One View on the Optimization of Thin-walled Cantilever Channel and Z-section Beams

Abstract

An approach to the optimization of the thin-walled cantilever open section beams subjected to thе bending and to the constrained torsion, whose consequencesis are particularly evident in the case of thin-walled profiles, is considered. The problem is reduced to the determination of minimum mass i.e. minimum cross-sectional area of structural thin-walled channel-section and Z section beam elements for given loads, material and geometrical characteristics. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. A general case when bending moments about two centroidal axes and the bimoment are acting simultaneously is derived, and then some particular loading cases are considered. A method of solving the optimal relation of the parts of the considered cross-section is described. Applying the Lagrange multiplier method, the equations, whose solutions represent the optimal values of the ratios of the parts of the chosen cross-section, are derived. The obtained results are used for numerical calculation