A discontinuous Galerkin formulation for variable angle tow composite plates higher-order theories

Abstract

A discontinuous Galerkin formulation for the mechanical behaviour of Variable Angle Tow multi-layered composite plates is presented. The starting point of the formulation is the strong form of the governing equations, which are obtained by means of the Principle of Virtual Displacement, the Generalized Unified Formulation and the Equivalent Single Layer assumption for the mechanical behaviour of the whole assembly. To obtain the corresponding discontinuous Galerkin formulation, an auxiliary flux variable is introduced and the governing equations are rewritten as a first-order system of partial differential equations. To link neighbouring mesh elements, suitably defined numerical fluxes are introduced and an Interior Penalty discontinuous Galerkin formulation is obtained and presented. hp-convergence analyses for straight-fiber composite plates and a comparison with the results available in the literature for variable angle tow plates show the accuracy of the proposed formulation as well as the computational savings in terms of overall degrees of freedom.