New Thermoelastic Green’s Functions by Using a New Integral Representation of Beltrami

New Thermoelastic Green’s Functions by Using a New Integral Representation of Beltrami–Michel Equations

Şeremet, Victor

New integral representations for thermal stresses in Beltrami–Michel equations are proposed in this paper. Using these representations, the author derived thermoelastic volume dilatation (TVD) on the boundary and inside a generalized octant. Then, applying the integral representations for the main thermoelastic Green’s functions (MTGFs) for Lame’s equations, there have been derived new structural formulas for MTGFs. These results are formulated in two theorems. According to structural formulas, many MTGFs for 22 boundary value problems (BVPs) of thermoelasticity may be obtained in terms of elementary functions by changing the respective well-known Green’s functions for Poisson’s equation (GFPE), its regular parts, and calculating some simple integrals. As an example of the application of structural formulas, new MTGFs for a particular BVP for an octant are derived in elementary functions that are very important for their numerical implementation, especially for the elaboration of new boundary elements. Validation of the obtained MTGFs is confirmed on the known MTGFs for a half-space. Graphical and numerical computer evaluation of the derived MTGFs using Maple 15 software is also included. Using the proposed integral representation and technique, it is possible to extend all the obtained results onto any domain of a Cartesian system of coordinates.