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Using the extended Stroh sextic formalism for thermo-anisotropic elasticity, we study the problem of an anisotropic elastic parabolic inhomogeneity embedded in an infinite anisotropic elastic matrix with separate thermomechanical properties when the matrix is subjected to uniform remote heat flux. We prove that the induced temperature, stresses and strains inside the parabolic inhomogeneity all take the form of the sum of a constant plus linear distributions of the two in-plane coordinates. Furthermore, the internal thermoelastic field of displacements, stresses and strains inside the parabolic inhomogeneity is obtained in explicit real form in terms of the fundamental elasticity matrices and the thermal moduli for both the inhomogeneity and the matrix.

An anisotropic elastic parabolic inhomogeneity under uniform heat flux