A Computationally viable higher‐order theory for laminated composite plates

Abstract

Abstract A variational higher‐order theory involving all transverse strain and stress components is proposed for the analysis of laminated composite plates. Derived from three‐dimensional elasticity with emphasis on developing a viable computational methodology, the theory is well suited for finite element approximations as it incorporates both C 0 and C −1 continuous kinematic fields and Poisson boundary conditions. From the theory, a simple three‐node stretching‐bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon/epoxy laminate for which an exact solution is available. Both the analytic and finite element results were found to be in excellent agreement with the exact solution for a wide range of the length‐to‐thickness ratio. The proposed higher‐order theory has the same computational advantages as first‐order shear‐deformable theories. The present methodology, however, provides greater predictive capabilities, especially, for thick‐section composites.