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Abstract

The use of curvilinear fibre paths to develop variable stiffness laminates is now recognised as a promising technique offering great potential for performance improvements over conventional ‘straight fibre’ laminates. Its manufacture is feasible by fibre placement technologies, such as automated fibre placement. However, these technologies present a set of limitations that need to be included in the design to guarantee the manufacturability and quality of the composite laminates. Although this approach experiences an increasing interest from the specialised literature, most of the works completed overlook the manufacturing reality and, as a result, variable stiffness laminates are not used in industry. This work aims to provide a review of the State-of-the-Art on design for manufacture of variable stiffness in order to highlight the current gaps and research needs. As a conclusion, tools for analysis of the effect of manufacturing defects, manufacturing optimisation of gaps/overlaps or cycle time and the systematic integration of manufacturing constraints in design, are the main challenges that will be faced in the future to be able to exploit the potential of this advanced tailoring technique.

Keywords

Variable stiffness design for manufacture automated fibre placement curvilinear fibre paths

Introduction

Fibre-reinforced composites are traditionally designed by stacking plies built by laying straight fibres following the conventional angles 0°, ±45° and 90°. The special properties are achieved by tailoring the stacking sequence of the laminate.¹ These designs do not take full advantage of the potential of composite materials.^2,3

Automated fibre placement (AFP)⁴ is a manufacturing technology of composite laminates that AFP offers the capability of steering individual fibre tows over the surface of a laminate.^5–7 Due to the variation of stiffness properties associated with the continuous change in fibre orientation throughout the laminate plane, these structures were termed as variable stiffness laminates.⁸ Allowing the layup of curvilinear fibres benefits from a better stress distribution and expands the design space compared to the conventional stacking sequence design problem.^9,10

The design and manufacturing of composite structures are interdependent.¹¹ The design will significantly influence manufacturing characteristics such as process efficiency, quality and processing time, and respectively, manufacturing will impose constraints to the design and determine the manufacturability of the structure. Moreover, manufacturing constraints are more restricted with curvilinear fibres than straight unidirectional fibres. Some limitations such as gaps and overlaps become more important, and constraints that did not have a major impact with straight fibres (maximum curvature) are critical in designs with curvilinear fibres. Therefore, taking into account the manufacturing process becomes essential.

Indeed, several authors have explored the improvement possibilities driven by the use of curvilinear fibre paths. However, as they mainly focus on theoretical optimisation, manufacturing reality is generally overlooked. As a result, few examples exist of practical applications of curvilinear fibre laminates and industry is not currently harnessing their potential.

The aim of this article is to provide a comprehensive review of the design for manufacture of laminates using curvilinear fibres. Hence, the question underlying this review is ‘how have researchers considered the manufacturing requirements in the design of variable stiffness laminates?’

First of all, fibre placement technologies are described, outlining the limitations of AFP along with novel technology developments. Subsequently, research completed in the design of variable stiffness laminates is reviewed from a manufacturing perspective describing the implementation of manufacturing constraints within the design. Finally, the literature is classified and analysed to determine the limitations of the existing research and areas requiring further development.

Manufacturing technologies of fibre placement

Automated tape laying (ATL), AFP and filament winding are the main technologies to automate the layup of carbon fibres.¹⁰ The work of Lukaszewicz et al.¹⁰ provides a deeper description of the aspects and limitations of these automated manufacturing technologies. AFP is a technology that places automatically multiple individual fibre tows onto a mandrel (Figure 1).

Figure 1.

AFP machine head.

The capability of the machine to control the speed of the tows individually, known as differential tow payout,¹³ provides the main potential of AFP as it enables the layup of curvilinear paths within each ply on complex surfaces.^14,15 Thus, AFP is found as the choice to manufacture structures with curvilinear fibres in the literature. AFP presents a set of characteristics that will affect the manufacturing of the designed composite components. The main issues are collected and described in Table 1.

Table 1.

Manufacturing limitations of fibre placement technologies.

