Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and C° finite elements

Abstract

A refined higher-order shear deformation theory has been developed for large amplitude, in the sense of von Karman, free vibration analysis of fibre reinforced cross-ply composite and sandwich laminates by assuming cubic variations of in-plane displacement components and a constant transverse displacement component through the thickness of the laminate. The theory accounts for warping of the transverse cross-section, which cannot be modelled with the Reissner-Mindlin first-order shear deformation theory. The displacement-based finite element method of analysis using C° isoparametric nine-node quadrilateral elements of the Lagrangian family is adopted. A special mass matrix diagonalization scheme is employed which conserves the total mass of the element and includes the effects due to rotary inertia terms. The validity and efficiency of the present development is then established by obtaining the solutions to a wide range of problems and comparing them with the available two- and three-dimensional closed-form and finite element solutions. Some new results are also generated in a non-linear context for future comparisons.