A new technique to derive the Green’s type integral formula in thermoelasticity

Abstract

New closed-form influence functions of a unit point heat source on elastic displacements and new Green’s type integral formula for a boundary-value problem (BVP) for a thermoelastic half-space are presented. The main difficulties in obtaining such results are observed in deriving the influence functions of a concentrated unit force onto elastic volume expansion and, also, in Green’s functions in heat conduction. For canonical Cartesian domains, these functions have been derived successfully for hundreds of BVPs and were published in a handbook. So, this paper shows the way to derive not only thermoelastic influence functions and Green’s type integral formulas for the half-space, but also for many new BVPs in thermoelasticity in other Cartesian canonical domains. Moreover, the technique proposed here may be applied in any orthogonal canonical domain provided by the lists of Green’s functions in heat conduction and influence functions for elastic volume expansion that are known.