Trefftz polynomials reciprocity based boundary element formulations for elastodynamics - Konkol, F.; Kompis, V. (Computer Assisted Methods in Engineering and Science, 2023)
In this paper Trefftz polynomials are used for the BEM (Boundary Element Method) based on the reciprocity relations. BEM provides a powerful tool for the calculation of dynamic structural response in the frequency and time domains. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE) , which are discretized only on the boundary [1]. Trefftz polynomials or other non-singular (e.g. harmonic), Trefftz functions [2] (i.e. functions satisfying all governing differential equations but not the boundary conditions) used in the Betti's reciprocity relations lead to corresponding BIE that do not contain any (weak, strong, hyper) singularities. Fundamental solutions are not needed and evaluation of the field variables inside the domain is simpler.