4. Analysis of Elastic-Plastic Buckling of Plates with Stiffeners by Finite Element Method

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Elastic-plastic buckling problems have been solved most effectively for engineering purposes by Rayleig's and Galerkin's method, the variational method. In recent years, however, the development of high speed digital computers has made a numerical approach, termed "the finite element method", more attractive in solving practical problems. Once, B. J. Kapur and K. K. Hartz dealt with elastic buckling of plates by the finite element method, employing rectangular finite elements and a nonconforming shape function. In this paper, using a conforming shape function and triangular finite elements, the finite element method has been expanded for solving problems of elastic-plastic buckling of plate. For plasticity either the incremental theory or the total strain theory of plasticity is used. The authors furthermore developed the finite element method to buckling of stiffened plate. Particular attention is paid to stiffeners furnished on one side of plate, as seen in most ship structures. In this case, the neutral plane of the stiffened plate moves away from the middle plane of the plate and additional stresses on the plate are induced at the instant of buckling of the stiffened plate. By the method, the effect of one side stiffening can be taken into account as well as torsional and axial rigidities of the stiffeners. Based on these theoretical developments a computer program was completed and several examples demonstrates the usefulness of the development.
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4. Analysis of Elastic-Plastic Buckling of Plates with Stiffeners by Finite Element Method

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