  A multilayered plate theory which takes into account transverse shear and
normal stretching is presented. The theory is based on a seven-unknowns
kinematic field with five warping functions. Four warping functions are related
to the transverse shear behaviour, the fifth is related to the normal
stretching. The warping functions are issued from exact three-dimensional
solutions. They are related to the variations of transverse shear and normal
stresses computed at specific points for a simply supported bending problem.
Reddy, Cho-Parmerter and (a modified version of) Beakou-Touratier theories have
been retained for comparisons. Extended versions of these theories, able to
manage the normal stretching, are also considered. All these theories can be
emulated by the kinematic field of the present model thanks to the adaptation
of the five warping functions. Results of all these theories are confronted and
compared to analytical solutions, for the bending of simply supported plates.
Various plates are considered, with special focus on very low
length-to-thickness ratios: an isotropic plate, two homogeneous orthotropic
plates with ply orientation of $0$ and $5$ degrees, a $[0/c/0]$ sandwich panel
and a $[-45/0/45/90]_s$ composite plate. Results show that models are more
accurate if their kinematic fields (i) depend on all material properties (not
only the transverse shear stiffnesses) (ii) depend on the length-to-thickness
ratio (iii) present a coupling between the $x$ and $y$ directions.
