Axisymmetric analysis of a thermoelastic isotropic half-space under buried sources in displacement and temperature potentials

ABSTRACT

Analytical and numerical investigations have been made to determine the solution of a thermoelastic isotropic half-space under buried mechanical load and heat flux based on Biot’s coupled thermoelasticity. Using a scalar potential function, the coupled governing equations have been uncoupled and a sixth order partial differential equation that governs the potential function is received. Applying the Hankel transform to suppress the radial variable, a sixth order ordinary differential equation with respect to depth is received. Solving that equation and utilizing the boundary and continuity conditions, the potential function is derived and displacements, temperature, and stress components are derived in the transformed domain in two regions. Applying the inverse Hankel transform, responses are derived in the physical domain as line integrals. The line integrals are calculated numerically through Mathematica software. Numerical results are depicted graphically for different cases of vertical load and heat flux. Effects of elastic and thermal properties as well as the depth of buried loads and frequency of excitation are investigated. Numerical evaluation shows that the agreement between the results of this study for surface excitation and the results reported in the literature is excellent.

KEYWORDS:

• Axisymmetric problem
• buried load
• partial differential equation
• potential method
• thermoelasticity