Buckling Behavior of Nonlinear Elastic Cantilever Columns with an Elliptical Cross Section

This study investigates the buckling behavior of nonlinear elastic cantilever columns, with emphasis on two aspects: the generalized moment of inertia (GMI) of the elliptical plane area, and the buckling behavior of cantilever columns fabricated using nonlinear elastic materials based on the Ludwick constitutive law. An explicit integration formula is developed to calculate the GMI of an elliptical cross section, and the geometric and material nonlinear differential equations that govern the elastica of the buckling columns are derived. To integrate the differential equations, the Runge-Kutta method is used, and an iterative method that improves upon the Regula-Falsi method is used to determine the unknown deflection of the free end of the column. As numerical examples, parametric studies of the GMIs and post-buckling behavior, including buckling loads, of nonlinear elastic cantilever columns with elliptical cross sections are extensively discussed.