Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations

Abstract

A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functions are obtained, the stiffness and mass matrices of the models are computed. These two models are compared to other models and to analytical solutions for the bending of simply supported plates. Four different laminates and a sandwich plate are considered. Their length-to-thickness ratios vary from 2 to 100. An additional analytical solution that simulates the behavior of laminates under the plane stress hypothesis – shared by all the considered models – is computed. Both presented models give results very close to this exact solution, for all laminates and all length-to-thickness ratios.