Analysis of Laminated and Sandwich Composites by a Zig-zag Plate Element with Variable Kinematics and Fixed Degrees of Freedom

A C° layerwise plate element with standard nodal d.o.f. and serendipity interpolation functions is applied to the analysis of laminates and sandwiches giving rise to strong layerwise effects. The element is obtained using an energy updating technique and symbolic calculus starting from a physically-based zig-zag model with variable kinematics and fixed d.o.f. able to a priori satisfy to displacement and stress continuity at the material interfaces. Non classical feature, a high-order piecewise zig-zag variation of the transverse displacement is assumed as it helps keeping equilibrium. Crushing of core is studied carrying apart a detailed 3D modelling of the honeycomb structure discretizing the cell walls with plate elements, with the aim of obtaining apparent elastic moduli at each load level. Using such apparent moduli, a 2D homogenized analysis is carried out simulating sandwiches as multi-layered structures Applications are presented to plates undergoing impulsive loading incorporating plies with spatially variable stiffness properties. It is shown that accurate predictions are always obtained in in the numerical applications with a very low computational effort. Compared to kinematically based zig-zag models, present physically based one is proven to more accurate, being always in a good agreement with exact 3D solutions.