Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

Abstract

PurposeThe purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived.Design/methodology/approachOn the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions.FindingsThe components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained.Practical implicationsFundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions.Originality/valueFundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.