Convergence of the Finite Element Method in the Theory of Elasticity

[+] Author and Article Information
M. W. Johnson

Department of Engineering Mechanics, University of Wisconsin, Madison, Wis.

R. W. McLay

Aerospace Division, The Boeing Company, Seattle, Wash.

J. Appl. Mech 35(2), 274-278 (Jun 01, 1968) (5 pages) doi:10.1115/1.3601191 History: Received August 23, 1966; Revised September 06, 1967; Online September 14, 2011


The foundations of the theory of the finite element method as it applies to linear elasticity are investigated. A particular boundary-value problem in plane stress is considered and the variational principle for the finite element method is shown to be equivalent to it. Mean and uniform convergence of the finite element solution to that of the boundary-value problem is demonstrated with careful consideration given to the stress singularities. A counterexample is presented in which a set of functions, admissible to the variational principle, is shown not to converge.

Copyright © 1968 by ASME
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