Buckling performance of variable stiffness composites considering material uncertainties via multiscale stochastic fibre volumes

The novel manufacturing techniques of composite laminates are leading to a reduction in the amount of defects present at the mesoscale level of variable stiffness plates (VSP), see for instance the Continuous Tow Shearing [1] method that permits to avoid the misalingments and skip the presence of gaps and/or overlaps among tows. Nevertheless, the inner constituents of the composite material might not be flaw-exempt, e.g: void content, variation in the fibre volume, presence of different phases, etc. This fact leads to the need of a multiscale analysis of the whole VSP, which have been demonstrated to be computationally expensive for classic composite structures. In the recent years, the Carrera Unified Formulation (CUF) [2] has been extended to the micromechanical [3] and multiscale [4] analysis of material composites, providing solutions that required fewer number of degrees of freedom and, thus, a reduction in terms of CPU time. By using the CUF framework, extended to both VSP [5] and micromechanics, this work aims to show how variations in the fibre volume content of the material affect the buckling performance of VSPs. For doing so, stochastic fibre volume fields are generated by means of the Covariance Matrix Decomposition (CMD) [6]. Each component of the random field is assigned to a micromechanical model in order to homogenise the material elastic properties, thus leading to a spatially varying distribution of such properties

Influence of fiber misalignments on buckling performance of variable stiffness composites using layerwise models and random fields

Additive manufacturing brought to the emergence of a new class of fiber-reinforced materials; namely, the Variable Angle Tow (VAT) composites. Automated fiber placement machines allow the fibers to be relaxed along curvilinear paths within the lamina. In theory, the designer can conceive VAT structures with unexplored capabilities and tailor materials with optimized stiffness-to-weight ratios. In practise, steering brittle fibers, generally made of glass or carbon, is not trivial and highly affected from the printer signature. This paper wants to explore the effect of fiber misalignment on the buckling response of laminated VAT composites. For doing so, we use the Carrera Unified Formulation (CUF), which allows to develop layerwise models with unprecedented accuracy in a straightforward and systematic manner. Variation patterns are generated at the layer scale by means of random fields through a Monte Carlo analysis. The stochastic variation (defects) is propagated through the scales and correlated with the global buckling response of VAT panels. The results show that layerwise models outperform equivalent single layer theories, since the former are able to foresee eventual switching between buckling modes, and thus making them fundamental in uncertainty analysis

Optimisation of multi-layered structures using a multispecies genetic algorithm and high-order structural models

Due to the intrinsic nature of aerospace engineering, structural weight has always been an aspect of utmost importance during the design stages of aircraft and spacecraft. Indeed, light alloys were preferred for the construction of such structures until the irruption of composite materials. Currently, composite materials might represent more than 50% of the structural components of aircraft thanks to its mechanical properties and improvements in manufacturing techniques. In the recent years, fabrication procedures have been oriented to the additive manufacturing strategies, such as automated fibre placement or fused deposition modelling, which lead to multi-layered structures. As mentioned before, weight optimisation is one of the key steps in structural design. However, nowadays procedures, such as polar or lamination parameters, are based on assumptions that may shrink the design space. In this work, a direct optimisation genetic algorithm (GA) is proposed. The presented GA is able to deal with discrete- and continuous-valued design variables, as well as including a multispecies capability, and new genetic operators. In this manner, several laminated structures can be considered at the same time in the optimisation loop in order to find the least-weight design that fulfils certain structural requirements. The latter are calculated by means of an in-house finite element code based on the well-known Carrera Unified Formulation (CUF), in which high-order structural models can be obtained and used to analyse the mechanical performance of multi-layered structures

Stochastic characterization of multiscale material uncertainties on the fibre-matrix interface stress state of composite variable stiffness plates

This work analyses the stochastic response of fibre and matrix scale stresses of Variable Angle Tow (VAT) laminates affected by multiscale uncertainty defects. The aim is to evaluate the influence of the innermost constituents on the overall structural response via an accurate mechanical characterization of both macro- and microscales. The Carrera Unified Formulation (CUF) is employed to obtain two-dimensional (2D) and one-dimensional (1D) models for both scales. Indeed, 2D layer-wise (LW) and 1D component-wise (CW) approaches are adopted for the macroscale and the microscale, respectively. The use of 2D and 1D models proves to be convenient as a superior computational efficiency is reached, this aspect being of great importance as many analyses are necessary for uncertainty quantification. The numerical results demonstrate the validity of the proposed methodology to obtain an accurate description of the 3D stress state at the different scales. A special focus is made on the fibre-scale stresses and how they may vary when affected by multiscale uncertainty

