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. Thestarting point of the formulation is the strong form of the governing equations, which are derived inthe context of the Generalized Unified Formulation and the Equivalent Single Layer approach fromthe Principle of Virtual Displacements. To express the problem within the discontinuous Galerkinframework, an auxiliary flux variable is introduced and the governing equations are rewritten as asystem 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 numericalfluxes, whose explicit expressions define the proposed Interior Penalty discontinuous Galerkinformulation. Furthermore, to account for the presence of generally curved boundaries of the consideredplate domain, the discretisation mesh is built by combining a background grid and an implicitrepresentation of the domain. hp-convergence analyses and a comparison with the results obtainedusing the Finite Element Method are provided to show the accuracy of the proposed formulation aswell as the computational savings in terms of overall degrees of freedom.