Discontinuous Galerkin models for composite multilayered shells with higher order kinematics

Abstract

Composite multilayered shells are widely employed in aerospace, automotive and civil engineering as weight-saving structural components. In multilayered shells, despite its versatility, the interplay between the curved geometry and the properties of the composite layers induces a complex distribution of the mechanical fields, which must be accurately resolved to safely employ generally curved composite shells as load-bearing structures. The problem can be addressed through the two-dimensional shell theories, which are based on suitable assumptions on the behavior of the mechanical fields throughout the thickness of the considered structures and are a viable strategy for reducing the computational complexity with respect to 3D models. After the wide investigation on the CLT and FSDT shell theories, motivated by the need of accurate models, researchers have introduced the so-called higher-order theories for plate and shells. These can be classified into Equivalent-Single-Layer (ESL) theories, whereby the layers are replaced by a single layer with equivalent mechanical properties, Layer-Wise (LW) theories, whereby each layer is treated independently, and sub-laminate theories, whereby groups of layers are replaced by groups of equivalent layers. A unified description of these approaches has been introduced by the Carrera Unified Formulation (CUF) [1], which provides a framework able to determine the best 2D theory in terms of computational efficiency versus solution accuracy for a given structural problem. In most cases, numerical models based on these theories are solved using the Finite Element Method [2]. Among the available numerical strategies alternative to FEM for solving problems governed by systems of partial differential equations, the discontinuous Galerkin (dG) method has been recognized as powerful in enabling the seamless use of high-order elements and hierarchical meshes with tunable hp-refinement. The dG approach has been successfully used for general plate theories described via the CUF [3,4]. In this work, for the first time, Equivalent-Single-Layer dG formulations for generally curved multilayered shells are proposed. To account for complex structures, the shell geometry is described by using NURBS whereas different order theories are obtained via a CUF-based description of the shell kinematic model. An Interior Penalty dG scheme, which allows for a high-order numerical solution of the governing equations throughout the shell modeling domain. The dG scheme is also coupled with the implicitly defined mesh technique, which allows to resolve curved boundaries with high-order accuracy by combining an easy-to-generate background grid and the implicit representation of the domain of analysis. Results are presented to show the accuracy and potentiality of the proposed approach. References [1] E. Carrera. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Archives of Computational Methods in Engineering, 10(3):215{296, 2003. [2] M. F. Caliri, A. J.M. Ferreira, V. Tita. A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method. Composite Structures, 156: 63-77, 2016. [3] V. Gulizzi, I. Benedetti, and A. Milazzo. An implicit mesh discontinuous Galerkin formulation for higher-order plate theories. Mechanics of Advanced Materials and Structures, 27(17):1494-1508, 2020. [4] V. Gulizzi, I. Benedetti, and A. Milazzo. A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates. Composite Structures, 242:112137, 2020.