Sensitivity analysis of variable stiffness composite plates by CUF-based layerwise models

Composite materials are increasingly used in many engineering fields thanks to their lightness and high mechanical properties. Currently, many research activities are focused on the optimization of structures using conventional composite materials, i.e. Constant Stiffness Composite Materials (CSCM). High-performance structures, such as those employed in aerospace engineering, could be further enhanced by using modern automated fibre placement machines, which brought to the emergence of a new class of composites; namely, the Variable Angle Tow (VAT) composites. The main idea of VAT composites is to have an increased freedom in the tailoring of the material properties since the fibres are no longer restricted to be straight and can actually have a curvilinear pattern within each layer. This work presents some sensitivity analyses based on a refined model developed in the domain of the Carrera Unified Formulation (CUF), which has been already demonstrated to be effective for the analysis of VAT structures. Essentially, CUF makes use of arbitrarily high-order kinematics to relax 3D elasticity equations into 1D or 2D theories [1]. Lagrange polynomials have been employed in this work to describe the cross-section variables, because refined 1D models are utilized, obtaining a layer-wise description of the primary variables. Layer-wise approach confirmed the highest accuracy in comparison with equivalent-single-layer models, also for VAT as demostrated by Demasi et al. [2]. The main objective is to study the effect of manufacturing processes on the mechanical response of VAT. Particular attention is focussed on the misalignments of the fibres, which ultimately affect the global properties of the structure. Such misalignment fields are generated by means of stochastic field theory exploiting the correlation matrix decomposition (CMD) method (like those presented in Broek et al. [3]), where relative distances between structural nodes are considered. Several numerical examples show the importance of using a layer-wise approach for sensitivity analysis and design of VAT composite panels, especially when buckling response and redistribution of stress fields are considere

Dynamic characterization of 3D printed lightweight structures

This paper presents the free vibration analysis of 3D printed sandwich beams by using high-order theories based on the Carrera Unified Formulation (CUF). In particular, the component-wise (CW) approach is adopted to achieve a high fidelity model of the printed part. The present model has been used to build an accurate database for collecting first natural frequency of the beams, then predicting Young's modulus based on an inverse problem formulation. The database is built from a set of randomly generated material properties of various values of modulus of elasticity. The inverse problem then allows finding the elastic modulus of the input parameters starting from the information on the required set of the output achieved experimentally. The natural frequencies evaluated during the experimental test acquired using a Digital Image Correlation method have been compared with the results obtained by the means of CUF-CW model. The results obtained from the free-vibration analysis of the FDM beams, performed by higher-order one-dimensional models contained in CUF, are compared with ABAQUS results both first five natural frequency and degree of freedoms. The results have shown that the proposed 1D approach can provide 3D accuracy, in terms of free vibration analysis of FDM printed sandwich beams with a significant reduction in the computational costs

Buckling Sensitivity of Tow-Steered Plates Subjected to Multiscale Defects by High-Order Finite Elements and Polynomial Chaos Expansion

It is well known that fabrication processes inevitably lead to defects in the manufactured components. However, thanks to the new capabilities of the manufacturing procedures that have emerged during the last decades, the number of imperfections has diminished while numerical models can describe the ground truth designs. Even so, a variety of defects has not been studied yet, let alone the coupling among them. This paper aims to characterise the buckling response of Variable Stiffness Composite (VSC) plates subjected to spatially varying fibre volume content as well as fibre misalignments, yielding a multiscale sensitivity analysis. On the one hand, VSCs have been modelled by means of the Carrera Unified Formulation (CUF) and a layer-wise (LW) approach, with which independent stochastic fields can be assigned to each composite layer. On the other hand, microscale analysis has been performed by employing CUF-based Mechanics of Structure Genome (MSG), which was used to build surrogate models that relate the fibre volume fraction and the material elastic properties. Then, stochastic buckling analyses were carried out following a multiscale Monte Carlo analysis to characterise the buckling load distributions statistically. Eventually, it was demonstrated that this multiscale sensitivity approach can be accelerated by an adequate usage of sampling techniques and surrogate models such as Polynomial Chaos Expansion (PCE). Finally, it has been shown that sensitivity is greatly affected by nominal fibre orientation and the multiscale uncertainty features