Multiscale surrogate-based framework for reliability analysis of unidirectional FRP composites

Abstract

In this paper, a Finite Element-based surrogate model is developed to efficiently estimate stiffness properties of unidirectional composite laminas, while accounting for geometric and material property uncertainties at micro, meso and laminate scale, all within a probabilistic framework. In the multi-scale build-up nature of composites, uncertainties occur in material properties and geometric characteristics. These uncertainties present a challenge in estimating composite material properties. The currently available property estimation/homogenisation tools are mainly divided into two categories: analytical methods constrained by configuration assumptions, and numerical homogenisation using Finite Element Analysis (FEA). The latter is more flexible and accurate, but computationally expensive. Hence, this paper develops a surrogate model based on a limited number of experimental FEA data points. Additionally, a transition phase is developed between micro and laminate scales that enables modelling of spatially varying uncertainties. As a result, this framework significantly decreases analysis duration compared with FEA techniques, and, because it is derived from FEA data points, can accurately represent a wide range of uncertainties.

Novel multi-zone self-heated composites tool for out-of-autoclave aerospace components manufacturing

“…As the demand for thermoset composites increases in number, size and complexity; the need for improved manufacturing techniques is vital. However, composites manufacturing is still a complex process that differs from alloys due to uncertainties inherited from their multi-phase compositing nature [4][5][6].…”

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

“…Performing RBDO for components that can be analysed analytically is simple compared with complex components that require numerical analysis with significant computational time. To demonstrate the feasibility of conducting an RBDO for numerically analysed components, an efficient FEA-based multi-scale reliability analysis developed by the authors (Omairey et al , 2019; Omairey et al , 2018) is used within a sequential deterministic and probabilistic optimisation strategy to reduce the mass of a composite component, while meeting a certain level of stiffness reliability, considering a wide range of uncertainties. An overview of this RBDO framework can be seen in Figure 2, and the required steps are explained in the following sections.…”

“…It takes the statistical information of uncertainties as an input and uses a large representative volume element (LRVE) that can model spatial variation of uncertainties, compared with a single RVE containing only one or two fibres, as shown in Figure 3. The LRVE is formed by correlating smaller RVEs in terms of material properties and geometric uncertainties, and employing a series of efficient surrogate models trained using a limited number of FE data points analysed using the periodic RVE homogenisation method [17], making it feasible to generate the large amount of probabilistic homogenised properties required to assess reliability accurately using Monte Carlo Simulation (MCS). Figure 3.…”

“…Also, material property uncertainties at the ply level are related to uncertainties at smaller scales. For example, ply stiffness properties in a fibre-reinforced composite are influenced by uncertainties in the fibre and matrix material properties, fibre volume ratio and fibre stacking (Sriramula and Chryssanthopoulos, 2009; Shi et al , 2020; Omairey et al , 2019; Omairey et al , 2018; Zhou et al , 2016; Shaw et al , 2010). However, combining multi-scale modelling with RBDO for fibre-reinforced composite components has received little attention to date.…”

“…The aim of this research is to create an efficient multi-scale RBDO method for fibre-reinforced composite materials, that accounts for a wide range of uncertainties (including geometric uncertainties at the fibre-matrix scale), uses MCS, to avoid issues with nonlinear and multi-modal limit state functions, a non-deterministic optimisation method, to avoid local minima and potentially include discrete design variables and a finite element model at the component scale. This is achieved by extending and combining our previous surrogate-based framework for an off-line multi-scale uncertainty propagation (Omairey et al , 2019) with an on-line sequential optimisation and reliability analysis approach and adaptive local surrogate modelling strategy. A novel feature of our multi-scale framework is an inclusive FEA-based material representation unit, known as a large representative volume element (LRVE) that interpolates the effect of spatially correlated micro and meso-scale material and geometrical uncertainties, yet is computationally efficient for integration within a developed sequential RBDO framework.…”