A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates

Abstract

In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide high-resolution on the representation of the primary variables and their derivatives; (iii) The implicitly-defined mesh technique, a meshing strategy based on an implicit representation of the plate domain, which allows resolving the presence of curved boundaries with high-order accuracy.Numerical tests are provided to investigate the effect of the penalty parameter and to show the optimal convergence of the proposed formulation, which is subsequently employed in combination with an implicitly-defined hierarchical quad-tree mesh to resolve the stress distribution in a rectangular plate and in a plate with a circular hole.