Vol.6, No3, 2006, pp. 121-128
UDC 624.014.072.21.04

Abstract

An approach to the optimization of a channel section in a thin-wall cantilever beam subjected to constrained torsion is considered. For given loads, material and geometry the problem is reduced to determination of minimal mass, i.e. minimal cross-section area of the thin-wall channel section of cantilever beam. That is why the cross sectional area is chosen to be the objective function. The selected criterion is strain constraint, i.e. the allowable angle of twist and the allowable angle of twist per unit length. By applying the Lagrange multiplier method, an equation of the fourth order is derived with solutions representing optimal ratios of cross section dimensions of chosen profile. The obtained results are used for numerical calculations applying the finite element method.

Keywords: optimization, cantilever beam, thin-wall bar, channel section, optimal dimensions, strain constraint