Abstract
This chapter contains description of Trefftz functions as a test function for solution of contact problems of bodies with curved surfaces, such as rolling elements, intrusions, and cavities with smooth shape. Trefftz functions are functions that satisfy all governing equations in the whole domain and can be in the form of polynomials, harmonic, or exponential. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the conventional boundary integral method. In this chapter, the use of Trefftz functions, especially Trefftz polynomials, Kelvin/Kupradze's, and Boussinesq functions are presented. The models described in this chapter are an effective way not only for the solution of contact problems (especially in modelling of the multibody contact) but also for some other types of problems such as cracks in bodies.
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