TRANSIENT AND FREE-VIBRATION ANALYSIS OF LAMINATED SHELLS THROUGH THE DISCONTINUOUS GALERKIN METHOD

Abstract

This paper presents a novel formulation for linear transient and free-vibration analysis of laminated shell structures based on Interior Penalty discontinuous Galerkin (DG) methods and variable-order through-the-thickness kinematics, whose combined use allows solving the shell problem with high-order accuracy throughout both the shell thickness and the shell modelling domain. The shell geometry is described via a generic system of curvilinear coordinates using either an analytical or a NURBS-based parametrization of the shell mid surface; the formulation also allows for the presence of cut-outs, which are implicitly represented by means of a level set function. After deriving the governing equations of the shell problem from the weak form of three-dimensional elasto-dynamics, the spatial discretization is performed via the DG approach, whereas the temporal timestepping by the Newmark scheme. Damping of the dynamic system is considered using the classical Rayleigh model. Various numerical tests and the corresponding comparison with reference solutions are provided to assess the accuracy of the proposed formulation.