Optimal Lay-up Research Articles

Flexural properties and optimisation of hybrid composites reinforced by carbon, glass and flax fibres

This paper presents a study on the flexural properties of hybrid composites (HC) reinforced by carbon, glass, and flax fibres, utilising Finite Element Analysis (FEA). Possible optimal layups are identified through the application of design rules, and regression-based models are developed to predict flexural strength. With the developed models, multi-objective optimisation is done to minimise the cost and weight subjected to a given minimum required flexural strength. By integrating numerical simulation, regression analysis, and optimisation techniques, this research offers a practical approach to the design and fabrication of HC with enhanced mechanical performance and cost-efficiency.

Optimal lamination angles via exact and efficient differentiation of the geometrically nonlinear finite element solution

Laminates allow tailoring the fiber orientations in the layers to obtain the desired mechanical response. The optimal layup design is a challenging task in the case of finite deformations and buckling. For an assigned design, an incremental-iterative finite element analysis is needed to compute the structural response. Gradient-based methods are very often the most efficient optimization tools. Their bottleneck is the gradient evaluation, generally possible only approximately by finite differences. This article shows how to compute the exact gradient of the geometrically nonlinear finite element solution with respect to the stacking sequence. The strategy relies on the implicit differentiation of the nonlinear discrete equations of a control equilibrium point corresponding to an assigned displacement. This provides the load factor gradient by a single fast-solution linear system with the already factorized tangent stiffness matrix, regardless of the number of design variables, and scalar products involving the partial derivatives of the discrete internal force vector, calculated in an exact and efficient way. Several applications demonstrate the efficiency and robustness of the approach.

Experimental study on the mechanical behavior of laminates made by fiber steering: influence of fiber angle and tow width

Abstract This work considers the effects of fiber trajectory and prepreg width on the material strength and failure behavior of variable stiffness composites. The test matrix was designed according to commonly used fiber placement trajectory and width of prepreg in engineering. Different trajectories were compared for tensile, compressive, bending, shear and CAI strengths. For tensile and compressive performance, curved ply specimens have varying degrees of decrease compared to straight ply specimens; For shear and bending performance, the optimal layup sequence is [±45/〈30|45〉]. For impact toughness, curved ply is significantly higher than straight ply, and the CAI strength of straight ply exceeds that of curved ply. For variable stiffness laminate with different fiber angles and tow widths, the maximum tensile, compressive and CAI strengths were reduced by up to 66%, 56%, and 27%, and the maximum bending strength, shear strength and impact toughness were increased by up to 53%, 23%, and 10.3%, respectively. The increase in width of prepreg leads to an increase in defects between fiber bundles which weakens the tensile/compressive performance but enhances the shear/bending performance.

Fracture parameters of woven jute fibre reinforced axial flow fan blade material: an experimental investigation and FEA analysis

Airflow required for the heat and mass transfer in industrial applications is often provided by axial flow fans. Glass fibre reinforced polymers (GFRP) are most often used to make these fan blades. The usage of glass fibres in composite materials is growing. By 2025, the global market for glass fibres will be worth 16.5 billion pounds. However, non-biodegradable composite reinforcement has major ecological and human health concerns, especially when reaching the end of its operational lifespan. Until now, industries have shown a strong inclination to use GFRP without adequately contemplating the potential consequences associated with their disposal. The economic viability of glass fibre recycling is questionable. However, natural fibres like jute and fibres extracted from vegetable plants are of much popular among academics and researchers due to their sustainability and ease of use. So, they’re suitable for making polymer composites. The amount of natural fibres that may be added to GFRP composites without materially altering their mechanical characteristics is a crucial factor in improving their decreased embodied emissions and biodegradability after service life. In this work the material represents an 18-ft axial flow fan blade material made of GFRP. This study used the term denotes the specific material utilised in the fabrication of 18-feet axial flow fan blades for industrial purposes. By substituting one layer of with woven jute and changing its position in it, the materials through are produced. All the materials are tested for fracture parameters like plane strain fracture toughness and Critical strain energy release rate as per ASTM D-5045. The results were validated by using finite element models implemented in a commercially available software ANSYS R19.2. The optimal layup sequence for fan blade material with single-layer woven jute reinforcement was found, which preserves fracture properties, also improves biodegradability after service life.

