Buckling loads of columns with varying cross sections

Abstract

The determination of buckling loads for columns with varying cross sections is an important problem in engineering design. Previous studies found that analytical solutions are available only for some cases of columns with simple varying cross sections. Many numerical methods have been developed in the past few decades that make it possible to carry out the buckling analyses for columns with arbitrarily varying sections. In this paper, a new numerical method is presented that transforms the eigenvalue problem of an ordinary differential equation into a special initial value problem; the eigenvalue (or the buckling load) can be evaluated by satisfying the boundary conditions specified at the ends of the column.