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A new approach to constructing Green’s functions and integral solutions in thermoelasticity

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Abstract

This paper is devoted to a new approach for the derivation of main thermoelastic Green’s functions (MTGFs), based on their new integral representations via Green’s functions for Poisson’s equation. These integral representations have permitted us to derive in elementary functions new MTGFs and new Poisson-type integral formulas for a thermoelastic octant under mixed mechanical and thermal boundary conditions, which are formulated in a special theorem. Examples of validation of the obtained MTGFs are presented. The effectiveness of the obtained MTGFs and of the Poisson-type integral formula is shown on a solution in elementary functions of a particular BVP of thermoelasticity for octant. The graphical and numerical computer evaluation of the obtained MTGFs and of the thermoelastic displacements of the particular BVP for an octant is also presented. By using the proposed approach, it is possible to derive in elementary functions many new MTGFs and new Poisson-type integral formulas for many canonical Cartesian domains.

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  1. Laboratory of Green’s Functions, Agrarian State University of Moldova, Mircesti Street 44, 2049, Chişinău, Moldova

    Victor Şeremet

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  1. Victor Şeremet
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Correspondence to Victor Şeremet.

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Şeremet, V. A new approach to constructing Green’s functions and integral solutions in thermoelasticity. Acta Mech 225, 735–755 (2014). https://doi.org/10.1007/s00707-013-0974-3

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  • DOI: https://doi.org/10.1007/s00707-013-0974-3

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