Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates

This paper presents analytical solutions of deflection and stress for orthotropic plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for orthotropic rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of orthotropic plates are investigated and discussed.