The use of a piecewise continuous polynomial basis function for the surface reduction of integral equations in thermoelastic analysis

The analysis of thermoelastic problems using the boundary element method in multi-dimensional solids is described. The integral equations are formulated by reducing the domain integral associated with the thermal body force to equivalent boundary integrals using piecewise polynomial basis functions and corresponding particular solutions of the governing inhomogeneous differential equation. Additionally, the use of functions associated with a specific temperature field applied at relevant geometric locations is also described. The accuracy of the temperature field representation is estimated by using a statistical parameter. An error estimate of the boundary element formulation due to an inaccurate representation of the temperature field is also derived. Issues regarding numerical performance and nature of solution algorithm are discussed in the framework of progressively more complex application problems.