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

Abstract

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Defects and uncertainties of adhesively bonded composite joints

“…Designing and analysing FRP composite materials is a more complicated process than metal alloys due to their multi-material build-up nature, which introduces more design variables [57]. For instance, designing alloy adherend will typically have the overlap thickness as the primary material design variable.…”

“…Their inherent and irreducible nature classifies them as aleatory uncertainties, often defined in the form of a probabilistic distribution [32]. If these uncertainties are not accounted for, composite performance at the joint will be non-optimal, potentially leading to poor reliability and failure [57]. The traditional approach to account for these uncertainties is to use safety factors.…”

“…10 The main design variables of alloys and composites. From [57] Fig. 11 Illustration of possible composite laminate damage because of excessive surface preparation adherend material properties, bond line thickness, spew fillet and taper geometries, and defects such as disbonds, cracks and delamination as shown in the Fig.…”