An Eshelby inclusion of parabolic shape in a Kirchhoff laminated anisotropic thin plate
type: Item
instance of: scholarly article
title: An Eshelby inclusion of parabolic shape in a Kirchhoff laminated anisotropic thin plate
zbMATH Open document ID: 1473.74087
author: Ping Yang
author: X. Wang
author: Peter Schiavone
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-08-18T00:00:00Z
review text: An analytical solution to the Eshelby problem of a parabolic inclusion with uniform strains and curvatures in a middle plane of an infinite laminated anisotropic thin plate is derived. With aid of the Stroh octet formalism, the elastic field in an infinite Kirchhoff plate was obtained. The plate contains a parabolic Eshelby inclusion. The uniformity of elastic fields of membrane stresses, bending moments, strains, curvatures inside the parabolic inclusion are shown. Non-uniform elastic field in the exterior of the parabolic inclusion was obtained. The internal uniform elastic field and the exterior non-uniform elastic field in the vertex of the parabola are determined explicitly. The obtained solution is employed to study the elastic field inside a through-thickness elliptical elastic inhomogeneous inclusion embedded within a parabolic inclusion. It was established that the elastic field inside the elliptical inhomogeneity remains uniform.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74S70
Mathematics Subject Classification ID: 74G05
zbMATH DE Number: 7383004
zbMATH Keywords: Stroh octet formalism
zbMATH Keywords: analytical solution
zbMATH Keywords: uniform mid-plane eigenstrain
reviewed by: V. L. Leontiev
MaRDI profile type: Publication
full work available at URL: s00033-021-01599-3
OpenAlex ID: W3192086180
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DOI: 10.1007/S00033-021-01599-3
description: scientific article; zbMATH DE number 7383004