A modified first-order-warping theory for shear deformation analysis

A modified first-order-warping theory which satisfies zero transverse shear stress conditions on the bottom and the top of the plate is developed. This theory takes into account the effects of non-linear distribution of the displacements through the thickness and the theory requires no shear correction coefficients. Using only one warping function with satisfaction of the transverse shear stress conditions leads to a high-order theory using only five mid-plane displacement parameters, as the Mindlin theory. A displacement finite element formulation is presented. The results from the present theory are compared to the low-order theory of Mindlin and exact solutions available in the literature.