  A multilayered plate theory which uses transverse shear warping functions
issued from three-dimensional elasticity is presented. Two methods to obtain
these transverse shear warping functions are detailed. The warping functions
are issued from the variations of transverse shear stresses computed at special
location points for a simply supported bending problem. 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 by the integration of equilibrium equations. Hence, an iterative
process is applied, the model being updated with the new warping functions, and
so on. 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 are considered, length-to-thickness values varying from 2 to
100. An additional analytical solution that simulates the behavior of laminates
under the plane stress hypothesis - which is retained by all presented models -
shows that the iterative model almost gives the exact solution for all
laminates and all length-to-thickness ratio values.

Classical Physics