Limitation	Description
Jagged boundary	As tows are cut normal to the layup direction, jagged or saw-tooth edges will appear at boundaries that are not normal to this direction. This results in small gaps, overlaps or a combination of both (the coverage percentage can be controlled)
Minimum cut length	Distance between the cutting mechanism and the compaction roller constitutes the shortest length a tow can be laid in a controlled manner¹⁶
Collision	Machine head collisions can occur with concave surfaces or complex geometries
Fibre bridging	Fibres may separate from the mould surface in concave surfaces with high radius as they are subjected to tensile forces in the feeding system
Maximum allowable curvature or minimum turning radius	Smallest radius of the fibres that can be laid without significant defects, such as local fibre buckling and ply wrinkling. When the tows are steered, the inner radius of the tow is smaller than the outer radius, resulting in compressive and tensile forces, respectively^11,17
Gaps and overlaps	Gaps and overlaps appear any time a course is not laid parallel to an adjacent one. In complex geometries and especially when fibre steering is introduced, these defects might be important
Fibre angle deviation	The tows in a course are placed parallel to one another, and thus, they will have different curvatures when the paths are steered, deviating from the fibre angle at the centre of the course
Deposition rate	It is the amount of material that can be laid for unit of time. It is the usual performance metric for fibre placement

Recently, modifications of the AFP technology as well as new developments have been performed, which aim at improving the manufacturing of laminates with curvilinear fibres in terms of fewer technology constraints and fewer defects in the parts:

Tailored fibre placement (TFP). It is an embroidery technique in which dry fibres are stitched onto a surface. Different studies using this technology have been performed.^2,18,19

Continuous tow shearing (CTS). As means to reduce the defects induced by AFP, a new way to place curvilinear fibres that make use of shear deformation instead of bending deformation of the fibres has recently been developed at Bristol University, reducing local fibre buckling and wrinkling and avoiding gaps and overlaps.^17,20

Design for manufacture of variable stiffness laminates

The effect of the manufacturing issues is constant throughout the practical applications of variable stiffness laminates found in the literature. For instance, tow kinking and wrinkling is noticed in the cylinders manufactured by Blom et al.²¹ and Wu et al.¹⁶ (Figure 2). Gaps and overlaps are observed in the cylindrical shells manufactured by Wu et al.¹⁶ and the flat plates manufactured by Tatting and Gürdal²² (Figure 3). To create the parts, a reference path was replicated shifting it along a direction (shifted method), resulting in overlaps and ply thickness build-up on the surface²³ (Figure 3(a)). The shift distance can be prescribed so that no thickness builds up; however, gaps will appear between fibre courses⁶ (Figure 3(b)). In many studies, the ply thickness is supposed to be constant for the optimisation of fibre angle orientations.^6,7,23,24 However, the buckling load for the physical specimens (plates manufactured with dry fibres) may not match the results from finite element analysis (FEA), when the thickness is considered constant.²⁵ Also, the thickness increase can double the nominal thickness,¹⁶ and this effect is even more pronounced in theoretical studies.²³ Moreover, jagged boundaries are omitted in most analysis, assuming smooth boundaries.²⁶ Tow-drops, course edges and overlaps constitute discontinuities and stress concentration regions that may amplify interlaminar stresses.¹³ Minimum cut length (MCL) may also impact the result of manufacturing as noticed in the cylinders manufactured by Blom et al.,²¹ where the fibres diverge from the intended steer path to follow the geodesic straight path (fibre straightening) (Figure 4). Consequently, manufacturing constraints reduce the superior structural performance of variable stiffness laminates over conventional laminates,⁵ and they cannot be ignored.

Figure 2.

Tow kinking in cylindrical shells.

Figure 3.

Manufactured plates with: (a) overlap method and (b) tow-drop method.

Figure 4.

Fibre straightening at the outside of a steered course.

