xia Yang; Hu Ping; Tang Limin

doi:10.6052/0459-1879-12-105

Volume 44 Issue 5

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Chinese Journal of Theoretical and Applied Mechanics > 2012 > 44(5): 839-850. > DOI: 10.6052/0459-1879-12-105 CSTR: 32045.14.0459-1879-12-105

Xia Yang, Hu Ping, Tang Limin. DIRECT FORMULATION OF QUADRILATERAL PLANE ELEMENT WITH QUASI-CONFORMING METHOD——INTO THE FORBIDDEN ZONE OF FEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(5): 839-850. DOI: 10.6052/0459-1879-12-105

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DIRECT FORMULATION OF QUADRILATERAL PLANE ELEMENT WITH QUASI-CONFORMING METHOD——INTO THE FORBIDDEN ZONE OF FEM

1.
School of Automotive Engineering, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
2. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

Funds: The project was supported by the National Natural Science Foundation of China (10932003,11272075),the National High Technology Research and Development Program of China (2009AA04Z101),the National Basic Research Project of China (2010CB832700) and the Great Project of Ministry of Industrialization and Information of China (2011ZX04001-21).

Received Date: April 17, 2012
Revised Date: May 27, 2012

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Abstract

Abstract

The direct formulation of quadrilateral plane element in rectangular Cartesian coordinate system has been a forbidden zone for finite element method.In this paper,the quasi-conforming finite element method is applied on this problem and a bilinear element as well as complete second-order element is constructed.Meanwhile,the convergence analysis of the elements is carried out with "Taylor expansion test" and the comparative study with isoparametric element is also considered.The results show the direct formulation of quadrilateral plane elements is feasible within the quasi-conforming framework,and there is not any convergence problem with these elements.Therefore the finite element theory concerning plane element can be unified by quasi-conforming framework.Compared with isoparametric elements,the bilinear element present in this paper is easy to formulate,with stable performance and explicit stiffness matrix for the plane problem analysis.
- quasi-conforming,
- plane element,
- finite element method,
- weak form derivative,
- Taylor expansion test

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