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

Abstract

An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotropic and multilayered shells with different geometrical configurations and boundary conditions, including the case of a non-smooth geometry. Comparisons with analytical solutions and finite-element simulations show the high-order accuracy as well as the capability and robustness of the proposed formulation, which can be a valuable tool for the analysis of generally-curved multilayered shells.