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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(1):43-47; doi:10.1093/qjmam/53.1.43
© 2000 by Oxford University Press
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Thermal stresses in a thin membrane covering an arbitrarily shaped object: equilibrium and derived identities

EH Mansfield

( Manatoba, Dene Close, Lower Bourne, Farnham, Surrey GU10 3PP, UK )

The stresses caused by a uniform temperature change are determined in a thin membrane attached to the surface of an arbitrarily shaped, relatively stiff object with a different coefficient of thermal expansion. A similar analysis applies when there is differential straining due to absorption of moisture. The equilibrium equations for an arbitrary region of membrane yield geometrical generalizations of the divergence theorem that find application in problems concerning surface tension.


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