A Contribution to the Theory of Thermal Stress in a Long Hollow Cylinder

概要

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The object of the present paper is to find the thermal stress in a long hollow cylinder, in which heat is transmitted at a uniform rate from the inner to the outer surface or in the reverse direction, considering the coefficient of thermal expansion and the shearing modulus of elasticity as functions of temperature. The writer has succeeded in a solution, perhaps hitherto unknown, in which the coefficient and the modulus may be of any forms whatever as empirical functions of temperature. Dividing the cylindrical wall into a number of coaxial thin cylindrical layers and assuming the coefficient and the modulus in any one layer as constant the radial, tangential and axial stresses at any point of any layer are found. At last the number of layers is taken as infinite in order to arrive at the exact solution. The tangential and axial stresses at the inner and outer surface are reduced to [numerical formula] For the determination of the definite integrals a graphical method may be conveniently used. If, besides the coefficient and the modulus, Poisson's constant be considered variable the stresses become [numerical formula] where [numerical formula]
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1922-01-30