Abstract
In this paper, based on the step reduction method and exact analytic method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergence of displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well. Four numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.
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Zhen-yi, J. An exact element method for the bending of nonhomogeneous Reissner's plate. Appl Math Mech 12, 1065–1074 (1991). https://doi.org/10.1007/BF02457489
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DOI: https://doi.org/10.1007/BF02457489