Generalized Thermoelasticity Problem of a Hollow Sphere Under Thermal Shock

Avijit Kar

Abstract

This problem deals with the thermo-elastic interaction due to step
input of temperature on the boundaries of a homogeneous isotropic
spherical shell in the context of generalized theories of
thermo-elasticity. Using the Laplace transformation the
fundamental equations have been expressed in the form of
vector-matrix differential equation which is then solved by eigen
value approach. The inverse of the transform solution is carried
out by applying a method of Bellman et al. Stresses, displacements
and temperature distribution have been computed numerically and
presented graphically in a number of figures for copper material.
A comparison of the results for different theories (CTE, CCTE,
TRDTE(GL), TEWOED(GN-II), TEWED(GN-III)) is presented. When the
outer radius of the shell tends to infinity, the corresponding
results agree with that of existing literature.

Keywords

Generalized thermo-elasticity, energy dissipation, Laplace transform, step input temperature, vector-matrix differential equation.

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