Method to derive thermoelastic Green's functions for cylindrical domains

摘要

This article presents a new method to derive Green's functions for boundary value problems (BVPs) of steady-state thermoelasticity for domains described in cylindrical system of coordinate. The proposed method is based on new integral representations for main thermoelastic Green's functions (MTGFs) in terms of Green's functions for incompressible Lame equations written in a cylindrical system of coordinates. The method is demonstrated on a BVP for cylindrical half-wedge for which MTGFs and Green-type integral formula are derived. The obtained MTGFs for half-wedge are validated by MTGFs for respective BVP for thermoelastic wedge that are obtained earlier using G convolution method (GCM). New MTGFs for octant, quarter-space, and half-space as particular cases of the cylindrical half-wedge also can be easily written. The advantages of the proposed method, called method of incompressible cylindrical integral representations (MICIR), in comparison with GCM, are: (a) it is not necessary to construct influence functions for elastic volume dilatation ((q)), caused by unit point body force; and (b) it is not necessary to compute complicated convolution (volume integral of product between ((q)) and Green's function G(T)) in heat conduction equation.