Deformation of a long thermoelastic rod of rectangular normal cross-section under mixed boundary conditions by boundary integrals

Using a well-known solution for steady temperature distribution in a rectangle, a boundary integral method is used to obtain an approximate solution for a plane problem of uncoupled thermoelasticity with mixed mechanical boundary conditions. The unknown functions in the cross-section are obtained in the form of series in Cartesian harmonics, enriched with harmonic functions that have a singular behavior at the transition points. The results are discussed and the functions of practical interest are represented on the boundary and also inside the domain. The locations where possible debonding may take place are noted