Solution in integrals of a 3D BVP of thermoelasticity: Green’s functions and integration formula for thermal stresses within a semi-bounded parallelepiped

Abstract

This article presents new constructive formulas for three-dimensional thermal stresses Green’s functions (TSGFs) for a generalized boundary value problem (BVP) of thermoelasticity for a semi-bounded parallelepiped. These results are formulated in a theorem, which is proved using the developed harmonic integral representations method. On the basis of derived constructive formulas, it is possible to obtain many analytical expressions for TSGFs to 32 BVPs within a semi-bounded parallelepiped. An example for a particular spatial BVP for a semi-bounded parallelepiped, TSGFs of which are presented in the form of a sum of elementary functions and double infinite series, containing products of exponential and trigonometric functions is included. These results are formulated in another theorem, which is proved by using the derived general constructive formulas for TSGFs. The integration formula of Green’s type, which permits to determine thermal stresses within a semi-bounded parallelepiped, caused by a distributed inner heat source and by heat fluxes given on the surface also is derived. A numerical example for a particular BVP within a semi-bounded parallelepiped, acted by a constant heat flux, given on a boundary half-strip, is presented.