Fiber Path Research Articles

Variable angle tow-steered curvilinear fibres-based rotating arbitrarily layered composite beams- a coupled vibration of chordwise-flapwise-torsional motions by higher-order beam theory

In the present work, variable angle tow-steered curvilinear fibres-based straight composite rotating beam is studied for its coupled vibrational behaviours from different beam planes by a higher-order beam formulation satisfying plane stress situation and combining with finite element methodology. The structural theory is extended to include all the vibrational motions including chord- and flap-wise motions, axial and torsional vibrations of beam. The centrifugal force stiffening and gyroscopic effects stemming from rotational motions are taken into the formulation. The generic differential equations of equilibrium for the proposed structural theory are evolved adopting virtual dynamic work, Hamilton’s principle and a suitable C1 continuity based elemental equations are obtained. The newly constructed finite element formulation is tested for solved problems that are known in the literature. Based on in-depth analysis, vibration features of curvilinear fibre-based rotating generally layered composite beam including coupled dynamic motions in terms of vibrational modes and their frequencies pertaining to chord- and flap-wise, axial, torsional motions are detailed presuming variable angles along the curvilinear fibre path at the centre and layer edge, short and long beams, hub-radius, beam cross-section, and high rotational speed effects.

Buckling optimization of variable-stiffness composite plates with two circular holes using discrete Ritz method and potential flow

Potential flow around two equal-radius cylinders is derived analytically and applied to generate the curvilinear fiber path of variable-stiffness composite (VSC) plates with two circular holes. As complex variable theory and conformal mapping are used to generate the potential flow around two equal-radius cylinders, the location and size of the two equal-radius circular holes are arbitrary. By changing the angle of incoming flow, the global fiber angle of a variable-stiffness lamina can be simulated and the local fiber orientation angle at any point is determined by the global potential flow field. Buckling performance of variously-shaped VSC plates with two circular holes are investigated via a novel numerical method − discrete Ritz method (DRM). DRM combines the extended interval integral, Gauss quadrature, and variable stiffness within a rectangular domain and builds a discrete energy system to simulate the plate, which allows the geometric boundaries of the plate to vary. The strain energy of a plate is modeled in the rectangular domain, discretized using Gauss points, and is characterized by variable stiffness, which characterizes both the material distribution and plate geometry simultaneously. After that, a three-dimensional sampling optimization (3DSO) method is adopted to optimize the curvilinear fiber configurations of VSC plates, and its buckling performances are compared with those of constant stiffness composites (CSC) with optimal straight fibers. Significant improvements on load-carrying capacity can be achieved compared to straight ones, demonstrating that using potential flow is one of the most efficient way to generate curvilinear optimal fiber path with maximum load-carrying capacity for VSC plates with material discontinuity. Moreover, DRM exhibits good precision and stability for buckling analysis of VSC plates with complex geometries.

Geometric Complexity Control in Topology Optimization of 3D-Printed Fiber Composites for Performance Enhancement.

This paper investigates the impact of varying the part geometric complexity and 3D printing process setup on the resulting structural load bearing capacity of fiber composites. Three levels of geometric complexity are developed through 2.5D topology optimization, 3D topology optimization, and 3D topology optimization with directional material removal. The 3D topology optimization is performed with the SIMP method and accelerated by high-performance computing. The directional material removal is realized by incorporating the advection-diffusion partial differential equation-based filter to prevent interior void or undercut in certain directions. A set of 3D printing and mechanical performance tests are performed. It is interestingly found that, the printing direction affects significantly on the result performance and if subject to the uni direction, the load-bearing capacity increases from the 2.5D samples to the 3D samples with the increased complexity, but the load-bearing capacity further increases for the 3D simplified samples due to directional material removal. Hence, it is concluded that a restricted structural complexity is suitable for topology optimization of 3D-printed fiber composites, since large area cross-sections give more degrees of design freedom to the fiber path layout and also makes the inter-layer bond of the filaments firmer.

Continuous tow shearing for the automated manufacture of defect-free complex 3D geometry composite parts

It has always been challenging to manufacture a composite structure with complex geometry using automated fibre placement (AFP) process. The tool surface is difficult to be tessellated using fibre tapes with a finite width, without producing gaps and overlaps, and fibre steering along non-geodesic fibre paths produces various defects such as tape buckling and pull-up. In this work, a defect-free fibre-steering process on a complex surface was demonstrated by realising the continuous tow shearing (CTS) process in three dimensions. A new head control algorithm was developed, which defines the head orientations and trajectories based on the pin-jointed net model to manipulate the fibre tow using both in-plane shear and out-of-plane twisting deformations. Fibre steering process utilising this new algorithm was tested on a doubly-curved surface, using an industrial robot arm equipped with a CTS prototype head, and its layup quality and accuracy were assessed by using a three-dimensional laser profile scanner. An experimental comparison with the conventional AFP process showed that the new control algorithm enables defect-free fibre steering on complex 3D surfaces allowing for simplifying the design and analysis of novel composite structures.

