Variational method of investigation of three-dimensional mixed problems of a plane cut in an elastic medium in the presence of slip and adhesion of its surfaces
type: Item
instance of: scholarly article
title: Variational method of investigation of three-dimensional mixed problems of a plane cut in an elastic medium in the presence of slip and adhesion of its surfaces
zbMATH Open document ID: 0545.73010
DOI: 10.1016/0021-8928(83)90011-4
author: R. V. Gol'dshtejn
author: Alexander A. Spector
published in: Journal of Applied Mathematics and Mechanics
publication date: 1984-01-01T00:00:00Z
review text: The mixed problem of the equilibrium of an elastic space is studied on the hypothesis that a plane cut, horizontal in the plane \(Z=0\), occupies a region in the elastic medium bounded by a known curve \(\Gamma\). The parallel surfaces of the cut are in contact or are separated on some parts of the region, unknown before-hand. The forces applied on the surfaces of the cut are anti-symmetric body-or surface forces. The author formulates the boundary value problem which is separated into two other ones, on the basis of the superposition principle. The two boundary value problems concern: 1. the pressure and the region of contact and 2. the shear stress and displacements. These problems are formulated in variational form by means of systems of equalities and inequalities for some nonquadratic functionals. The resultant statements of the study concern: 1. existence and uniqueness conditions for the solutions, 2. the qualitative behaviour of the solution and of its integral characteristics. The variational formulation of the problem allows to construct a numerical solution using methods of mathematical programming.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3868722
zbMATH Keywords: regions of local adhesion and slippage
zbMATH Keywords: equivalent variational statement of input boundary value problem
zbMATH Keywords: equilibrium of an elastic space
zbMATH Keywords: plane cut
zbMATH Keywords: anti-symmetric body-or surface forces
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: qualitative behaviour
zbMATH Keywords: integral characteristics
zbMATH Keywords: mathematical programming
reviewed by: Ştefan Zanfir
MaRDI profile type: Publication
full work available at URL: 0021-8928(83)90011-4
OpenAlex ID: W1972523846
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description: scientific article; zbMATH DE number 3868722