Automated Fiber Placement Laminate Level Optimization for Mitigation of Through Thickness Defect Stacking

Manufacturing composite structures with Automated Fiber Placement (AFP) requires detailed process planning that is rigorous and time consuming. To facilitate, accelerate and perpetuate process planning knowledge, the Computer Aided Process Planning (CAPP) tool was developed. CAPP assists process planners in identifying optimal layup strategies for each ply of a laminate. This paper expands the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: genetic algorithm, differential evolution, particle swarm, and greedy search. The algorithms identify optimal combinations of ply-level layup strategies by analyzing defect stacking using two objective functions. These approaches are evaluated through a digital case study performed on a complex tool surface. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack-up.

An Accelerated Process Optimization Method to Minimize Deformations in Composites Using Theory-guided Probabilistic Machine Learning

While aerospace manufacturing and assembly technologies have significantly evolved, challenges persist in mitigating process-induced deformations (PIDs) in composite parts. Physics-based-simulation optimization strategies have been developed to address these challenges. However, they often prove ineffective or inefficient because of the time-consuming, costly, and deterministic characterization efforts they require. This study introduces a novel characterization- and simulation-free optimization approach for predicting and minimizing PIDs in composite parts. The method uses a theory-guided machine learning (TGML) framework, consisting of limited element-level experiments and Gaussian Process Regression (GPR) with integrated closed-form domain knowledge. This paper showcases the effectiveness of the proposed TGML method for two case studies, where an optimal layup and cure cycle are found and validated after a mere six experiments and without any material characterization or simulation efforts. The method presented in this paper aims to offer a cost-efficient and generalizable process optimization procedure to potentially mitigate PIDs in composite parts.

The Impact of Bend–Twist Coupling on Structural Characteristics and Flutter Limit of Ultra-Long Flexible Wind Turbine Composite Blades

Flutter is an instability phenomenon that can occur in wind turbine blades due to fluid–structure interaction, particularly for longer and more flexible blades. Aeroelastic tailoring through bend–twist coupling is an effective method to enhance the aeroelastic performance of blades. In this study, we investigate the impact of bend–twist coupling on the structural performance and flutter limit of the IEA 15 MW blade, which is currently the longest reference wind turbine blade, and determine the optimal layup configuration that maximizes the flutter speed. The blade is modeled by NuMAD and iVABS, and the cross-section properties are obtained by PreComb and VABS. The accuracy of the blade model is verified in terms of stiffness and frequency. The bend–twist coupling is implemented by changing the fiber angle of the skin and spar cap considering symmetric and asymmetric layups. The flutter limits of both the baseline and the bend–twist coupled blade are evaluated based on HAWC2. The results show that the angle of spar cap carbon fiber has a greater effect on the blade’s structural properties and flutter speed than the skin fiber. Varying the spar cap carbon fiber angle increases the flutter speed, with the effect being more significant for the symmetric layup, up to 9.66% at a fiber angle of 25 degrees. In contrast, the variation in skin fiber angle has a relatively small impact on flutter speed—within ±3%.

Optimization design and secondary buckling of bio-inspired helicoidal laminated plates under thermomechanical loads

Bio-inspired helicoidal carbon fiber reinforced polymer composite (CFRPC) laminates are one of the novel composite structures that have potential applications in many engineering fields. The optimization design of helicoidal layups with linear, nonlinear Recursive, Fibonacci, Exponential and their combination-form arrangements are carried out using ABAQUS and ASA algorithm on Isight platform. Two cases of the compressive postbuckling under uniaxial compression and the thermal postbuckling under uniform temperature rise of helicoidal CFRPC laminated plates stacked with optimal layups are performed and the secondary buckling and mode jumping in the postbuckling region are examined for the first time. Numerical investigations are carried out for 16-ply symmetrical helicoidal laminated plates with various width-to-thickness ratios under different boundary conditions and are compared with quasi-isotropic counterparts. The results show that the bio-inspired helicoidal CFRPC laminated plates can enhance the buckling load and the buckling temperature as well as the compressive and the thermal postbuckling strength. In some cases, the secondary buckling and mode jumping may occur for rectangular helicoidal laminated plate in the postbuckling region.

