On dynamic analysis of laminated composite and sandwich plates using finite element method
Two new multi-layered plate bending elements (DKT/CST and DKT/LST) are developed based on a combination of the three model Discrete Kirchhoff theory (DKT) triangular plate bending element, the three model constant strain triangle (CST) and the six noded linear strain triangle (LST). Both frequency independent and frequency dependent damping of viscoelastic materials are considered. An iterative complex eigensolver is used to compute the natural frequencies and model loss factors. Several bench mark problems are solved using these new multi-layer plate elements. As the plate bending elements previously developed on the basis of Kirchhoff's theory are inadequate for thick plate analysis, several quadrilateral Mindlin plate bending elements are developed to study the behaviour of Mindlin plates. The plate bending elements based on Mindlin theory require shear correction factors in their formulations. Hence two new Co assumed strain finite element formulations of a refined third order theory which does not require shear correction factors, are developed and used to analyse isotropic, orthotropic, and layered anisotropic composite and sandwich plates under free vibration, damping and transient loading conditions. Parametric effects of plate aspect ratio, length to thickness ratio, degree of orthotropy, number of layers and lamination scheme on the natural frequencies (free vibration), model loss factors (damping) and dynamic (transient) responses have been shown. The results presented in this investigation could be useful in better understanding the behaviour of sandwich laminates under dynamic conditions and potentially beneficial for designers of sandwich structures.