Enhanced zigzag theory for static analysis of composite plates

Abstract

An enhanced efficient zigzag theory is presented for the static response in elastic composite plates under mechanical loading. The number of variables is six, which is one more than the conventional zigzag theory. Transverse shear stresses have been obtained through the use of constitutive equations in both symmetric and antisymmetric laminates under uniformly and sinusoidally applied mechanical load. The theory has a good representation of all the three displacement components. This is obtained by using individual descriptions for each layer as is observed in three-dimensional elasticity solution. Interlaminar continuity conditions on all displacement components, all transverse stresses and on the gradient of transverse normal stress as well as transverse shear-free conditions on the top and the bottom surfaces have been utilized to make the primary variables independent of number of layers in the laminate. Equilibrium equations and boundary conditions are derived from variational principle. Navier solution is obtained for simply supported square and rectangular plates. The accuracy of the present theory is assessed by comparison with three-dimensional (3D) elasticity solution. It is found that refinement of the transverse displacement alone is not sufficient to make the new theory capable of providing good accuracy in calculation of transverse stresses from constitutive equations, though some improvement is obtained in case of symmetric laminates.