Elastodynamic analysis with hybrid stress finite elements

The stress model of the hybrid finite element formulation is applied to the solution of free and forced vibration problems. The formulation develops from the independent approximation of the stresses in the domain of the element and of the displacements on its boundary. The inertia force field is determined from the stress approximation to solve locally the dynamic equilibrium condition. Implementation of the time discretisation procedure leads to dependent approximations for the displacement, velocity and acceleration fields. Duality is used to establish the finite element description of each fundamental condition of elastodynamics. Nodal interpolation is replaced by the use of orthogonal and naturally hierarchical bases associated with generalised finite element variables. The resulting solving systems are symmetric, sparse, p-adaptive and well suited to parallel processing. The performance of the element is assessed through a comprehensive set of two-dimensional testing problems.