An exact exponential theory for the bending of simply supported laminated orthotropic plates

A laminated orthotropic plate theory is developed on the assumption that inplane displacements vary exponentially across plate thickness. Analytical solutions are obtained for simply supported, symmetric and anti-symmetric cross-ply rectangular laminates under transverse loading. The numerical results are compared with solutions of the three-dimensional elasticity theory, the third-order shear deformation theory, and the first-order shear deformation theory. It is found that the present exact exponential theory provides very accurate displacements and stresses in comparison to the three-dimensional elasticity theory. In particular, both transverse shear from constitutive equations and transverse normal stresses from equilibrium equations are more accurate than previously developed theories, even for small length-to-thickness ratios.