Nonlinear finite element analysis of thick composite plates using cubic spline functions

A nonlinear, thick, composite plate element is developed in which the usual Kirchhoff hypothesis of plane sections remaining plane and undeformed after loading is abandoned. The displacement field is characterized by the sum of displacements with respect to a reference surface and displacements through the thickness. The through-the-thickness deformations are modeled by imposing a cubic spline function and allowing the rotations at interlaminar boundaries to be degrees of freedom in the element. The theory is developed by considering the Lagrangian strains in conjunction with the second Piola-Kirchhoff stress. This formulation leads to a quasi-threedimensional element that encompasses large displacements with moderately large rotations but is restricted to small strains. Comparisons of linear and nonlinear thick orthotropic plate solutions with those of previously published analytical and numerical results show the validity of the method.