Analytical solutions for bending of clamped layered composite plates using a higher-order theory

Analytical solutions are presented for the bending of clamped laminated plates using a higher-order shear deformation theory. Unlike the first-order shear deformation theory, the higher-order theory does not require a shear correction factor. The displacement field of the higher-order theory contains the same number of dependent variables as in the first-order shear deformation theory, and also accounts for the cubic variation of the in-plane displacements through the thickness. Closed-form solutions are not tractable for clamped composite plates due to the boundary conditions and anisotropy of the plate and hence approximate methods are required. In the present work, a method based on Lagrange multipliers is used to enforce the boundary conditions not satisfied by the assumed series. Results are presented for antisymmetric cross-ply and angle-ply plates to study the influence of anisotropy, aspect ratio, and loadings on the deflections and stresses of clamped plates.