In addition to the aforementioned limitations, further considerations must be taken into account when designing variable stiffness laminates: continuity and continuous paths modelling. Ensuring continuity along the composite structure is one of the main issues related to variable stiffness design.²⁷ For instance, using a finite element method (FEM) for optimising fibre orientations is likely to result in discontinuities between elements if constraints are not imposed. Sudden changes are noticed in the optimal fibre orientations where the two principal stresses have approximately equal absolute values and opposite sign, and in areas of low stress values⁹ (Figure 5(a)). The manufacturing of such designs with curvilinear fibres is not possible,²⁸ and post-processing would be required.²⁹ Also, the solution from finite element (FE) is in the form of a discrete distribution of fibre orientations. Continuous fibre paths adequate for manufacturing need to be modelled following the optimal fibre orientations. These two issues can be avoided by designing the laminates parameterising reference fibre paths that are optimised, instead of discretising the structure and optimising discrete fibre orientations.¹¹

Figure 5.

Optimal fibre angle distribution design of plate with a hole in tension: (a) rapidly changing fibre angles are present and (b) smooth change of fibre angles between elements.

The methods developed in the literature to tackle these manufacturing requirements in design are summarised in Table 2, along with the limitations found. The objective is to ensure the manufacturability of structurally optimal designs. Methods need to be developed for both to introduce manufacturing requirements into the optimisation procedures used to design variable stiffness laminates and to analyse the effect on performance of these manufacturing limitations. The main constraints considered by existing research are minimum turning radius, gaps and overlaps, MCL, continuity, modelling continuous paths and fibre angle deviation. Other defects, such as fibre kinking, bumps and waves, can occur during fibre placement for which it may be necessary to debulk the laminate between plies and reduce the placement rate,¹⁶ which will increase the cycle time and effort of the fibre placement process.

Table 2.

Findings and limitations of existing research on design for manufacture of variable stiffness laminates.

Manufacturing issue	Related findings	Limitations	References
Maximum allowable curvature	− Definition of curvature, k, for a function of a single variable, f(x)	− Fibre paths need to be represented by functions of a single variable. Thus, only applicable to simple 2D structures	15,30
	− Average curvature constraint per ply based on an approximation of path curvature, k, defined as the rate of change in fibre angle, that is, the norm of the divergence of the fibre angle. It results in smooth fibre angle distributions	− This constraint does not guarantee manufacturability as the curvature constraint must be satisfied at every point within the structure	31
	− Maximum fibre curvature as a local point-wise curvature constraint. A CA paradigm is used to locally evaluate the curvature at each element of the structure. Both global and local curvature constraints can be included	− Curvature not directly computed from physical paths but from FE results (discrete fibre angle distributions). However, results are promising with this method	11,32
	− Functional definition of a reference fibre path with constant curvature (that it is replicated to create a ply), so the curvature evaluation is trivial	− Defining this reference path highly restricts the design space	33
	− A maximum curvature value of 1.575 m⁻¹ (635 mm turning radius) has been extensively used	− Maximum curvature values depend on the material and technology,³² among other factors. They are not known	5,7,14,22,33 –35
Continuity	− Inclusion of constraints in the variation of the fibre orientation angles between adjacent elements of the FEM. In addition, the design variables can be associated with nodes rather than elements to improve smoothness of the distribution of optimal fibre angles	− Properties over an element have to be approximated from those at the element nodes	1,36
	− Heuristic pattern-matching technique to maintain continuity of fibre orientations among neighbouring elements in the FEM (Figure 5(b))		28,37
	− Use of lamination parameters instead of fibre orientations as design variables for optimisation, because the design space is convex³⁸	− Optimal lamination parameter distribution needs to be converted into fibre orientations thereafter	9
Continuous paths modelling	− Colour coding the vectors that indicate the direction of the fibres	− It provides a better visualisation of the direction of the paths, but there is still a discrete distribution	9,28,37,39
	− Streamline analogy to generate continuous fibre paths from optimal fibre angle distributions	− Generally, it does not provide functions for the paths that can be easily handled for post-processing to include other manufacturing constraints	11,23,40
	− Functional representations of the fibre paths: NURBS, linear and non-linear angle variation, Lagrangian polynomials, Bezier curves, constant angle and constant curvature paths	− Using parameterisations of the fibre paths limits the design space¹¹	8,14,20,33, 35,41 –46
Gaps and overlaps	− Tow-dropping method (dropping the tows individually along a path) to overcome thickness build-up	− It creates resin-rich areas that may act as a hot-spot for stress and damage⁶	22
	− Experiments supporting the use of overlaps over the tow-drop method for strength and buckling. Overlaps may be advantageous as they can act as integral stiffeners⁷	− Results are highly dependent on the case study. Thus, differences are found between the conclusions of different studies. For instance, the differences between the work of Croft et al.⁴⁷ and Blom et al.²⁶ can be explained by the defect reduction occurred during curing¹⁰ in the case of Croft et al.⁴⁷ Furthermore, the effect of fibre curvature was considered and found relevant in the work of Blom et al.,²⁶ while 0° plies were utilised by Croft et al.⁴⁷	7,16,48,49
	− Experimental tests on flat coupons to evaluate the effect of individual manufacturing induced defects (Figure 6). Generally, the results indicated a small influence of the defects on the ultimate strength, with overall less than 5% and 13% modification (positive or negative) for laminates with and without a hole, respectively. Usually defects (gaps or overlaps) that improve one mechanical property also deteriorate another one		47
	− Theoretical analysis of the effect of gaps and overlaps on performance, which were of an order of 25%		26
	− Method to design and simulate parts including manufacturing restrictions on curvature constraint, gaps and overlaps, and course width. The results for a plate with a hole showed that the manufacturable solution (Figure 7(b)) presents only 1% lower critical buckling load, but 16% reduction of the longitudinal compressive failure with respect to the ‘ideal’ case (Figure 7(a)), without considering the course width	− Effect of gaps and overlaps are analysed, but they cannot be controlled	5,7
	− 3D FE strategy enabled to account for local effects and interlaminar stresses by meshing each course independently,¹³ and the effect of tow-drops⁵⁰		13,50
	− Method to calculate and analyse the gaps and overlaps of a design. The analysis is done using FE and the so-called defect layer method, which makes use of fewer elements than previous methods	− Non-consideration of possible stress concentrations at the gap areas. Gap/overlap analysis is completed after the optimisation	49
	− The increase in thickness is not unique, but a function of the selected start locations for the fibre courses. Based on that, a method to optimise the course locations for minimum ply thickness and maximum surface smoothness is proposed		23
Minimum cut length	− Fibre straightening effect can be avoided by cutting tows on the inside so that the adjacent tows force it to follow the curve		21
Fibre angle deviation	− Fibre angle deviation increases with the course width. However, the analysis of cylinders shows less than 2% reduction on the buckling load by increasing three times the course width		21

