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The following chapter, adapted from , 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 . 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.
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Many researches have been carried out on this particular type of instability [44, 52, 264]. It has been shown that the main factors governing the phenomenon are the moment of inertia with respect to lateral bending \(I_y\), the torsional moment of inertia J and the warping constant \(C_w\), see Eq. 9.24. These quantities describe the stiffness of the section with respect to lateral bending and torsion. Remarkable importance has also the position of the shear centre and the point of application of the vertical load. These factors influence the entity of the twisting action when the buckling begins.
- Stochastic Optimisation Applied to Multi-axial Bending of Lightweight Beams
Federico Maria Ballo
- Springer International Publishing
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- Chapter 9
in-adhesives, MKVS, Hellmich GmbH/© Hellmich GmbH, Krahn Ceramics/© Krahn Ceramics