Curved hexahedral hybrid-mixed stress elements for structural dynamics

Curved hexahedral finite elements based on the hybrid-mixed stress formulation are proposed for structural dynamic analysis of three-dimensional solids. The stress and displacement in the domain of an element and the displacement on its boundary are simultaneously and independently approximated using sets of complete and linearly independent non-nodal Legendre polynomials. The element geometry is given in terms of its corner and mid-edge points using the same interpolation functions of the traditional isoparametric 20-node brick element. Symmetric, highly sparse and well conditioned solving systems are obtained. Numerical tests are carried out using h- and p-refinements to assess the behavior of these new hexahedrons.