Buckling analysis of multilayered structures using high-order theories and the implicit-mesh discontinuous Galerkin method

Abstract

This work presents a novel formulation for the linear buckling analysis of multilayered shells. The formulation employs high-order Equivalent-Single-Layer (ESL) shell theories based on the through-the-thickness expansion of the covariant components of the displacement field, whilst the corresponding buckling problem is derived using the Euler’s method. The novelty of the formulation regards the solution of the governing equations, which is obtained via implicit-mesh discontinuous Galerkin (DG) schemes. The DG method 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, the DG method may be naturally employed with non-conventional meshes and is combined in this work with the implicitly-defined mesh technique, whereby the mesh of the shell modelling domain is constructed by intersecting an easy-to-generate background grid and a level set function that implicitly represents the cutouts. Several numerical examples are considered. First, the buckling loads are computed for plates and cylindrical shells modelled by different ESL theories and characterized by various materials, geometry and boundary conditions. Then, the buckling load of a plate with a circular defined cutout is computed for different diameter-to-plate’s width ratios. The obtained results are compared with those available in the literature or those obtained using finite-element analyses and demonstrate the accuracy and the robustness of the proposed approach.