The method of boundary equations of the Hammerstein-type for contact problems of the theory of elasticity when the regions of contact are not known
type: Item
instance of: scholarly article
title: The method of boundary equations of the Hammerstein-type for contact problems of the theory of elasticity when the regions of contact are not known
zbMATH Open document ID: 0659.73080
DOI: 10.1016/0021-8928(85)90084-X
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: Novel formulations are given for the classical and non-classical, three- dimensional contact problems. The inequality-type constraints do not appear in the formulations as they do in the method of variational inequalities and in existing formulations of the contact problems. The complete system of equations of a contact problem consists of one boundary equation of the Hammerstein-type and the usual equation of equilibrium for the compressive force and moments acting on the bodies. If the mutual rotations of the bodies and their closeness are known, the solution of the boundary Hammerstein-type equation readily yields the contact pressure and region of contact. By formulating the problem in this manner and using modern methods of the theory of operator equations we can investigate the existence and uniqueness of the solutions and some of their properties in very general cases (e.g. those of the multiconnectivity of the regions of contact sought). Moreover, the possibility arises of solving the problem using existing methods of solving Hammerstein-type equations. Two types of problems, one of them classical, are used to study the correctness of the formulation of the contact problem.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 45E99
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 45L05
Mathematics Subject Classification ID: 45M99
zbMATH DE Number: 4078971
zbMATH Keywords: elastic half-space
zbMATH Keywords: frictionless embedding
zbMATH Keywords: stamp
zbMATH Keywords: continuous dependence of solution on parameter
zbMATH Keywords: weak singularity
zbMATH Keywords: regularized boundary conditions
zbMATH Keywords: Winkler-type covering
zbMATH Keywords: system of equations of a contact problem
zbMATH Keywords: boundary equation of the Hammerstein-type
zbMATH Keywords: equation of equilibrium
zbMATH Keywords: compressive force and moments
zbMATH Keywords: existence
author: Boris A. Galanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4078971