Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: Convergence and accuracy

Abstract

The aim of this work is to investigate and compare the accuracy and convergence behavior of two different numerical approaches based on Differential Quadrature (DQ) and Integral Quadrature (IQ) methods, respectively, when applied to the free vibration analysis of laminated plates and shells. The numerical methods at issue allow to solve the strong and the weak forms of the governing equations of these structural elements. A completely general approach is presented to evaluate numerically derivatives and integrals by using several basis functions (polynomial approximation) and grid distributions (discretization). The convergence analyses are performed for three different approaches: Strong Formulation (SF), Weak Formulation (WF) with C1 continuity conditions, and Weak Formulation (WF) with C0 continuity conditions. For each approach, a set of convergence graphs is shown, by varying both basis functions and discrete grids, in order to define the combinations that provide the best accuracy with reference to the exact solutions available in the literature.