Positional description applied to the solution of geometrically non-linear plates and shells.

In this work the finite element method (FEM) is applied to simulate orthotropic laminated plates and shells presenting large deformations. Alternatively to co-rotational and strain or stress assumed enhanced solid-like elements, a total Lagrangian technique based on unconstrained vectors and position description is proposed. As a consequence, there is no necessity to apply the linearized finite rotation formulae, as for example the Euler–Rodrigues one. The proposed laminate orthotropic strategy can be used for any order isoparametric curved elements; in this study we only explored cubic elements. Equilibrium is achieved from the principle of minimum total potential energy. Examples are solved in order to demonstrate the precision and robustness of the proposed procedure comparing results to analytical and other numerical solutions.

► Laminate shell element developing large deformation not using rotation schemes. ► Full 3D stress–strain relations for shell element—not solid. ► Validation for various literature benchmarks. ► Use of parallel programming for large and fast solutions.