New Nonpolynomial Shear-Deformation Theories for Structural Behavior of Laminated-Composite and Sandwich Plates

TLDR

The study proposes and implements new nonpolynomial shear‑deformation theories for laminated‑composite and sandwich plates. The authors develop theories with nonlinear transverse shear stress distribution, traction‑free boundary conditions, and governing equations derived by virtual work, solved by a generalized closed‑form Navier‑type method for bending, buckling, and free‑vibration analysis. The formulation handles all five‑degree‑of‑freedom shear‑deformation theories, accurately predicts structural responses, shows that shear deformation choice affects analysis type, and predicts responses efficiently at comparable computational cost to other single‑layer theories.

Abstract

In the present study, new nonpolynomial shear-deformation theories are proposed and implemented for structural responses of laminated-composite and sandwich plates. The theories assume nonlinear distribution of transverse shear stresses, and also satisfy the traction-free boundary conditions at the top and bottom layers of the laminates. The governing differential equations are derived for a generalized shear-deformation theory by implementing the dynamic version of principle of virtual work and calculus of variations. A generalized closed-form solution methodology of the Navier type is implemented to ensure the validity and efficiency of the present theories for bending, buckling, and free-vibration responses of the laminated-composite and sandwich plates. It is observed that the proposed formulation in conjunction with the solution methodology is capable of handling all existing five-degree-of-freedom-based shear-deformation theories. The comparison of results also shows that the adequate choice of shear deformation leads to an accurate prediction of structural responses. The influence of shear deformation on the type of analysis performed is also observed in this study. The theories are also capable of an efficient prediction of the responses of structures at a similar computational cost as that of other equivalent single-layer theories.