Assessment of recent zig-zag theories for laminated and sandwich structures

Abstract

Abstract The flexural response of laminated composite and sandwich beams/plates under static distributed loading, classical and non-classical boundary conditions (simply-supported, cantilever and propped-cantilever) and geometric/constitutive heterogeneity of layers is analysed. As structural models, a recently developed equivalent single-layer zig-zag model by the authors, a discrete-layer model and a sublaminate model developed from it in this paper are used. Their contribution is to consider the continuity of the transverse normal stress and its through-thickness gradient at layer interfaces, as prescribed by the elasticity theory in addition to kinematic and transverse shear stress interlayer continuity customary considered in the literature. To this purpose, a piecewise variation of the three displacement components is adopted. The zig-zag amplitude expressions are obtained in closed-form from the enforcement of stress continuity conditions. To be refined without affecting costs, the equivalent single-layer model has variable kinematics and just five unknowns. Instead, sublaminate and discrete-layer models are refined by increasing the number of computational layers and variables. The aim of this paper is to assess whether the equivalent single-layer model having a computational cost comparable to that of classical models can be as accurate ad discrete-layer and sublaminate models. Benchmarks are presented, for which exact elasticity and approximate solutions are available for comparisons in literature. It is illustrated the utility of considering a variable kinematics for obtaining accurate stress predictions from constitutive equations and the transverse normal deformability for keeping equilibrium. The equivalent single-layer model is shown as accurate as discrete-layer and sublaminate models in all cases examined.