Optimization of geometry for the lateral buckling process of a cantilever beam

Abstract

Using the large displacement theory (theory of the third order according to Chwalla), this paper deals with the lateral buckling process of a slender, elastic cantilever beam with a changeable height of a rectangular cross section and represents it with a system of nonlinear differential equations. Based on a mathematical model of the lateral buckling process, which considers the geometric and boundary conditions, an optimal geometry of a cantilever beam is obtained using the calculus of variation. A comparison between the properties of the beam with optimized geometry and those of a referential beam with a constant cross section is shown. The result of the optimization process is, besides a higher critical load, a higher carrying capacity of the optimal geometry beam in the postbuckling region. For a verification of the theoretical results an experiment of the lateral buckling process had been done.