The equations of generalized thermoelasticity for an anisotropic medium are derived. Also, a uniqueness theorem for these equations is proved. A variational principle for the equations of motion is obtained.

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In this paper the equation of equilibrium for a nonhomogeneous isotropic elastic solid under shear has been solved in rectangular Cartesian coordinates as well as in cylindrical polar coordinates. The modulus of rigidity of the material is assumed to vary in lateral as well as vertical directions. As an example, the above solution has been used to solve the problem of a Griffith crack in an infinite solid under shear.

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