FEM: finite element method; FE: finite element; CA: cellular automata; NURBS: non-uniform rational basis spline; 2D: two-dimensional; 3D: three-dimensional.

Figure 6.

Effect of AFP manufacturing induced defects on the tensile, compressive, in-plane shear, open-hole tensile (OHT) and open-hole compressive (OHC) strength of composite laminates.

Figure 7.

Curvilinear fibre paths on a plate with a central hole: (a) ideal ply and (b) manufacturable ply (the course width is considered).

The lack of efficient software tools could limit the physical capabilities of AFP machines and introduce difficulties to the design process. Attempts to create software specifically for the design for manufacture of laminates with curvilinear paths can be found in the work of Schueler and Hale.⁵¹ The Steered Composite Analysis and Design System (SCADS) is an integrated design and analysis system for fibre placement technologies that controls the design of tows rather than plies, and as such allows for the analysis of manufacturability. However, the definition of the fibre paths is rather limited. Kärger and Kling⁵² developed a method, called As-built Feedback Method, to implement manufacturing data in the design models. It generates an as-built FE model that accounts for the effect in performance of discontinuities in the actual manufactured layup, showing the discrepancies with the theoretical design model (as design model).

Alternative software solutions have been developed to improve the programming of the AFP robot trajectories. The fibre path designs have to be correctly translated into data for the robots. This data generally take the form of a point-cloud that the control system has to follow.¹⁰ Debout et al.⁵³ optimised the machine tool paths to reduce the manufacturing time by smoothing the orientation and kinematic behaviour of the machine head. The generation of points or tags is commonly programmed off-line, although studies have been done for real-time processes via sensory-based feedback.⁵⁴

Discussion

The literature has been identified mainly through online searching using Scopus. Different keywords were used as seen in Figure 8, where it is also noted the significantly inferior number of papers on variable stiffness compared to constant stiffness. As a result, a large body of conference papers and journal articles was built. This literature was completed with other existing publications and web-based articles gathered through other sources in a less structured manner. Papers related to variable stiffness laminates that were found relevant^{1,2,5–11,13–30,32–52,55–69} (a total of 63 papers) have been analysed to assess whether they perform or develop a set of tasks (Figure 9(a)).

