Keywords: laminated composite plate, optimisation, RBDO, OSF, ACO, PSO.

Laminated composites provide not only a high structural performance, but also minimize the cost of such structures [1]. For instance, in the aerospace industry each kilogram less in the structure leads to the reduction of roughly 25,000 euros [2]. Thus, optimisation techniques have been applied to take the structure to the limit. However, the optimisation of laminated composites can be classified as a non-convex and multimodal optimisation problem. For such problem, the evolutionary algorithms are well-suited, and they are well able to handle this kind of function. Among others, we can cite: the genetic algorithm (GA), the particle swarm optimisation (PSO), and the ant colony optimisation (ACO).

In deterministic optimisation the uncertainties of the system (i.e. dimensions, model, material, loads, etc) are not taken into account. Doing so, the resulting optimum solution may lead to a lower level of reliability and, as a consequence, a higher risk of failure. Thus, it is the objective of reliability based design optimisation (RBDO) to design structures that should be both economic and reliable.

The optimum safety factor (OSF) approach [3] is based on the reliability and sensitivity analysis, and contains the advantages of both the reliability-based and the deterministic design procedures. The advantages of the former is the satisfaction of a required reliability level (i.e. target reliability index) and the advantage of the latter is that there is no need for additional computational time because the designer can use the results of the sensitivity analysis of the constraint function obtained during the optimisation process when considering the deterministic variables as random ones [3].

This paper aims at optimizing laminated composite plates taking into account uncertainties in the structure dimensions. Two different evolutionary algorithms are used as optimisation tools: PSO and ACO. The objective function of the optimisation is the weight minimization of the structure. The OSF approach is used as an RBDO methodology. The coupling of evolutionary strategies and the OSF method applied to laminated composite plates is the main feature of this paper. The following conclusions can be drawn from the analysis pursue in the paper:

• The PSO performed better than the ACO, obtaining better mean value and smaller standard deviation results;
• The coupling of the ACO and the PSO with the OSF successfully performed the RBDO for a laminated composite plate;
• The OSF is able to perform the RBDO of structures with a very little extra computational effort than the deterministic optimization.

1

R.M. Jones, "Mechanics of composite materials", second edition, Taylor and Francis, Philadelphia, USA, 1999.

2

R & G. Faserverbundwerkstoffe, eight edition, 2006.

3

G. Kharmanda, N. Olhoff, A. El-Hami, "Optimum values of structural safety factors for a predefined Reliability level with extension to multiple limit states", Structural and Multidisciplinary Optimisation, 26, 421-434, 2004. doi:10.1007/s00158-004-0405-0

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