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Multi-scale reliability-based design optimisation framework for fibre-reinforced composite laminates

Sadik Lafta Omairey (School of Engineering, University of Aberdeen, Aberdeen, UK and Brunel Composites Centre, College of Engineering, Design and Physical Sciences, Brunel University London, London, UK)
Peter Donald Dunning (School of Engineering, University of Aberdeen, Aberdeen, UK)
Srinivas Sriramula (School of Engineering, University of Aberdeen, Aberdeen, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 14 August 2020

Issue publication date: 15 June 2021




The purpose of this study is to enable performing reliability-based design optimisation (RBDO) for a composite component while accounting for several multi-scale uncertainties using a large representative volume element (LRVE). This is achieved using an efficient finite element analysis (FEA)-based multi-scale reliability framework and sequential optimisation strategy.


An efficient FEA-based multi-scale reliability framework used in this study is extended and combined with a proposed sequential optimisation strategy to produce an efficient, flexible and accurate RBDO framework for fibre-reinforced composite laminate components. The proposed RBDO strategy is demonstrated by finding the optimum design solution for a composite component under the effect of multi-scale uncertainties while meeting a specific stiffness reliability requirement. Performing this using the double-loop approach is computationally expensive because of the number of uncertainties and function evaluations required to assess the reliability. Thus, a sequential optimisation concept is proposed, which starts by finding a deterministic optimum solution, then assesses the reliability and shifts the constraint limit to a safer region. This is repeated until the desired level of reliability is reached. This is followed by a final probabilistic optimisation to reduce the mass further and meet the desired level of stiffness reliability. In addition, the proposed framework uses several surrogate models to replace expensive FE function evaluations during optimisation and reliability analysis. The numerical example is also used to investigate the effect of using different sizes of LRVEs, compared with a single RVE. In future work, other problem-dependent surrogates such as Kriging will be used to allow predicting lower probability of failures with high accuracy.


The integration of the developed multi-scale reliability framework with the sequential RBDO optimisation strategy is proven computationally feasible, and it is shown that the use of LRVEs leads to less conservative designs compared with the use of single RVE, i.e. up to 3.5% weight reduction in the case of the 1 × 1 RVE optimised component. This is because the LRVE provides a representation of the spatial variability of uncertainties in a composite material while capturing a wider range of uncertainties at each iteration.


Fibre-reinforced composite laminate components designed using reliability and optimisation have been investigated before. Still, they have not previously been combined in a comprehensive multi-scale RBDO. Therefore, this study combines the probabilistic framework with an optimisation strategy to perform multi-scale RBDO and demonstrates its feasibility and efficiency for an fibre reinforced polymer component design.



This work was supported by the University of Aberdeen Elphinstone scholarship scheme.


Omairey, S.L., Dunning, P.D. and Sriramula, S. (2021), "Multi-scale reliability-based design optimisation framework for fibre-reinforced composite laminates", Engineering Computations, Vol. 38 No. 3, pp. 1241-1262.



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