Axially symmetric thermal stress of a penny-shaped crack subjected to general temperature
type: Item
instance of: scholarly article
title: Axially symmetric thermal stress of a penny-shaped crack subjected to general temperature
zbMATH Open document ID: 0833.73041
DOI: 10.1007/BF00788881
author: J. V. S. Krishna Rao
author: Norio Hasebe
published in: Archive of Applied Mechanics
publication date: 1996-02-26T00:00:00Z
review text: The authors consider in the cylindrical coordinates \((r, \varphi, z)\) the thermoelastic equations \(2(1 - \nu) ({\partial^2u \over \partial r^2} + {1 \over r} {\partial u \over \partial r} - {u \over r^2}) + (1 - 2 \nu) {\partial^2u \over \partial z^2} + {\partial^2w \over \partial r \partial z} = 2(1 + \nu) \alpha {\partial \theta \over \partial r}\), \((1 - 2 \nu) ({\partial^2w \over \partial r^2} + {1 \over r} {\partial w \over \partial r}) + 2 (1 - \nu) {\partial^2w \over \partial z^2} + {\partial \over \partial z} ({\partial u \over \partial r} + {u \over r}) = 2(1 + \nu) \alpha {\partial \theta \over \partial z}\), with respect to the displacement \((u,w)\), and the temperature distribution \(\theta\) satisfying the Laplace equation. All functions are independent of \(\varphi\). Different boundary conditions are considered for \(0 < r < a\) and \(r > a\). The problem has been solved in closed form using Hankel transforms and Abel integral equations.
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 755127
zbMATH Keywords: thermoelastic equations
zbMATH Keywords: Laplace equation
zbMATH Keywords: Hankel transforms
zbMATH Keywords: Abel integral equations
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 755127