Parametric resonance and bifurcation analysis of thin-walled asymmetric gyroscopic composite shafts: An asymptotic study

Nonlinear geometries and cross-sectional asymmetry can be among the most critical contributing factors affecting the performance and stability of composite shafts. The influence of these factors, which should be devoted to particular attention in the design of these systems and have not been investigated yet, are evaluated analytically in this study. The shaft is simply supported, made of orthotropic multi-layers, and spinning at a constant speed. To express the nonlinear system’s behavior, which is due to the large amplitude of the vibrations, it is assumed that the shaft is under the stretching assumption. Moreover, a rectangular cross-section is used to model the asymmetry that results in parametric excitation in the system. To accurately investigate the behavior of composite material, an optimal lay-up is employed. The gyroscopic coupling is included because of Rayleigh beam theory, and Euler’s angles are employed to achieve the angular velocities. The analytical study of the parametrically excited system, obtained by the method of multiple scales, is performed in two categories of resonant and nonresonant cases. In the nonresonant case, the analytical investigation suggests that the asymmetric shaft behaves like a symmetric one therefore, the parametric excitations do not have a significant impact. This claim is confirmed by numerical results. Also, the presence of the gyroscopic coupling and hollowness of the shaft causes the beating phenomenon in the system. However, in the resonant case, the presence of parametric excitation plays a pivotal role. The results also show that under certain conditions and despite the presence of damping, asymmetric balanced rotors can have a nontrivial stable amplitude. This response exists as long as the parametric excitation effects dominate the damping effects. Although damping reduces the vibrations’ amplitude, it can improve the stability of the system and eliminates unstable responses. Furthermore, the time response and frequency response curve of the system is carefully evaluated for various geometric design parameters and operation speed. Depending on the operating speed, the system can experience supercritical or subcritical pitchfork bifurcation. In addition, a detailed description of the system’s Campbell’s diagram, damping effect, and bifurcation is provided. Furthermore, it is proved that internal resonance cannot occur in the system. The accuracy of the analytical responses of the resonant case is compared with numerical ones. Stability of trivial and nontrivial responses is discussed in the time response and phase portrait of the system simultaneously. Finally, in the undamped system, multi-frequency responses are appeared as homoclinic and heteroclinic closed orbits.

Efficient structural optimisation of composite materials aircraft wings

Contemporary computational analysis of modern aircraft structures demands rapid and efficient, yet accurate enough tools for the conceptual and preliminary design stages. On that front, a novel optimisation framework, utilising low-cost numerical tools for sizing composite materials aircraft wings subject to stiffness, strength and dynamic aeroelastic constraints is proposed herein. The structural representation of the numerical model is based on the well-established equivalent-plate methodology, capable of reducing the size and computational cost of the associated problem. An equivalent-plate model of a modern transport aircraft wing is developed and compared to its equivalent 3D Finite Element Method model. Results by means of natural frequencies and modes, indicate excellent accordance between the numerical models. An optimisation framework is then presented, with the ply thicknesses of a baseline lay-up being assigned as design variables. The developed framework succeeds to guide the mass of the wing to a minimum while satisfying the constraints under a critical loading scenario. Optimal lay-ups for the skins, spar webs and ribs as well as spar and rib caps dimensions are obtained. The presented optimisation framework, exhibiting high accuracy and efficiency, constitutes a robust numerical tool for the early design stages of composite aircraft wings.

Optimization of Composite Cylindrical Shell Structures for Hydrostatic Pressure Loading

Abstract Deep-sea structures will collapse/implode under hydrostatic pressure when the structure dives below an instability threshold, leading to catastrophic failure. To better understand how the layup angle of composite cylindrical shells influences this instability threshold, this work explores how composite cylinders can achieve the highest (optimum) critical collapse pressure under hydrostatic loading conditions. To perform this analysis, a closed-form analytical cylinder buckling solution developed by previous work is used in conjunction with different cylindrical geometrical configurations and composite properties for glass, carbon, and intraply hybrid composite properties for woven and unidirectional structures. The results show that a composite structure's optimum layup configuration is unique to the structure's geometry and material system. However, general trends are observed for these different systems, such as how symmetric and asymmetric constructions place the axial-resistant layers near the neutral plane of the composite system. In addition, both constructions need an increase in shear-resistance layers as the L/D ratio decreases regardless of the material system. Lastly, the analytical approach presented in this work can be used to accurately determine the optimum layup angle for thin composite cylindrical structures that are subjected to external hydrostatic pressure.

