engleski

Dynamic analogies for proving the convergence of boundary value plate problems

This paper describes a procedure for proving the convergence and for estimating the numerical solution error of boundary value problems. The procedure is based on the transformation of a discrete boundary value problem into an equivalent discrete dynamic eigenproblem. Discrete dynamic eigenproblem has physical meaning in convergence analysis because a mass represents the measure of domain discretization. The convergence and accuracy of numerical solution of boundary value problem depend on the convergence of discrete dynamic eigenproblem spectrum. The developed procedure is relatively simple, easy to perform ; in this paper it is used to evaluate the convergence and accuracy of numerical solution of the thin plate bending problem. The plate is discretized with four-node finite elements. One translational and two rotational degrees of freedom, which are independent of each other, are associated to each node of the plate. The shape functions satisfy a homogenous differential equation of plate bending. The developed procedure gives the greatest global error which can appear for a chosen discretization. The performance of the proposed method is illustrated by the solution procedure of two examples: a simply supported square thin plate and a cantilever square thin plate.

computational mechanics; finite element modelling; plate elements; convergence; accuracy; dynamic analogies

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