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The following chapter introduces, with an example, the major topics of the optimal design of complex mechanical systems. An application to structural design is dealt with. The example has been derived from  and adapted to this book.
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As an effective design process should always produce an optimal solution, optimisation and design are reputed to be the same process by the Authors.
b and h may vary, respectively, within two well-defined ranges.
If, for a generic optimisation problem, the objective functions were to be maximised, changing their signs would transforms the maximisation problem into a minimisation one, so the presented example dealing with minimisation is quite general.
b and h are precisely parameters, with the property that they have to be varied, thus they are variable parameters which is a nonsense as parameters do have fixed values. To avoid misunderstanding these variable parameters are named design variables to distinguish them from actual parameters having fixed values.
Vilfredo Pareto (1848–1923) was an Italian engineer who later became a famous sociologist and economist at the University of Lausanne.
E.g. minimising only m( b, h) or only y( b, h)).
The assumptions are that the design variables space is closed and the objective functions are continuous functions of the design variables .
This seems the main reason why, presently, very few designers are instructed to apply the optimisation theory based on Pareto-optimality.
When all of the simulations have been made on the basis of all possible combinations of design variables, the construction of all Pareto-optimal sets is performed by selecting the so-called dominating solutions from the dominated ones .
- Introduction to the Optimal Design of Complex Mechanical Systems
Federico Maria Ballo
- Springer International Publishing
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