Figure 8.

Number of papers returned by Scopus for searches with different keywords, 09/13 (‘extended’ accounts for all keywords that refer to variable stiffness, for example, curvilinear fibres).

Figure 9.

Analysis of variable stiffness papers: (a) general criteria, (b) manufacturing-related criteria and (c) structural and manufacturing along time.

It is noteworthy that the number of papers actually providing software that can be used to design composite laminates, beyond the case study conducted in the research, is very small. Alternatively, papers performing physical tests (less than 25% of the total number of papers) are fewer in number compared to those carrying out a theoretical analysis and optimisation for structures.

Most of the papers focus on structural analysis and optimisation. A considerably high amount of studies, approximately half of them, take into account the manufacturing dimension, although no papers consider all the manufacturing constraints, which, in fact, will be present in the manufacturing by AFP. Therefore, manufacturability of the variable stiffness laminate is generally not guaranteed.

An analysis reveals that none of the papers cover all the criteria. In addition, the number of papers performing structural optimisation and manufacturing analysis together accounts for less than half of the overall structural optimisation papers. The same split is seen for physical tests and structural optimisation, where the majority of the optimisation is theoretical.

Manufacturing optimisation papers are sparse and those analysed are mainly focused on manufacturing technologies (for instance tow shearing) rather than the introduction of manufacturing objectives in the structural optimisation process. Those papers performing manufacturing analysis or optimisation are further analysed based on the following criteria: AFP (if the manufacturing constraints derived explicitly from the use of AFP), tow/course width, overlaps/gaps, turning radius, MCL, cycle time (the paper considers the cycle time of the manufacturing process or attempts to improve it), productivity/quality (productivity of the manufacturing process and quality of the manufactured parts are taken into account), continuity (applies only when the laminate is discretised to carry out design optimisation), variable stiffness (the paper deals with curvilinear fibre paths) and multi-objective optimisation (MOOP including manufacturing-related objectives). A histogram depicting the results is shown in Figure 9(b) (complete results are shown in Table 3 in Appendix 1).

From the chart results, AFP is the main manufacturing technology considered when designing composites with curvilinear fibres. The remaining papers are applied either to manual layup or TFP.

The main manufacturing constraint generally included in the optimisation procedures is the maximum curvature or minimum turning radius allowed for the fibres. Overlaps and gaps are also a focus of attention when designing these laminates as it is a recurrent feature when using curvilinear paths. Computing the gaps and overlaps used to require the modelling of the course width so a number of papers consider this characteristic in order to design manufacturable plies.

Improving the cycle time of the manufacturing process has not been considered in the design of variable stiffness structures, although laying up curvilinear fibres will affect it. One review article that acknowledges this gap in the research is Lukaszewicz et al.,¹⁰ which proposes different research pathways to improve the cycle time.

Research has been completed to improve the productivity of the manufacturing process and quality of the manufactured parts. Generally, such papers do not consider design optimisation. There are papers proposing alternative manufacturing techniques or technologies (like tow shearing)^17,20 or detailing the manufacturing of composite structures giving guidelines for better results.¹⁶

When using design approaches involving the discretisation of structures, the manufacturing constraints taken into account, if any, are selected to ensure the continuity of the fibre angle distribution. In a few cases, methods to model complete continuous tow paths are developed.

An example of multi-objective optimisation with manufacturing objectives was only found in the work of Blom et al.,²³ a work that focuses on the reduction of thickness due to overlaps. The remaining few studies dealing with multi-objective optimisation focus on different structural objectives. The subjects of optimisation of structural performance objectives and manufacturing objectives simultaneously have not been found in the literature.

