Optimum design of thin-walled I-beam subjected to stress constraint

This paper deals with the problem of optimization of a thin-walled open section I-beam loaded in a complex way, subjected to the bending, torsion and constrained torsion. A general case of bending moments about two centroidal axes, the torsion and the bimoment acting simultaneously, is derived and then some particular loading cases are considered. The problem is reduced to the determination of minimum mass, i.e. minimum cross-sectional area of structural thin-walled beam elements of the chosen shape for the given complex loads, material and geometrical characteristics. The optimization parameters have been determined by Lagrange's multipliers method. The area of the cross-section has been selected as the objective function. The stress constraint is introduced and used as the constraint function. The obtained results are used for numerical calculation.