Author(s)

Y.A. Melnikov & V.V. Shubenko

Abstract

Green's function attacks geometric non-linearity in a bending of plates Y.A. Melnikov", V.V. ShubenW "Department of Mathematics and Statistics, Middle Tennessee State University, Murfreesboro, ^Department of Applied Mathematics, Dniepropetrovsk State University, Dniepropetrovsk ABSTRACT Special iterative procedure has been developed to linearize the boundary value problems modelling the geometrically non-linear bending of thin plates. Green's functions for two-dimensional biharmonic equation as well as Green's matrices for Lame's system of the displacement formulation for the plane problem in theory of elasticity are used for creating the algorithm to attack the linearized problems at each single iterative loop. The particular Green's functions and matrices needed in such a treatment had been constructed in advance by using the technique advocated by Melnikov [1] and evolved by Dolgova and Melnikov [2,3]. Numerical results are given showing a high level of an effectiv

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