A global–local discontinuous Galerkin finite element for finite-deformation analysis of multilayered shells

Abstract

We present a global-local finite element formulation for the analysis of doubly-curved laminated composite shells. The proposed formulation is applicable to a wide range of problems, including those involving finite strains/rotations, nonlinear constitutive behavior, and static or dynamic structural response. Moreover, in dynamic analysis applications, it can be combined with either explicit or implicit time integration schemes. The global-local framework is based on the superposition of a global displacement field, spanning the thickness of the entire laminate, and local (i.e. layerwise) displacement fields associated with each layer in the laminate. This approach affords highly-resolved representations in regions of critical interest, and allows a smooth transition from higher to lower resolution zones. Discontinuous Galerkin fluxes are used to enforce interlaminar continuity conditions in perfectly-bonded laminates, and the cohesivezone methodology is used to represent interfacial delamination. Stresses and surface normals are referred to the initial configuration in the proposed total Lagrangian formulation. Assumed natural strain and enhanced assumed strain techniques are employed to alleviate shear locking and other pathologies that are known to afflict bilinear shell elements. The performance of the proposed finite element is examined with the aid of several numerical examples involving thick as well as thin shells.

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

“…Since the penalty parameter is generally dependent on the mesh (length-scale h e ), element type, and material parameters (e.g., see [98][99][100]), and as a result, cannot be estimated a priori, we conduct a sensitivity analysis to study the influence of this penalty parameter on the phase-field solution obtained for this problem using Scheme [Q4](Q9).…”

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

“…The DG method has been successfully employed for the static analysis of plates and shell structures modelled via the CLT [35][36][37] and the FSDT [38,39]. More recently, it has also been used to solve the governing equations of static elasticity and piezoelectricity associated with ESL [40][41][42] and LW [43][44][45] theories for multilayered plates and shells.…”

Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells

“…In most cases, numerical models based on these theories are solved using the Finite Element Method (FEM). Recent formulations include high-order FEM approaches [33,34], the work by Versino et al [35,36,37] on a four-node finite element for doubly-curved laminated shells modelled via a refined zig-zag theory, the FEM models based on the CUF [38], and the modified FSDT for piezoelectric shells by Mallek et al [39]. The reader interested in a more comprehensive review on shell theories and the related FEM models is referred to Ref.…”