A new unconstrained third-order plate theory for Navier solutions of symmetrically laminated plates

Among the many higher order plate theories, the third-order shear deformation plate theory (TSDT) of Reddy is, perhaps, the most widely adopted model in the study of laminated plates. It, however, imposes a restriction that transverse shear stress vanishes on the top and bottom surfaces of the plate. Such requirement, although reasonable in many engineering applications, is not valid when the plate is subject to shear traction parallel to the surface. To account for such problems, the present plate model releases the constraints of vanishing transverse shear stress on the top and bottom plate surfaces. This unconstrained third-order shear deformation plate theory (UTSDT) is particularly useful for the study of a plate with contact friction or present in a flow field where the boundary layer shear stress is significant. The governing differential equations of UTSDT are of similar complexity as that of TSDT but it yields more accurate solutions. In addition, it is more flexible as it can be degenerated to the first-order shear deformation plate theory (FSDT) of Reissner and Mindlin if the higher-order rotation coefficients are neglected and a shear correction factor is considered, or to the TSDT if the relevant rotation coefficients are constrained. The present study further develops the unconstrained theory in composite laminates. Navier solutions for bending and stress analysis of multilayered and symmetrically laminated composite plates are presented. It is concluded that the present plate model provides more accurate solutions than that of TSDT, with similar level of analytical complexity, when compared with the 3D elasticity exact solutions.