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 cohesive-zone 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.