# IMPLICIT MESH DISCONTINUOUS GALERKIN FOR VARIABLE ANGLE TOW MULTILAYERED PLATES

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## Abstract

This works presents a novel computational scheme for variable angle tow (VAT) multilayeredplates [1]. The characteristic features of the proposed scheme are the combineduse of a discontinuous Galerkin (dG) formulation and an implicitly defined mesh. Theformulation is based on the principle of virtual displacements (PVD) and the EquivalentSingle Layer (ESL) assumption for the mechanical behavior of the VAT plates [2].The problem is first placed within the dG framework by suitably introducing an auxiliaryvariable and by rewriting the set of equations governing ESL VAT plates as a firstordersystem of differential equations. Following Arnold et al.[3] and by introducingsuitably defined average and jump operators, the primal formulation for ESL theories ofVAT multilayered plates is obtained. Two dG formulations are considered, namely theInternal Penalty and the Compact Discontinuous Galerkin methods, which are obtainedby suitably specifying the corresponding numerical fluxes.Subsequently the numerical implementation is discussed. First, the mesh elements aredefined using a reference background quad-tree grid and the implicit representation of theconsidered domain’s boundaries. Then, the elemental matrices are computed using thealgorithm proposed by Saye [4] for the integration over implicitly defined domains andboundaries. To show the potential of the scheme, numerical tests are performed on VATplates with simple and more complex geometries such as curved edges and cutouts.References[1] Oliveri, V., Milazzo, A., “A Rayleigh-Ritz approach for postbuckling analysis ofvariable angle tow composite stiffened panels,” Comput Struct, 196, page 263-276(2018).[2] Carrera, E., Demasi, L., “Classical and advanced multilayered plate elements basedupon PVD and RMVT. part 1: Derivation of finite element matrices,” Int J NumerMeth in Eng, 55, page 191-231 (2002).[3] Arnold, D.N., et al., “Unified analysis of discontinuous Galerkin methods for ellipticproblems,” SIAM J Numer Anal, 39, page 1749-1779 (2002).[4] Saye, R., “Implicit mesh discontinuous Galerkin methods and interfacial gaugemethods for high-order accurate interface dynamics, with applications to surfacetension dynamics, rigid body fluidstructure interaction, and free surface flow: PartI,” J Comput Phys, 344, page 647-682 (2017).
Lingua originale English 1 Published - 2018

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