Variational formulation of a contact problem for linearly elastic and physically nonlinear shallow shells
type: Item
instance of: scholarly article
title: Variational formulation of a contact problem for linearly elastic and physically nonlinear shallow shells
zbMATH Open document ID: 0535.73092
DOI: 10.1016/0021-8928(82)90018-1
author: G. I. L'vov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1983-01-01T00:00:00Z
review text: The shell is described by a parametric equation of the form \(R=R(x_ 1,x_ 2)\in C^{(2)}(S)\), where S is a finite sum of bounded star domains. After shell deformation it is necessary to satisfy the condition \(f(R)+U\cdot \text{grad} f(R)\geq 0, \forall(x_ 1,x_ 2)\in S\), where \(U(x_ 1,x_ 2)\) is the displacement vector of the middle surface. For this thin shell in interaction with a smooth absolutely rigid stamp (without friction in the contact domain) a variational problem is analysed. Using the Sobolev space and the Lions-Stampachia method of variational inequalities this problem is reduced to a problem of a Lagrange functional. The existence and uniqueness conditions of the solution of this problem are established in this work.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
zbMATH DE Number: 3850622
zbMATH Keywords: physically nonlinear shallow shells
zbMATH Keywords: minimizing a Lagrange functional
zbMATH Keywords: set of allowable displacements
zbMATH Keywords: smooth absolutely rigid stamp
zbMATH Keywords: without friction
zbMATH Keywords: Sobolev space
zbMATH Keywords: Lions-Stampachia method of variational inequalities
zbMATH Keywords: existence
reviewed by: Sergiu T. Chiriacescu
MaRDI profile type: Publication
full work available at URL: 0021-8928(82)90018-1
OpenAlex ID: W2047177049
cites work: On the Hertz problem for linearly and nonlinearly elastic bodies of finite dimensions
cites work: Q4053162
cites work: On some direct methods and theexistence of solution in the nonlinear theory of elastic nonshallow shells of revolution
cites work: Q4743891
description: scientific article; zbMATH DE number 3850622