Orthotropic von Karman plates using higher order elements

The nonlinear behaviour of orthotropic plates subject to transverse loading is studied in this paper using higher order finite elements. The formulation procedure for elements with up to 25 nodes is established and derivation of the tangential stiffness matrix based on the classical von Karman nonlinear theory is presented. These elements are derived by employing a high order polynomial displacement function to represent the in-plane and the bending displacements. By adopting separate variables for the transverse deflections and the rotations of the plate, the effect of transverse shear deformation can be included in modelling thin to moderately thick plates, thus enabling the effect of transverse shear on the nonlinear behaviour of plates to be included. The Newton-Raphson method for solving nonlinear equations is adopted to obtain the final state of equilibrium of the system. Several numerical examples are presented and the results are compared with available experimental data as well as analytical and numerical solutions obtaned by other conventional methods. Satisfactory agreement on the nonlinear performance of the plates as predicted by the present method is demonstrated.