A layerwise mixed least-squares finite element model for static analysis of multilayered composite plates

A layerwise finite element model is developed in a mixed least-squares formulation for static analysis of multilayered composite plates. The model assumes a layerwise variable description of displacements, transverse stresses and in-plane strains, taken as independent variables. The mixed formulation allows to completely and a priori fulfil the known image requirements, which refer to the zig-zag form of displacements in the thickness direction and the interlaminar continuity of transverse stresses, due to compatibility and equilibrium reasons, respectively. This contrasts with layerwise displacement-based models that usually cannot a priori account for the interlaminar continuity of transverse stresses. In addition, the benefit of mixed least-squares formulation, as opposed to mixed weak form models, is that it leads to a variational unconstrained minimization problem, where the finite element approximating spaces can be chosen independently. Numerical examples are shown to assess the layerwise mixed least-squares model predictive capabilities compared to three-dimensional elasticity solutions and also other finite element results available in literature. Most notably, the present model is able to achieve accurate results in very good agreement with three-dimensional solutions and is shown to be insensitive to shear-locking.