Optimum Design of Elastic-plastic Column

Abstract

A method of optimum design for maximizing the buckling load of an elastic-plastic column of given volume, length, and material is presented. The column material is assumed to obey Ramberg-Osgood's deformation law and the buckling load is computed by means of the finite element method taking account of the tangent modulus theory. Rosen's gradient projection method is used for determining the optimum shape. Numerical results obtained for a simply supported column with similar cross section are shown to be in reasonably good agreement with the analytical solution proposed in a previous paper. As for new treated examples of columns with other cross sections and boundary conditions, it also seems that reasonable solutions are obtainable by the proposed method. Furthermore, we treat the problems including the constraint on a lower bound of the cross sectional areas of columns.