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# IVANO BENEDETTI

## IMPLICIT MESH DISCONTINUOUS GALERKIN FOR VARIABLE ANGLE TOW MULTILAYERED PLATES

### Abstract

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