Study on the reliability of Shanley's plastic buckling model by using the finite element method

The continuum modeling of the finite element method is used to study the reliability of Shanley's plastic buckling theory which generalizes Engesser's tangent-modulus theory and Karman's reduced-modulus theory. The study includes the deformation behavior that is the basis of the development of classical theories, the change of deformation behavior following the variation of the slenderness ratio of the column model, the adequacy of the classical approach of simply using certain effective moduli in Euler's formula to define the buckling load and the difference of factors which affect Shanley's buckling load and the buckling load of finite element results. Buckling loads of different column models are obtained from the converged finite element solutions. They are compared with Shanley's buckling loads. In solving the nonlinear finite element systems, the incremental/iterative procedure is used to update the response history. An accelerated iteration method based on improving a modified Newton-Raphson scheme is used for obtaining converged solutions of the discretized nonlinear algebraic systems.