Geometric non-linear analysis of thin flat plates under end shortening, using different versions of the finite strip method

Abstract

Two finite strip methods are developed for predicting the geometrically non-linear response of rectangular thin plates with simply supported ends when subjected to uniform end shortening in their plane. Although the formulations of both finite strip methods are based on the concept of the principle of minimum potential energy, the first finite strip method utilizes a semi-energy finite strip, whereas in the second finite strip method (which is designated by the name full-energy finite strip method) all the displacements are postulated by the appropriate shape functions. It is noted that in the semi-energy finite strip approach, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form while the von Kármán's compatibility equation is solved to obtain the corresponding in-plane displacement forms. The developed finite strip methods are then applied to analyze the post-local-buckling behavior of some representative thin flat plates for which the results are also obtained through the application of finite element method, employing general purpose MSC/NASTRAN package. Through the comparison of results and the appropriate discussion, the knowledge of the level of capability of different versions of finite strip method is significantly promoted.