The Bubnov-Galerkin method in the nonlinear theory of hollow, flexible multilayer orthotropic shells
type: Item
instance of: scholarly article
title: The Bubnov-Galerkin method in the nonlinear theory of hollow, flexible multilayer orthotropic shells
zbMATH Open document ID: 0604.73086
DOI: 10.1016/0021-8928(85)90067-X
author: V. F. Kirichenko
author: N. S. Surova
author: V. A. Krysko
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The existence of solutions of a strongly nonlinear system of differential equations describing, in the framework of the kinematic Timoshenko model adopted for the whole packet in toto, the behaviour of a flexible, multilayer shell whose very layer is made of an inhomogeneous orthotropic material, is proved. To obtain an approximate solution of the problem in question, a procedure is proposed and justified, using the Bubnov- Galerkin method based on constructing an auxiliary quasilinear system of equations. A similar approach makes is possible to extend the method of studying the convergence of the BG method to strongly nonlinear systems of elliptic type equations, and to achieve the convergence of the sequence of approximate solutions to the exact solution in a space of any prescribed degree of smoothness, without imposing additional constraints on the initial data of the problem.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 3976542
zbMATH Keywords: existence of solutions
zbMATH Keywords: strongly nonlinear system of differential equations
zbMATH Keywords: kinematic Timoshenko model
zbMATH Keywords: flexible, multilayer shell
zbMATH Keywords: inhomogeneous orthotropic material
zbMATH Keywords: Bubnov-Galerkin method
zbMATH Keywords: auxiliary quasilinear system of equations
MaRDI profile type: Publication
cites work: On a general theory of anisotropic shells
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cites work: On the existence of solutions of the nonlinear theory of shallow shells
full work available at URL: 0021-8928(85)90067-x
OpenAlex ID: W2053919952
description: scientific article; zbMATH DE number 3976542