General solution and Green’s function for fluid-saturated infinite and semi-infinite orthotropic poro-thermoelastic materials

Abstract

In this study, two-dimensional (2D) steady-state general solution and Green’s function for orthotropic materials under the influence of poro-thermoelasticity (PTE) are investigated. Using the superposition principle and operator theory, the complete general solution of corresponding governing equations is calculated and stated in terms of harmonic functions. Based on these compact general solutions, the 2D Green’s function for a steady line fluid source and line heat source in the interior of an infinite orthotropic PTE plane and on the surface of a semi-infinite orthotropic PTE plane is presented. Consequently, eight newly implemented harmonic functions with undetermined constants are obtained. The equilibrium, boundary, and continuous conditions are used to obtain undetermined constants, and the corresponding coupled field is obtained by inserting these harmonic functions into the general solution. All coupled field’s components are described in terms of elementary functions, which can be used as the benchmarks for various numerical codes and approximate solutions.