An implicit mesh discontinuous Galerkin formulation for higher-order plate theories

In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented. The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighboring mesh elements is then retrieved by introducing suitably defined numerical fluxes, whose explicit expressions define the proposed Interior Penalty discontinuous Galerkin formulation. Furthermore, to account for the presence of generally curved boundaries of the considered plate domain, the discretisation mesh is built by combining a background grid and an implicit representation of the domain. hp-convergence analyses and a comparison with the results obtained using the Finite Element Method are provided to show the accuracy of the proposed formulation as well as the computational savings in terms of overall degrees of freedom.