Keywords: structural optimization, reliability, robustness, progressive collapse, multi-objective, Pareto.

Structural design optimization typically aims at detecting the optimum design by minimizing the cost (or weight) of a structure subject to certain behavioral constraints (mainly on member stresses and nodal displacements or inter-storey drifts) as imposed by design codes. Although structural optimization applications are usually treated within a deterministic setting ignoring uncertainties in material properties, geometric parameters, loads etc., non-deterministic concepts are increasingly being taken into account in the design optimization process. Currently, reliability-based design optimization (RBDO) appears to be the most common approach applied to structural design optimization problems under uncertainty. RBDO is a single-objective optimization procedure with an incorporated structural reliability constraint: the objective is to minimize the cost (or weight) of a structure, while reliability is addressed by pre-specifying the maximum allowable failure probability of the structure for the final design.

Apart from considering cost criteria and failure probability constraints within the structural design process, attention has been focused (especially during recent years) also on incorporating structural robustness requirements. Treating structural robustness is a further step beyond controlling structural reliability. A robust structure is generally capable, in the event of damage, of sustaining consequences in an acceptable/tolerable way. Thus, robustness is directly related to structural damage tolerance and its evaluation becomes a probabilistic assessment task when uncertainties are involved in the formulation of the problem at hand. A risk-based measure of robustness is employed in the present work, which involves the calculation of structural damage and failure probabilities and accounts for consequences due to potential damage and failure in the structure considered.

Structural robustness can be incorporated in the design optimization process by adding a related constraint or objective. The robustness-based optimization formulations presented in this work are built upon the conventional RBDO procedure, therefore they inherit the constraint of RBDO on system failure probability. Hence, a single-objective reliability and robustness-based optimization formulation is introduced, which appends a robustness constraint to standard RBDO. Moreover, a multi-objective optimization formulation is proposed, which maintains control over structural reliability through the inherited RBDO constraint, but upgrades robustness to being pursued through an optimization objective (together with structural cost or weight). The multi-objective version produces several tradeoff optimal structural designs (Pareto-optimal solutions), as opposed to the single structural design located by the single-objective version.

Single and multi-objective genetic algorithms (GAs) serve as implementation platforms for the optimization methodologies considered in the present work. The numerical results reported demonstrate the effectiveness of the proposed optimization approaches and justify the incorporation of robustness in the structural design optimization process. Hence, the overall aim of this work is to present optimization procedures capable of producing cost-effective structural designs with acceptable damage/failure probabilities and high robustness.

purchase the full-text of this chapter (price £20)

go to the previous chapter
go to the next chapter
return to the table of contents
return to the book description
purchase this book (price £88 +P&P)