Variable stiffness laminates have experienced increasing interest from the specialised literature, especially since 2005 (Figure 9(c)). Also the importance of manufacturing seems to be recognised as manufacturing analyses and the introduction of manufacturing constraints in design and structural optimisation are increasing their presence in current research.

As a conclusion, the main goal pursued by most of the studies including manufacturing is to ensure that the laminates are manufacturable, but this does not guarantee the design will be free of manufacturing difficulties or defects. This results in laminates with lower performance than initially predicted analytically or numerically.

Research opportunities

Further research and development are needed in the following areas to be able to industrially exploit variable stiffness composite structures.

Design and analysis software tools

Commercial software for computer-aided design (CAD), such as computer-aided three-dimensional interactive application (CATIA), or FEA, such as ABAQUS or MSC NASTRAN, does not allow the user to easily define parts with curvilinear paths. Therefore, manufacturing analysis is usually not possible with current software. As a consequence, researchers often neglect the effect that overlaps or gaps can have in the performance of the structure.

Research works that include manufacturing constraints tend to develop their own analysis method that is generally problem-specific. Developing generic capabilities, integrated in commercial software, to design variable stiffness laminates and analyse manufacturing features, such as gaps/overlaps and curvature, would be highly valuable.

Impact of manufacturing features and defects on performance

The effect of overlaps or tow-drops has been studied, but conclusive results have yet to be achieved. The robustness of variable stiffness designs to manufacturing defects and off-design operating conditions requires further research.¹¹

Parameters of the manufacturing process, such as cycle time, have not been quantified. It is known that more effort and control is required to get good quality parts when laying curvilinear fibres (i.e. slower deposition rates will be used when compared to conventional composite structures), but numerical values have not been found.

In addition, design rules, like best practices, are not available for variable stiffness composite design as they are for constant stiffness. Physical tests supporting design rules have not been conducted as they are available for conventional fibre orientations, due to the high costs involved.²³

Real case studies

Generally, papers apply the optimisation procedures to parts with simple geometries that are subjected to single load conditions (flat plates or beams); the applicability of the developed techniques to complex structures would require validation as manufacturing issues are expected to arise. Those papers designing complex structures tend to simplify the part geometry so as to be able to analyse and design it using academic software tools. So it is not clear how manufacturing constraints (requiring global analysis and generally expensive computational costs) would be handled to design real structures. The introduction of manufacturing issues in the design of real structures is still an area of ongoing research that will eventually establish the real potential of variable stiffness over conventional laminate design.

Integration of different research areas in a systematic method or tool for design

Structural optimisation, analysis and manufacturing have been independently studied and most of the papers are problem dependent. For instance, the design for manufacture research tends to relate to conventional fibre angles. The manufacturing of real structures will, however, encounter every aspect previously commented. Therefore, an approach or framework to address the design problem, while methodologically integrating the manufacturing process is still needed.

Conclusion

As a conclusion, research has already been completed regarding manufacturing issues of variable stiffness structures, although there is no practical implementation of the findings. The reason is that the integration of manufacturing in the design phase for variable stiffness structures has not been successfully solved.

The optimisation of manufacturing remains independent from structural optimisation. In fact, they are often conflictive objectives. The structural optimisation has been the subject of a larger body of research works. This fact could result in, for instance, a variable stiffness design presenting a high percentage improvement over the corresponding constant stiffness, but requiring a much longer cycle time to manufacture. Besides that the variable stiffness design obtained may not be manufacturable. The influence of manufacturing defects and the modelling of such defects in analysis software are also required in order to validate variable stiffness laminates for industrial applications.

To sum up, the use of curvilinear fibres presents great potential to improve the performance of composite structures. However, the design and manufacturing are more complex. Therefore, a trade-off has to be found between the potential improvements and the increasing design complexity. More research is needed in this field to reduce the impact of the issues of using curvilinear fibres so their potential may be harnessed more effectively in industrial applications.

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Airbus Group Innovations, UK.

References

Setoodeh

Abdalla

IJsselmuiden

. Design of variable-stiffness composite panels for maximum buckling load. Compos Struct 2009; 87(1): 109–117.

