Hybrid-Thefftz displacement and stress elements for elastodynamic analysis in the frequency domain - Teixeira de Freitas, João António (Computer Assisted Methods in Engineering and Science, 1997)
Two alternative models of the hybrid-Trefftz finite element formulation to solve linear elastodynamic problems are presented. In the displacement model, the displacements are approximated in the domain of the element and the tractions are approximated on its boundary. The fields selected for approximation in the complementary stress model are the stresses in the domain and the displacements on the boundary of the element. In both models the domain approximation functions are constrained to satisfy locally the governing wave equationn. A Fourier time approximation is used to uncouple the solving system in the frequency domain. The formulations are derived from the fundamental relations of elastodynamics and the associated energy statements are obtained a posteriori. Sufficient conditions for the existence and uniqueness of statically and kinematically admissible solutions are presented. Numerical implementation is briefly discussed.