A refined nonlinear theory of plates with transverse shear deformation

A higher-order shear deformation theory of plates accounting for the von Karman strains is presented. The theory contains the same dependent unknowns as in the Hencky-Mindlin type first-order shear deformation theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact solutions of simply supported plates are obtained using the linear theory and the results are compared with the exact solutions of three-dimensional elasticity theory, the first order shear deformation theory, and the classical plate theory. The present theory predicts the deflections, stresses, and frequencies more accurately when compared to the first-order theory and the classical plate theory.