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RESEARCH PAPERS

On Certain Approximations in the Finite-Element Method

[+] Author and Article Information
R. W. McLay

Department of Mechanical Engineering, University of Vermont, Burlington, Vt.

J. Appl. Mech 38(1), 58-61 (Mar 01, 1971) (4 pages) doi:10.1115/1.3408767 History: Received October 20, 1969; Revised January 30, 1970; Online July 12, 2010

Abstract

Approximations made outside of the variational principle used in the finite-element method are examined for a restricted problem in elasticity. They are shown to be rigorous from the standpoint of a generalized variational principle in which Lagrange multipliers are utilized. The convergence of the Ritz solution to the exact solution is demonstrated. The bound is shown to be a function of the quality of both the displacement functions and other approximate functions in the analysis.

Copyright © 1971 by ASME
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