Thermo-elastic analysis of a finite plate containing multiple elliptical inclusions

• The thermo-elastic problem of a finite multi-connected region is studied, on which only few works have been reported.
• A specific series form which is consistent with elliptical inner boundaries is adopted to obtain a higher accuracy.
• An improved least squares method is derived to deal with the irregular outer boundary of the finite plate.

This paper presents a series solution to the thermo-elastic problem of a finite plate containing multiple elliptical inclusions subjected to a steady-state temperature variation field. The first step of the solution is to transform the thermo-elastic problem into a general elastic problem without considering thermal influence in which the Muskhelishvili's theory of elasticity can be employed. Then the complex potentials inside the inclusions are presented in the form of Faber series, while those in the multi-connected matrix are expressed as a superposition of multiple specific series consistent with elliptical inner boundaries. Finally, all the complex potentials are substituted into the boundary conditions to be derived in assistance with Fourier series expansions and a least squares method with constraints. Additionally, the thermal stresses obtained by the present solution are compared with those by both an analytical solution and the finite element method, while interfacial thermal stresses as well as equivalent thermal expansion coefficients of a rectangular plate are investigated.