A non-uniform rational B-splines (NURBS) based optimization method for fiber path design

This work presents a systematic optimization method utilizing non-uniform rational B-splines (NURBS) to represent fibers in composites and design their paths. Beyond mean compliance, the objective function incorporates repulsive energy to prevent fiber knots and intersections. Utilizing NURBS control points as design variables reduces the number of design variables and expands the solution space, as they can reach any point within the design domain under the guidance of the sensitivity of the objective function in the method of moving asymptotes. Additionally, the p-norm technique for curvature constraints represents an innovative adaptation to avoid sharp turns in fibers. The work can also add fibers during optimization and enable the design of multi-layer fiber-enhanced composite structure to address various design challenges associated with optimizing fiber paths. Numerical examples show that the mean compliance decreases by 60∼70 % compared to initial configurations, and the computation time is reduced by 80 % compared to similar cases in prior work.

Evolution of variable angle tow composite structures: Data analysis and relevance of the theme

Variable angle tow composites were developed to increase stiffness in notched laminates. Scientific advancements in manufacturing and fiber path optimization have since improved variable angle tow composites. This study uses bibliometric analysis to track the evolution of variable angle tow composites in the literature. Bibliometric analysis is a useful tool for measuring paper contributions and accurately assessing performance, aiding authors in the research process. This article presents a co-occurrence map of keyword frequency in research papers. Furthermore, an experimental section highlights manufacturing defects found in variable angle tow composites produced by filament winding, showing that manufacturing real structures in variable angle tow composites poses a significant challenge. Lastly, the perspectives of variable angle tow composite applications are discussed.

Continuous fiber path optimization in additive manufacturing: A gradient-based B-spline finite element approach

Additive manufacturing of continuous fiber enables the control of local material distribution and mechanical characteristics. This localized control is realized through fiber path generation and optimization, which is one of the core problems in the additive manufacturing of continuous fiber. Current fiber path generation and optimization methods mostly try to infill topology-optimized parts or align the fiber with the maximum stress directions, which may lead to sub-optimality or time-consuming computations. This paper provides a different approach to optimize the fiber path directly by parameterizing it with B-splines and manipulating its control points. A finite element model with B-spline fiber parameterization is established, with an analytical fiber-in-element probability. This framework streamlines the computation of local and global stiffness and mass matrices, enabling effective and efficient prediction of loading responses, stiffness, and natural frequencies. The probability framework also allows efficient calculation of the gradients of the stiffness and mass matrices, leading to a gradient-based fiber path optimization. The effectiveness and accuracy of both the finite element and optimization methods are verified with simulation and experiment case studies. Results demonstrate enhancements in stiffness and strength with less fiber usage compared to a commonly adopted principal stress direction method.

Enhanced amygdala-anterior cingulate white matter structural connectivity in Sahaja Yoga Meditators.

To study the white matter connections between anterior cingulate cortex, anterior insula and amygdala as key regions of the frontal-limbic network that have been related to meditation. Twenty experienced practitioners of Sahaja Yoga Meditation and twenty nonmeditators matched on age, gender and education level, were scanned using Diffusion Weighted Imaging, using a 3T scanner, and their white matter connectivity was compared using diffusion tensor imaging analyses. There were five white matter fiber paths in which meditators showed a larger number of tracts, two of them connecting the same area in both hemispheres: the left and right amygdalae and the left and right anterior insula; and the other three connecting left anterior cingulate with the right anterior insula, the right amygdala and the left amygdala. On the other hand, non-meditators showed larger number of tracts in two paths connecting the left anterior insula with the left amygdala, and the left anterior insula with the left anterior cingulate. The study shows that long-term practice of Sahaja Yoga Meditation is associated with larger white matter tracts strengthening interhemispheric connections between limbic regions and connections between cingulo-amygdalar and cingulo-insular brain regions related to top-down attentional and emotional processes as well as between top-down control functions that could potentially be related to the witness state perceived through the state of mental silence promoted with this meditation. On the other hand, reduced connectivity strength in left anterior insula in the meditation group could be associated to reduced emotional processing affecting top-down processes.

