This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are directly taken into account into the stress-based construction of the model. A dual displacement-based finite-element discretization is implemented using the FEniCS software package and a remeshing strategy is proposed based on a novel error indicator. The error indicator is built based on the 3D stress field directly deduced from the layerwise generalized stresses and compared to a reconstructed stress field based on the model generalized displacements. The proposed error indicator is shown to identify the most critical parts of a laminate structure associated with complex 3D stress fields such as boundaries or stress concentration/singularity regions (near free-edges or delamination fronts). Through the combination of thickness discretization and in-plane mesh refinement in regions of interest, the proposed framework therefore offers an attractive alternative to 3D solid finite elements for an accurate prediction of stress states in composite laminates.

Building upon recent works devoted to the development of a stress-based layerwise model for multilayered plates, we explore an alternative finite-element discretization to the conventional displacement-based finite-element method. We rely on a mixed finite-element approach where both stresses and displacements are interpolated. Since conforming stress-based finite-elements ensuring traction continuity are difficult to construct, we consider a hybridization strategy in which traction continuity is relaxed by the introduction of an additional displacement-like Lagrange multiplier defined on the element facets. Such a strategy offers the advantage of uncoupling many degrees of freedom so that static condensation can be performed at the element level, yielding a much smaller final system to solve. Illustrative applications demonstrate that the proposed mixed approach is free from any shear-locking in the thin plate limit and is more accurate than a displacement approach for the same number of degrees of freedom. As a result, this method can be used to capture efficiently strong intra- and inter-laminar stress variations near free-edges or cracks.