Optimization Of Geometry For The Lateral Buckling Process Of A Cantilever Beam
Free (open access)
R. Drazumeric, F. Kosel & T. Kosel
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. Keywords: elastic stability, lateral buckling, geometry optimization, calculus of variation, large displacement theory. 1 Introduction Lateral buckling of a bent cantilever beam is a stability problem, where a small lateral disturbance in an unstable equilibrium state produces a spatial deflection of the beam, and as a result a combination of bending and torsional load appears. This transition causes an additional load on the beam, so in the design process it should be ensured that the load does not exceed its critical value. That is the reason why, in cases of slender elements where the stability limit is the main criterion, the load carrying capacity of the material is poorly exploited. One possible way of increasing the stability limit and better exploit the load carrying capacity of the element is to optimize its geometry.
elastic stability, lateral buckling, geometry optimization, calculus of variation, large displacement theory.