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

Abstract

A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous nature, it can be naturally employed with nonconventional meshes. In this work, it is combined with the implicitly defined mesh technique, whereby the mesh of the shell modeling domain is constructed by intersecting an easy-to-generate background grid and a level set function implicitly representing the cutouts. Several numerical examples are considered for the buckling loads of plates and shells modeled by different theories and characterized by various materials, geometry, boundary conditions, and cutouts. The obtained results are compared with literature and finite-element solutions, and they demonstrate the accuracy and the robustness of the proposed approach.