Time domain analysis of geometrically nonlinear vibrations of composite laminated plates by the hierarchical finite element method

Abstract

A hierarchical finite element for laminated composite plates is formulated. The element is general, in the sense that it applies to symmetric or asymmetric plates. Compared with h-version elements, it has the major advantages of requiring a small number of degrees of freedom for accuracy and of being free from shear locking. The first order shear deformation laminated plate theory is followed, that is the transverse normals do not remain perpendicular to the mid-surface after deformation. The element derived is employed to study the non-linear dynamic behaviour of some composite laminated plates, in the time domain. The direct integration of the system of equations of motion is carried out by Newmarks method. In order to describe the characteristics of the motions computed, time plots, phase planes, Fourier spectra and Poincaré maps are defined.