Numerical implementation of a hybrid-mixed finite element model for Reissner–Mindlin plates

The implementation of a hybrid-mixed formulation for Reissner–Mindlin stress elements is presented. The stress-resultants and the mid-surface displacements in the domain of the element and the displacements on its boundary are simultaneously and independently approximated using Legendre polynomials. The properties of these functions are exploited to derive and encode directly the analytical expressions for all the intervening finite elements arrays, thus avoiding numerical integration. As a consequence of orthogonality, the Legendre approximation yields governing systems which can be manipulated using efficient procedures to store, operate and solve highly sparse systems. The analysis of two standard tests is used to illustrate the implementation of the finite element formulation.