Influence of fibre steering on the bearing performance of bolted joints in 3D printed pseudo-woven CFRP composites

Aiming to improve the bearing performance of bolted joints in carbon fibre reinforced polymer (CFRP) composites, this study investigates the impact of steered fibre paths around the hole edge within pseudo-woven (interlaced) composites that are manufactured by 3D printing. The influence of fibre steering on the crack initiation and propagation was examined through double-lap bearing tests performed on four distinct cases. Parallel to the comprehensive experimental study, digital image correlation (DIC) and X-ray computed microtomography (micro-CT) scans were performed to aid in understanding and identifying the various damage mechanisms in each specimen type. Results revealed that different patterns provided varying bearing abilities, with an employed pattern improving the initial bearing strength, initial fracture energy and ultimate fracture energy of the 3D printed pseudo-woven composite by 23.5%, 363.7% and 29.6%, respectively. Consequently, fibre steering in composites is found to be a promising method to tailor the bearing behaviour of bolted joints as required.

Open loop flutter control of optimally oriented smart variable stiffness plates under hygrothermal environment

The present study investigates the impact of hygrothermal effects on the free vibration and flutter characteristics of a smart variable stiffness composite laminate (VSCL). This research seeks to underscore the inherent advantages of VSCLs in contrast to conventional straight fibre constant stiffness composite laminates (CSCLs). Utilizing curvilinear fibres, VSCLs offer a heightened level of customization, culminating in notably enhanced structural performance. The Genetic Algorithm is employed to obtain optimal fibre paths for the variable stiffness laminates. Introducing an active fibre composite layer as an actuator atop the optimally oriented VSCL laminate enhances its capabilities. A parametric inquiry into the influence of hygrothermal loading on the smart structure's free vibration and flutter traits is undertaken. While hygrothermal loading imparts vulnerability to the laminate, the introduction of voltage to the active fibre composite layer counteracts this weakening effect, effectively augmenting stiffness and concurrently enhancing the flutter parameters (velocity, frequency) intrinsic to the plate structure.

A strength optimization approach for manufacturable 3D printed variable stiffness laminates with a strain-based approximation

The 3D printed continuous carbon fiber reinforced polymers (CFRP) are promising lightweight structures with outstanding mechanical performance. In this work, we propose a structure-manufacture integrated optimization approach for strength maximization of variable stiffness 3D printed CFRP composites by tailoring the steered printing paths. The rule of mixture is modified to evaluate material properties and strength of the printed laminates considering the effect of fiber volume fraction. To make this approach applicable to CFRP with asymmetric layups, a strain-based two-level convex approximation for the failure index based on the Tsai–Wu failure criterion is proposed, which can take the tension-bending coupling effect into consideration. The local failure indices are aggregated using the p-norm formula to reduce the size of the strength optimization model. In order to guarantee the manufacturability of the optimal design, the curvature of the steered printing fiber paths is constrained using a hybrid control method within the approach. The numerical cases show that the strength enhancement of the 3D printed variable stiffness laminates depends on the load, where an improvement between 35% and 46% can be achieved under the tension. Moreover, the proposed method can not only converge stably, but also be capable of optimizing structures with complex geometry.

A modified equally-spaced method (MEQS) for fibre placement in additive manufacturing of topology-optimised continuous carbon fibre-reinforced polymer composite structures

This study proposes a modified equally-spaced (MEQS) method for the path design of continuous fibres in additive manufacturing (AM) of topologically optimised composite structures. The MEQS method addresses the low fibre infill rate issue of the traditional Equally-Spaced (EQS) method by utilising the Offset method to generate looped printing paths around the internal cavities and gaps between continuous fibre paths. The developed MEQS method was first illustrated against EQS and Offset methods using an open-hole composite plate in which topology and material orientation were simultaneously optimised using the discrete–continuous parameterisation (DCP) method. Actual printing path-based finite element modelling showed that the MEQS method achieves a 25.32% increase in stiffness compared to the Offset method. Experimental testing of the additively manufactured open-hole composite plates showed that the MEQS method improves the stiffness and strength by 15.52% and 27.38%, respectively, compared to the Offset method. The proposed MEQS was further demonstrated through two other case studies by finite element modelling, showing that the stiffness of MEQS has increased by an average of 66.71% and 14.95% compared to EQS and Offset, respectively.

