Bicriteria optimization of cold-formed thin-walled beams with monosymmetrical open cross sections under pure bending

This work deals with the problem of optimal design of selected channel section shapes under bending moment. The optimization problem is given as the bicriteria one, where the cross-sectional area of the thin-walled beam is the first objective function, while the deflection of the beam is the second one. The geometric parameters of cross section were selected as design variables. The set of constraints includes global and local stability conditions, the strength condition, and technological and constructional requirements in the form of geometric relations. The optimization problem was formulated and solved with the help of the Pareto concept of optimality and preference functions. The numerical procedures include discrete, continuous and discrete–continuous sets of the design variables. Results of numerical analysis are presented in the form of tables, cross section outlines and diagrams. At the end of the work, the results are discussed and the directions of further research are provided.