On the integrable case of a Riemann-Hilbert boundary value problem for two functions and the solutions of certain mixed problems for a composite elastic plane
type: Item
instance of: scholarly article
title: On the integrable case of a Riemann-Hilbert boundary value problem for two functions and the solutions of certain mixed problems for a composite elastic plane
zbMATH Open document ID: 0613.73114
DOI: 10.1016/0021-8928(85)90009-7
author: I. V. Simonov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: A method for solving the Riemann-Hilbert boundary value problem with piecewise-constant coefficients is generalized. It is shown that the following static problems of a composite elastic plane with three kinds of connection conditions allow of exact solutions: 1) the splicing line is weakened by a system of loaded slots and a transverse shear crack or the edges of one of the slots are partially contacting, or one of the slots is cleaved by a rigid insert; 2) the splicing line is reinforced by a system of thin rigid inclusions and there is one arbitrarily located delamination zone; 3) the elastic half-planes are contacting (with slip) on a certain section of their boundaries, and mixed boundary conditions in the displacements and stresses are given on the rest of the boundaries.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 74R05
zbMATH DE Number: 3993093
zbMATH Keywords: integrable case
zbMATH Keywords: Riemann-Hilbert boundary value problem
zbMATH Keywords: piecewise- constant coefficients
zbMATH Keywords: static problems
zbMATH Keywords: composite elastic plane
zbMATH Keywords: three kinds of connection conditions
zbMATH Keywords: exact solutions
zbMATH Keywords: splicing line
zbMATH Keywords: weakened
zbMATH Keywords: reinforced
zbMATH Keywords: slip
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90009-7
OpenAlex ID: W2072831882
cites work: Q5814091
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cites work: Stress state of a fiber in a viscoelastic matrix
cites work: Deformation of a composite elastic plane weakened by a periodic system of the arbitrarily loaded slits
cites work: Q5562285
cites work: Q5530582
cites work: Uniqueness for Elastic Crack and Punch Problems
description: scientific article; zbMATH DE number 3993093