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On an iteration method of finding a solution of a nonlinear equilibrium problem for the Timoshenko plate
Author(s) -
Peradze J.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100016
Subject(s) - mathematics , boundary value problem , mathematical analysis , nonlinear system , algebraic equation , galerkin method , dirichlet boundary condition , mixed boundary condition , free boundary problem , physics , quantum mechanics
A boundary value problem of Timoshenko plate equilibrium in axially symmetric displacements is considered. From the given system of ordinary differential equations an integro‐differential equation is singled‐out with respect to the plate deflection w that, together with the Dirichlet boundary conditions, makes up a boundary value problem. After finding w, other plate displacement characteristics u and ψ are defined. To approximate the problem solution for w, the Galerkin method is used. It leads to a nonlinear system of algebraic equations that is solved by the iteration method. The convergence of the iteration process is established and the error estimates are obtained for the displacement characteristics under some natural conditions. All constants from these conditions and the inequalities for the error are expressed explicitly through the initial data of the problem. The numerical examples illustrating the convergence conditions are given.