Buckling and free vibration of elastic plates using simple and mixed shear deformation theories

Summary Simple and mixed shear deformable theories accounting for the transverse shear, in the sense of Reissner-Mindlin's thick plate theory, are employed in the construction of variational statements for rectangular flat plates. Analytical solutions for natural frequencies and buckling loads of anisotropic plates under various boundary conditions are developed. A variety of simply-supported, clamped and free boundary conditions is considered, and comparisons with the existing literature are made.