Quasi-static problems of thermoelasticity for infinite and semi-infinite elastic media



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The present investigation is a study of quasistatic problems of thermoelasticity for infinite and semi-infinite elastic media. The general solutions to the basic equations for quasl-static, uncoupled thermoelasticity theory are derived for problems of infinite and semi-infinite elastic bodies. Two particular problems are considered: one is a line heat source moving at a constant velocity perpendicular to its length in an infinite elastic body; the other is a moving temperature discontinuity on the surface of a semi-infinite elastic body. It is shown that the thermal stress field for the first problem is identical with Fox's result. For the second problem, the normal displacement of the plane boundary and the normal stress (in the horizontal direction) on the the plane boundary are obtained in closed form. The closed-form solution for the normal displacement is new, while the stress is the same as that found by Jahanshahl. Numerical results for the normal displacement and stress for different values of velocity are presented in graphical form.