Non-polynomial zigzag theories with C° finite element formulation for buckling analysis of laminated composite and sandwich plates

Abstract

In this present work, non-polynomial zigzag theories (algebraic zigzag theory (AZT), exponential zigzag theory (EZT), hyperbolic zigzag theory (HZT), inverse hyperbolic zigzag theory (IZT), logarithmic zigzag theory (LZT) and trigonometric zigzag theory (TZT)) are performed for buckling response of laminated composite and sandwich plates. The present models assume parabolic variation of out – plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag models able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. An efficient eight noded C° continuous isoparametric serendipity element is established and employed to examine the buckling analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical examples are carried out to study the effects of span to thickness ratio, ply orientation, lay-up number, modular ratio, loading condition and boundary condition on the buckling response. To ensure the capability of the proposed models, higher modes of buckling are obtained for laminated plates and sandwich plates. Further, the efficiency and superiority of the proposed models is ascertained by comparing it with 3 D elasticity solution and also with various existing shear deformation theories in the literature. Most remarkably, the present models are accurately estimates the buckling load parameter and they are insensitive of shear-locking.