A Method of the Green's Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange

An approach for solution construction of the one-dimensional non-static heat conduction problems and corresponding quasi-static thermoelasticity problems for layered bodies of canonical form under convective-radial heating is proposed accounting temperature dependence of physical-mechanical material properties. This approach is based on employment of the Kirchhoff's substitution, distribution technique, and constructed the Green's functions for corresponding linear non-static heat conduction problems and static elasticity problems. The solution of the heat conduction problems is reduced to the solution of integro-differential equations. In analysis of thermoelasticity problems for a layered cylinder and sphere; the elastic moduli and Poisson's ratios are assumed to be continuous within each phase and are approximated by transient piecewise-constant functions.