Layer thickness and path width setting in 3D printing of pre-impregnated continuous carbon, glass fibers and their hybrid composites

3D printing has been successfully applied in the manufacturing of variety continuous fiber and hybrid fiber reinforced composites. The process parameters have a significant impact on the overall performance of the printed parts. This paper investigates the effects of layer thickness and path width on the bending strength and surface roughness of printed pre-impregnated continuous carbon fiber, glass fiber, and their hybrid composites. Additionally, the microstructures of the fracture surfaces of the printed parts were analyzed. The results indicate that the optimal combination of bending strength and surface accuracy for printed single fiber parts is achieved when the printing layer thickness is set to 30%–40% of the fiber filament diameters. Furthermore, finely matched path width settings significantly improve the surface accuracy of printed hybrid carbon/glass fiber composites. Notably, the bending strength of printed interlayer hybrid fiber composite specimens increased by 35% compared to the specimens uniformly set according to the carbon fiber path width.

White Matter Fiber Tracking Method with Adaptive Correction of Tracking Direction.

The deterministic fiber tracking method has the advantage of high computational efficiency and good repeatability, making it suitable for the noninvasive estimation of brain structural connectivity in clinical fields. To address the issue of the current classical deterministic method tending to deviate in the tracking direction in the region of crossing fiber region, in this paper, we propose an adaptive correction-based deterministic white matter fiber tracking method, named FTACTD. The proposed FTACTD method can accurately track white matter fibers by adaptively adjusting the deflection direction strategy based on the tensor matrix and the input fiber direction of adjacent voxels. The degree of correction direction changes adaptively according to the shape of the diffusion tensor, mimicking the actual tracking deflection angle and direction. Furthermore, both forward and reverse tracking techniques are employed to track the entire fiber. The effectiveness of the proposed method is validated and quantified using both simulated and real brain datasets. Various indicators such as invalid bundles (IB), valid bundles (VB), invalid connections (IC), no connections (NC), and valid connections (VC) are utilized to assess the performance of the proposed method on simulated data and real diffusion-weighted imaging (DWI) data. The experimental results of the simulated data show that the FTACTD method tracks outperform existing methods, achieving the highest number of VB with a total of 13 bundles. Additionally, it identifies the least number of incorrect fiber bundles, with only 32 bundles identified as wrong. Compared to the FACT method, the FTACTD method reduces the number of NC by 36.38%. In terms of VC, the FTACTD method surpasses even the best performing SD_Stream method among deterministic methods by 1.64%. Extensive in vivo experiments demonstrate the superiority of the proposed method in terms of tracking more accurate and complete fiber paths, resulting in improved continuity. The FTACTD method proposed in this study indicates superior tracking results and provides a methodological basis for the investigating, diagnosis, and treatment of brain disorders associated with white matter fiber deficits and abnormalities.

Effect of Fiber Path on the Buckling Behavior of Delaminated Composites Reinforced with Woven Fabrics; Analytical and Numerical Study

Effect of Fiber Path on the Buckling Behavior of Delaminated Composites Reinforced with Woven Fabrics; Analytical and Numerical Study

Simultaneous optimization of fiber paths and geometric dimensions for fiber composite laminates using double neural network-surrogate model and genetic algorithm

CFRP is characterized by its anisotropic properties. Therefore, further structural weight reduction might be achieved by introducing the fiber direction as a design variable. For this study, steering fiber laminates defined by a Bezier curve are applied to a skin panel of CFRP stiffened panels. Then, simultaneous optimization of the fiber paths and stringer dimensions is performed to minimize the panel weight. We propose a new surrogate model that combines two neural networks and Latin hypercube sampling. Stiffness, manufacturability, and buckling load are introduced as constraints. Also, optimization is performed using the surrogate model and a genetic algorithm (GA). Furthermore, the stringer dimensions and fiber directions are optimized for straight fiber laminates. Comparison of steering fiber laminates and straight fiber laminates demonstrated that the introduction of steering layup into skin plates can reduce the stringer weight by up to 25.6%. An effective method for designing the geometric dimensions and layup path is provided.

