Finite Element Method for Buckling Analysis of Plate Structures

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Abstract
A finite element method using thin‐plate elements is presented. The method is capable of predicting the buckling capacity of arbitrarily shaped thin‐walled structural members under any general load and boundary conditions. The linear and geometric stiffness matrices for the thin‐plate element are derived explicitly based on the principle of minimum total potential energy, thereby eliminating the need for numerical integration. The proposed plate element contains 30 degrees of freedom (dof): 14 dof for the in‐plane (membrane) action and 16 dof for the out‐of‐plane (bending) action. Several numerical examples of thin‐walled structural members involving local, distortional, and flexural‐torsional buckling failure modes are presented to demonstrate the accuracy, efficiency, and versatility of the method.