Post-Buckling Analysis of Plates using the Semi-Energy Finite Strip Approach
A geometrically non-linear finite strip for the post-local-buckling analysis of geometrically perfect thin-walled prismatic structures under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat plates.
The results are discussed in detail and compared with those obtained from finite element (FEM) analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose MSC/NASTRAN package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-local-buckling problem of plate structures.