Hybrid finite element formulations for elastodynamic analysis in the frequency domain

Three alternative sets of hybrid formulations to solve linear elastodynamic problems by the _nite element method are presented[ They are termed hybrid mixed\ hybrid and hybrid Tre}tz and di}er essentially on the _eld conditions that the approximation functions are constrained to satisfy locally[ Two models\ namely the displacement and the stress models\ are obtained for each formulation depending on whether the tractions or the boundary displacements are the _eld chosen to implement interelement continuity[ A Fourier time discretization is used to uncouple the solving system in the frequency domain[ The basic space discretization criterion is implemented directly on the fundamental relations of elastodynamics and used to derive the stress and displacement models of the hybrid mixed formulation[ The hybrid and hybrid Tre}tz formulations are presented in sequence as the variants of the hybrid mixed formulation obtained by progressively increasing the constraints on the approximation bases[ Numerical implementation aspects are brie~y discussed and the performance of the _nite element models is illustrated with numerical applications