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.
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On Certain Approximations in the Finite-Element Method
R. W. McLay
Department of Mechanical Engineering, University of Vermont, Burlington, Vt.
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McLay, R. W. (March 1, 1971). "On Certain Approximations in the Finite-Element Method." ASME. J. Appl. Mech. March 1971; 38(1): 58–61. https://doi.org/10.1115/1.3408767
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