Accelerating the Layup Sequences Design of Composite Laminates via Theory-Guided Machine Learning Models.

Experimental and numerical investigations are presented for a theory-guided machine learning (ML) model that combines the Hashin failure theory (HFT) and the classical lamination theory (CLT) to optimize and accelerate the design of composite laminates. A finite element simulation with the incorporation of the HFT and CLT were used to generate the training dataset. Instead of directly mapping the relationship between the ply angles of the laminate and its strength and stiffness, a multi-layer interconnected neural network (NN) system was built following the logical sequence of composite theories. With the forward prediction by the NN system and the inverse optimization by genetic algorithm (GA), a benchmark case of designing a composite tube subjected to the combined loads of bending and torsion was studied. The ML models successfully provided the optimal layup sequences and the required fiber modulus according to the preset design targets. Additionally, it shows that the machine learning models, with the guidance of composite theories, realize a faster optimization process and requires less training data than models with direct simple NNs. Such results imply the importance of domain knowledge in helping improve the ML applications in engineering problems.

Structural design optimization of composite materials drive shafts

Composite materials drive shafts attract particular interest in recent years. Their high strength, light weight and high fatigue and corrosion resistance make them suitable for high specification mechanical and marine applications. In the context of the present work, advanced finite element models that simulate the static and dynamic mechanical behaviour of composite drive shafts are combined with optimization algorithms in order to determine the optimum lay-up of a composite shaft according to the desired specifications. The composite shaft is also combined with metallic flanges and the performance of the combined system is also investigated. The created models facilitate the structural design optimization of composite material drive shafts and constitute the basis for the future implementation of the simulation driven digital twins of composite materials drivetrain systems.

Reduction of free-edge effects around a hole of a composite plate using a numerical layup optimization

The stacking sequence has a great influence on the performance of composite structures especially when it comes to stress concentration effects. In the current research, various orientation angles and layups for a composite plate with a central hole are investigated and the optimized layup is determined for the desired thickness. The objective of the optimization is the minimization of the interlaminar peeling stress around the hole. Failure strength around the hole is the basis of the constraint incorporating Hashin’s failure criteria for each lamina individually. For this purpose a two-step analysis is carried out: Primarily a finite element analysis is performed using ABAQUS to determine the constraint for orientation angles. Then, the pattern search method is utilized to obtain the optimized layup using the interaction of MATLAB and ABAQUS software. Moreover, a sensitivity analysis is carried out to determine the effect of the material properties, the size of the hole and the initial guess applied for the pattern search solution upon the optimal layup sequence.

Layer-wise optimization of elliptical laminates with curvilinear fibers

The lay-ups of symmetric variable stiffness composite laminated elliptical plates with curvilinear fibers are optimized for the maximum frequencies of the lowest three modes using the layer-wise optimization method. Two design variables and three constraints are considered. The fiber paths are constructed using the method of shifted paths. The laminate is modeled as one curved hierarchical finite element. The formulation is based on the first-order shear deformation theory. The blending function method is used to model accurately the geometry. New results for the optimal lay-ups that maximize the natural frequencies of the lowest three modes are obtained. The method is validated based on convergence test and comparison with published results for symmetric constant stiffness composite laminated elliptical plates with rectilinear fibers. A parametric study is performed showing the effects of aspect ratio, thickness ratio, modulus ratio, number of layers, and boundary constraint on the optimal solutions.

Dynamic stability optimization of laminated composite plates: An isogeometric HSDT formulation and PSO algorithm

An isogeometric analysis framework based on the non-uniform rational B-spline (NURBS) and the higher-order shear deformation theory (HSDT) is developed to study the geometry-accurate dynamic instability behavior of the shear-sensitive generally laminated composite plates. The developed approach is combined with the particle swarm optimization (PSO) technique to modify the layup orientations of the laminate corresponding to the minimum dynamic instability opening (DIOI) value. Based on the accuracy assessment results, the convergence rate of the developed method is higher than the classical finite element method. Moreover, the frequency accuracy of cubic NURBS is stabilized for high degrees of freedom denoting their high computational efficiency. The optimization procedure reveals that the mode shapes of the plates with optimal layups are more complex than their non-optimal case. The optimal ply angles are mostly oriented along the maximum-curvature path, perpendicular to the loading direction, and parallel to the supported edges. The mixed-type supports leads to lower DIOI values for optimal layups concerning the homogeneous supports. The pure compressive force expands the fundamental dynamic instability region (DIRI) for the generally laminated plates and leads to wide-range frequency instabilities. However, the combination of compressive force with lateral or shear force increases the lower bound of the DIRI for optimal layups. The minimization of DIOI value does not necessarily increase the lower bound of DIRI for optimal layups.

