The optimization of a thin walled I-beam subjected to displacement constraint

Abstract

One approach to the optimization of a thin walled cantilever I-beam subjected to constrained torsion is considered. The aim of this paper is the determination of the minimum mass i.e. minimum cross sectional area of structural thin-walled I-beam elements for given loads, material and geometrical characteristics. That is why the area of the cross section is assumed to be the objective function. The displacement constraints are introduced: allowable angle of twist and allowable angle of twist per unit length. The starting points during the formulation of the basic mathematical model are the assumptions of the thin walled beam theory from one side and the basic assumptions of the optimum design from the other. Applying the Lagrange multiplier method, the equation of the second order, which solutions represent the optimal values of the ratios of the parts of the chosen cross section, is formed. The obtained results are used for numerical calculation applying The Finite Element Method.