Optimization of geometry for lateral buckling process of a cantilever beam in the elastic region

Using the large displacement theory (theory of the third order according to Chwalla), the paper deals with lateral buckling process of a slender, elastic cantilever beam with a changeable cross-sectional area 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 main feature of the optimized geometry beam is a constant maximal reference stress, obtained by the deformation energy theory, along the whole length of the beam in a deflected form which means that in terms of stability the material is completely exploited. The result of this feature is, besides higher critical load, also higher carrying capacity of the optimal geometry beam in the postbuckling region.