Rectilinear crack in a composite orthotropic plane
type: Item
instance of: scholarly article
zbMATH Open document ID: 1078.74639
author: K. N. Arkhipenko
author: A. F. Krivoj
publication date: 2001-11-11T00:00:00Z
Mathematics Subject Classification ID: 74R10
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 1670291
zbMATH Keywords: fundamental solution
zbMATH Keywords: generalized functions
zbMATH Keywords: Riemann problem
zbMATH Keywords: singular integral equations
MaRDI profile type: Publication
title: Rectilinear crack in a composite orthotropic plane
published in: Visnyk Odes'kogo Derzhavnogo Universytetu. Seriya Fizyko-Matematychni Nauky
review text: A matrix of fundamental solutions for a composite orthotropic plane is constructed. This is the matrix-function from the space of generalized functions of slow growth, \(S'(R^2)\) elements of which describe stress-strain state of inhomogeneous plane with concentrated jumps of stresses and displacements at arbitrary point. Construction of this matrix is reduced to the matrix Riemann problem in the space \(S'(R^2)\). Solution of the latter problem is constructed on the basis of analytic properties of the generalized Fourier transform. Using the fundamental matrix, the problem on arbitrary thin defects in inhomogeneous orthotropic plane can be reduced to singular integral equations. The technique is illustrated by a problem of rectilinear crack with the tip at the interface of materials.
description: scientific article; zbMATH DE number 1670291