On shallow shell equations
type: Item
instance of: scholarly article
title: On shallow shell equations
zbMATH Open document ID: 1180.35361
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2009-10-12T00:00:00Z
review text: The author presents explicit formulas for the shallow shell model consisting of a coupled system of a wave equation and a plate equation, where the middle surface is viewed as a natural manifold with the induced metric from the classical Euclidean space of three dimensions. The Green formula for the shallow shell is given by the displacement field which expresses the relationship between the interior and the boundary. Next, the ellipticity of the strain energy for the shallow shell is studied under some curvature assumptions on the middle surface. Finally, the motion equations for shallow shells are obtained in terms of the displacement field as an unknown. The new ingredients in these formulas are that they take a form which is not described by a coordinate patch to provide the shell theory with the modern geometry.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35L76
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 5613328
zbMATH Keywords: wave equation
zbMATH Keywords: plate equation
zbMATH Keywords: Bochner's technique
zbMATH Keywords: Weitzenbock's formula
author: Peng-Fei Yao
reviewed by: Jerzy August Gawinecki
MaRDI profile type: Publication
full work available at URL: dcdss.2009.2.697
OpenAlex ID: W1983525749
DOI: 10.3934/DCDSS.2009.2.697
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description: scientific article; zbMATH DE number 5613328