Stochastic Optimisation Applied to Multi-axial Bending of Lightweight Beams

The following chapter, adapted from [129], deals with the stochastic optimisation of complex mechanical systems like a beam subject to bending and torsion [88, 177, 178]. The adopted (and proper) theoretical basis for such an optimisation is multi-objective programming [152]. Multi-objective programming allows the designer to find a preferred solution by means of a proper selection among the set of optimal solutions called “Pareto-optimal set”. The designer, by means of the addressed selection, defines a set of parameters (design variable set) which defines the system under consideration. The choice (selection) is made after the optimal combination of the system performances has been identified by the designer.