On generalized Kelvin solutions in a multilayered elastic medium
type: Item
instance of: scholarly article
title: On generalized Kelvin solutions in a multilayered elastic medium
zbMATH Open document ID: 0844.73008
DOI: 10.1007/BF00042082
author: Zhong Qi Yue
published in: Journal of Elasticity
publication date: 1996-09-02T00:00:00Z
review text: An elastic layer of finite thickness made of \(n\) dissimilar homogeneous isotropic elastic layers adheres two dissimilar homogeneous isotropic elastic half-spaces. The interfacial conditions are assumed to be fully bonded (continuity of the displacement and traction vector fields), and an elastostatic state (displacement, strain and stress) is produced either by a concentrated force acting on an internal point of the \(k\)-th layer \((k = 0, 1, 2, \dots, n)\), or by a force uniformly concentrated on a circle situated in the \(k\)-th layer in parallels to the interface planes. The elastostatic state for such an infinite layered body is obtained in the form of double improper integrals, by combining a Fourier-Hankel transform method with a backward transfer matrix technique, and the integrals are analysed with regard to their convergence and singular properties. Numerical results obtained by computer programs for the integral solutions are included. The reviewer notes a number of misprints, e.g. (i) the definitions of symbols \(R\) and \(R_a\) below (24a) and (26), respectively, have little to do with eqs. (24a) and (26); (ii) the reference item [45] on pages 11, 18 and 21 should read [46].
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 829848
zbMATH Keywords: concentrated force
zbMATH Keywords: elastostatic state
zbMATH Keywords: double improper integrals
zbMATH Keywords: Fourier-Hankel transform method
zbMATH Keywords: backward transfer matrix technique
zbMATH Keywords: convergence
zbMATH Keywords: singular properties
MaRDI profile type: Publication
cites work: Q3229113
cites work: A numerical solution for axially symmetrical elasticity problems
cites work: Numerical solutions in axisymmetric elasticity
cites work: Green’s Functions for Axisymmetric Problems of Dissimilar Elastic Solids
cites work: Elastic fields in two joined transversely isotropic solids due to concentrated forces
cites work: Die Bestimmung des Spannungs- und Verschiebungszustandes eines geschichteten K�rpers mit Hilfe von �bertragungsmatrizen
cites work: Static response of a multilayered medium under inclined surface loads
cites work: Computation of stresses and displacements in a layered elastic medium
cites work: Spannungs- und Stabilit�tsproblem eines elastisch-querisotropen Schichtsystems
cites work: Elastisches Mehrschichtsystem unter asymmetrischer Belastung
cites work: Force at a point in the interior of a layered elastic half space
cites work: Q4080804
cites work: Finite layer analysis of layered elastic materials using a flexibility approach. Part 2—Circular and rectangular loadings
cites work: Three-dimensional elastostatics of a layer and a layered medium
cites work: Static Loads in Layered Halfspaces
cites work: General Image Method in a Plane-Layered Elastostatic Medium
cites work: Solution for the thermoelastic problem in vertically inhomogeneous media
cites work: Analysis of a Vertical Crack in a Multilayered Medium
cites work: Three-dimensional analysis of cracks in layered transversely isotropic media
cites work: Q3854711
cites work: Generalized displacements of a rigid elliptical anchor embedded at a bi-material geological interface
cites work: On elastostatics of multilayered solids subjected to general surface traction
cites work: On certain integrals of Lipschitz-Hankel type involving products of bessel functions
description: scientific article; zbMATH DE number 829848