Influence of modal coupling and geometrical imperfections on the nonlinear buckling of cylindrical panels under static axial load

Abstract

The aim of this work is to analyse the influence of the nonlinear modal coupling and initial geometrical imperfection on the post-buckling path (perfect case) or nonlinear equilibrium path (imperfect case) of a simply supported, axially loaded cylindrical panel. The cylindrical panel is described by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure, generating a precise low-dimensional model that satisfies out-of-plane boundary conditions and considers the forthcoming nonlinear modal coupling due to quadratic and cubic terms in a nonlinear equilibrium equation. The discretized equations of motion are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel’s nonlinear static equilibrium path with its structural stability analysis. The results show the influence of geometry on the nonlinear response of the cylindrical panel, unveiling an intricate competition between different types of bifurcation diagrams (stable symmetric, unsymmetrical, and unstable symmetric). Completing the presented results, the initial geometrical imperfection could change the stability of the initial nonlinear equilibrium path (from unstable to stable) depending on the applied amplitude of the imperfection and its shape. It is possible to observe that the influence of the geometrical imperfection on the nonlinear equilibrium path of the imperfect cylindrical panel is determinant.