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Research Papers

General Representations of Polynomial Elastic Fields

[+] Author and Article Information
Min-Zhong Wang

State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering,  Peking University, 100871 Beijing, P. R. China

Bai-Xiang Xu

Department of Mechanical and Process Engineering,  Institute of Applied Mechanics, TU Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany

Ying-Tao Zhao

Department of Mechanics,  School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, P. R. China

J. Appl. Mech 79(2), 021017 (Feb 24, 2012) (8 pages) doi:10.1115/1.4005556 History: Received December 20, 2010; Revised April 20, 2011; Posted January 30, 2012; Published February 13, 2012; Online February 24, 2012

For hybrid finite elements based, for example, on complementary energy functional, polynomial trial functions of stress fields are required. Systematic schemes are given for the 2D and 3D elasticity, respectively. For 2D problems, the paper shows that there are maximal four independent polynomials for the nth order homogeneous polynomial Airy stress functions: two for the first order, three for the second order, and four for the nth order (n not less than 3). For 3D problems, there are 3(2n + 1) independent polynomials for the nth order homogeneous polynomial displacement. The corresponding stress field can be given directly. As examples, explicit expressions of the corresponding independent polynomials are listed: up to the tenth order for the 2D case and up to the third order for the 3D case.

Copyright © 2012 by American Society of Mechanical Engineers
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