Stress Analysis of Composite Aircraft Wing using Coupled Fluid-Structural Analysis

Aircraft wings are designed with very low factor of safety to keep the aircraft weight minimum. Thus, for safe design of wings, stress analysis should be carried out under accurately estimated aerodynamic loads and this can be achieved only through coupled fluid-structure analysis. Moreover, modern aircraft wings are made of laminated composite structures and thus the purpose of this study is to employ ANSYS coupled fluid-structure analysis to find the best layup of composite wing of an aircraft that results in higher specific strength and specific stiffness. Firstly, Computational Fluid Dynamics (CFD) analysis has been carried out to find the actual aerodynamic load which is the pressure distribution around a three-dimensional wing. Then, this pressure distribution from CFD was used as a load input for detailed static structural analysis of the wing. Initially, strength and stiffness of an isotropic wing is evaluated and then the material of the wing was changed to composite laminates to achieve better structural performance with higher strength and stiffness to weight ratio. Stress analysis was carried out for different layups to predict the optimum layup that results in high strength and stiffness coupled with the least weight and it was found that the wing made of symmetric cross-ply laminate performs the best.

Performance assessment of meta-heuristics for composite layup optimisation

This paper investigates the performance of several meta-heuristic algorithms, including Particle Swarm Optimisation (PSO), different variants of Differential Evolution (DE), Biogeography-Based Optimisation (BBO), Cultural Algorithm (CA), Optics-Inspired Optimisation (OIO), and League Championship Algorithm (LCA), for optimum layup of laminated composite plates. The study provides detailed Pseudo codes for different algorithms. The buckling capacity maximisation of a 64-layer laminated composite plate under various load scenarios has been considered as the benchmark problem, in which the design variables are the stacking sequences of layers. A Deep Statistical Comparison (DSC) method is employed to rank the performance of different algorithms. The DSC uses a nonparametric two-sample Kolmogorov-Smirnov test to conduct the performance comparisons between the algorithms. The overall performance rankings obtained from the DSC suggest that the LCA, OIO, and PSO algorithms perform remarkably better in comparison to other algorithms. The comparisons provide some interesting conclusions on the performance of different algorithms.

Optimization of Free Vibration and Flutter Analysis of Composite Plates Using a Coupled Method of Genetic Algorithm and Generalized Differential Quadrature

In this study, the optimization of free vibration and flutter analysis of a composite plate with the implementation of different boundary conditions is investigated. The governing equations of a composite plate are obtained using the first shear deformation theory (FSDT) of plates. The first-order piston theory is utilized to simulate aerodynamic loads, including arbitrary yaw angle over the panel area. The coupled method of genetic algorithm with well-known generalized differential quadrature (GDQ) method is then developed to obtain optimal layup, which led to maximum fundamental frequency and optimized critical flutter aerodynamic pressure. To achieve this aim, the free vibration and flutter analysis of a composite plate will be conducted via the obtained eigenvalue problem by establishing the discretized governing equations and applying boundary conditions. The obtained results are compared and validated with the available results in the literature, which show high accuracy and a fast rate of convergence. Also, the influence of changing in the yaw angle, number of layers, thickness-to-length ratio, boundary conditions and turning symmetric layup to asymmetric layup is studied.

Comparative Analysis of the Selection of Lay-Up Stacking of Polymer Composite Load-Bearing Elements for the Tail Section of Fuselage Structure of the Light Aircraft

The problem of the selecting the optimal lay-up stacking of polymer composite materials for the load-bearing elements of the rear part of fuselage structure is considered. The comparison of two approaches to the design of the load-bearing elements is carried out. The first of them is the use of multilayered composite material for the load-bearing elements, the stacking angles of which is selected from a given discrete set, and the second is the use of composite material with a continuous range of variables in fabric lay-up angles. As a result design optimization, it is shown that using an optimization method with a continuous range of lay-angles allows reducing the weight of the load-bearing elements by 12.79%