Optimizing fiber paths of tow-steered laminated composites for parametric stability using isogeometric analysis and genetic algorithm

An isogeometric formulation is presented for fiber path optimization of tow-steered composite laminates (TSCL) with minimal parametric instabilities. Here, the fiber path functions of a TSCL is expressed smoothly by Cp−1 continuous non-uniform rational B-splines (NURBS) for engineering shapes, providing accurate field solutions. In this way, the motion equations of a TSCL plate is developed based on the third-order shear deformation theory (TSDT) and the Bolotin’s approximation is used to determine the parametric instability region. Primarily, the accuracy and efficiency of presented framework is measured for a TSCL example with respect to the existing solutions. Then, the optimal fiber paths of TSCL plates are searched using the genetic algorithm (GA) for various geometries, force component combinations, and dynamic-to-static force ratios. Results reveal that the optimal fiber paths are not necessarily symmetric even for regular domains, demonstrating the non-uniform coupling of bending and twisting stiffness in TSCL plates. The optimal design of TSCL fiber paths necessitates the consistency of local stiffness distribution and the resultant bending–twisting mode shape, specially when the dynamic force is high with respect to the static one. Geometry, force component combination, and dynamic-to-static force ratio impose case-specific fiber paths for optimal TSCL plates, requiring both minimal deformation and instability opening.

Design method of variable slippage coefficient non‐geodesic filament‐wound composite pressure vessels

AbstractPrevious studies on the design methods of filament winding paths for composite pressure vessels have mainly focused on geodesic and constant slippage coefficient non‐geodesic patterns, neglecting the design of variable slippage coefficients along the fiber path. In this paper, a design method of variable slippage coefficient non‐geodesic filament wound composite pressure vessels is proposed. The study begins by establishing a meridian rotation mapping model and deriving fiber path equations on the shell surface. Subsequently, the fiber paths, curvature characteristics, slippage coefficients, and shell stress responses of the shell under variable geometrical parameters are simulated and analyzed. Next, the winding parameters are optimized while considering bandwidth and stable winding constraints. The optimal winding parameters are determined, and filament winding simulations are conducted on composite pressure vessels. Results demonstrate the feasibility of the proposed method for variable slippage coefficient fiber path winding mode, providing a new and effective filament winding path design approach for composite pressure vessels.Highlights Establishment of meridian rotation mapping model and simulation of shell fiber paths under variable geometric parameters. The fiber paths, curvature characteristics, slippage coefficients, and winding angles of the shell under variable geometrical parameters are simulated and analyzed. Stress response analysis of shells based on Tsai‐Wu failure criterion and classical lamination theory stress field dimensionless modeling. Construction of winding parameter optimization strategies and bandwidth error evaluation based on stable winding and fiber bandwidth constraints. Simulation of variable slippage coefficient non‐geodesic filament winding for composite pressure vessels with different parameters.

Topology optimization for additive manufacturing of CFRP structures

Combining design optimization and additive manufacturing (AM) enables the full exploitation of the potential for heightening the performance of carbon fiber reinforced plastic (CFRP) structures. This study simultaneously conducts topology optimization and fiber path design by employing the radial basis function (RBF) based level set function (LSF). Fiber paths are determined instinctively for the inherent advantages of the LSF, and fiber orientations are parameterized accordingly. Manufacturing drawbacks such as gaps and overlaps can be avoided by introducing a fast-marching method. To verify the effectiveness of the optimization method, three groups of optimized and empirical designs are fabricated by the AM technique, respectively, and the experimental tests are further carried out. Finite element (FE) models are also reconstructed based on the printing schemes, and then the FE simulation is validated by the experimental tests. With the proposed optimization method, stiffnesses for all three groups of the optimal samples are significantly improved compared with the empirical counterparts. The FE modeling technique is capable of reproducing the experimental results. This study paves a new way to develop an integrated framework of optimization, additive manufacturing, experimentation, and validation to deliver high-performance CFRP structures.

Coupled vibration analysis of bolted variable angle tow plates under combined nonlinear effects

To establish a dynamical modal of variable angle tow (VAT) plate accurately, the fiber path and fiber orientation of the VAT plate are described by high-order polynomials. Then, a simplified nonlinear joint model with interface dynamic partitioning is proposed to simulate the interface mechanical behavior of bolted joints. Based on these, a nonlinear semi-analytic dynamic model of the bolted VAT plate is built, which considers both material and joint nonlinearity and can accurately predict nonlinear vibration response. After verifying the proposed modeling method, a special bolted VAT plate is used as the analysis object for free vibration and forced vibration analysis. Firstly, the frequency veering behavior of the VAT plate caused by variations in boundary stiffness, connection stiffness, and fiber orientation is studied. Then, by analyzing the forced vibration response of the bolted VAT plate, it is found that under the combined effect of the modal interaction, material nonlinearity, and joint nonlinearity, the bolted VAT plate exhibited complex but rule-based nonlinear dynamic behavior. More importantly, the research work done in this paper has certain guiding significance for the optimization design of vibration resistance of a bolted VAT thin-walled structure with variable stiffness parameters and joint parameters as design variables.