Abstract
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.
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Zhen-yi, J., Kai-yuan, Y. An exact element method for bending of nonhomogeneous thin plates. Appl Math Mech 13, 683–690 (1992). https://doi.org/10.1007/BF02451534
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DOI: https://doi.org/10.1007/BF02451534