Temmen

Degenhardt

Raible

Tailored fibre placement optimisation tool. In: ICAS, 25th international congress of aeronautical sciences, Hamburg, 3–8 September 2006, pp.2462–2471. Edinburgh: Optimage Ltd.

Walker

Smith

RE.

A technique for the multiobjective optimisation of laminated composite structures using genetic algorithms and finite element analysis. Compos Struct 2003; 62(1): 123–128.

Sebaey

González

Lopes

. Damage resistance and damage tolerance of dispersed CFRP laminates: design and optimization. Compos Struct 2013; 95: 569–576.

Lopes

Gürdal

Camanho

PP.

Tailoring for strength of composite steered-fibre panels with cutouts. Compos Part A: Appl S 2010; 41(12): 1760–1767.

Lopes

Camanho

Gürdal

. Progressive failure analysis of tow-placed, variable-stiffness composite panels. Int J Solids Struct 2007; 44(25–26): 8493–8516.

Lopes

Gürdal

Camanho

PP.

Variable-stiffness composite panels: buckling and first-ply failure improvements over straight-fibre laminates. Comput Struct 2008; 86(9): 897–907.

Olmedo

Gürdal

. Buckling response of laminates with spatially varying fiber orientations. In: 34th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, La Jolla, CA, 19–22 April 1993, vol. 4, pp.2261–2269. Reston, VA: AIAA.

Setoodeh

Optimal design of variable-stiffness fiber-reinforced composites using cellular automata. PhD Thesis, Delft University of Technology, Delft, 2005.

10.

Lukaszewicz

DH-JA

Ward

Potter

KD.

The engineering aspects of automated prepreg layup: history, present and future. Compos Part B: Eng 2012; 43(3): 997–1009.

11.

Ijsselmuiden

ST.

Optimal design of variable stiffness composite structures using lamination parameters. PhD Thesis, Delft University of Technology, Delft, 2011.

12.

Evans

DO.

Fiber placement. In: Miracle

Donaldson

(eds) ASM handbook, vol. 21. Materials Park, OH: ASM International, 2001, pp.1135–1140.

13.

Fagiano

Computational modeling of tow-placed composite laminates with fabrication features. PhD Thesis, Delft University of Technology, Delft, 2010.

14.

Nagendra

Kodiyalam

Davis

. Optimization of tow fiber paths for composite design. In: 36th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, New Orleans, LA, 10–13 April 1995, pp.1031–1041. New York: AIAA.

15.

Waldhart

Analysis of tow-placed, variable-stiffness laminates. MSc Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1996.

16.

Tatting

Smith

. Design and manufacturing of tow-steered composite shells using fiber placement. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Palm Springs, CA, 4–7 May 2009, report no. 2009-2509, pp.1–18. Reston, VA: AIAA.

17.

Kim

Hazra

Weaver

. Limitations of fibre placement techniques for variable angle tow composites and their process-induced defects. In: 18th international conference on composite materials, Jeju, South Korea, 21–26 August 2011, pp.1–6, http://www.iccm-central.org/Proceedings/ICCM18proceedings/data/2.%20Oral%20Presentation/Aug23(Tuesday)/T11%20Processing%20and%20Manufacturing%20Technologies/T11-3-IF1097.pdf

18.

Gliesche

Hübner

Orawetz

Application of the tailored fibre placement (TFP) process for a local reinforcement on an ‘open-hole’ tension plate from carbon/epoxy laminates. Compos Sci Technol 2003; 63: 81–88.

19.

Rolfes

Tessmer

Degenhardt

. New design tools for lightweight aerospace structures. In: Topping

BHV

Mota Soares

(eds) Progress in computational structures technology. Stirling: Saxe-Coburg Publications, 2004, pp.1–30.

20.

Kim

Potter

Weaver

. Continuous tow shearing for manufacturing variable angle tow composites. Compos Part A: Appl S 2012; 43(8): 1347–1356.

21.

Blom

Stickler

Gürdal

. Design and manufacture of a variable-stiffness cylindrical shell. In: Proceedings of the SAMPE Europe 30th international conference, Paris, 23–25 March 2009, pp.1–8. Oerlingen, Switzerland: SAMPE Europe.

22.

Tatting

Gürdal

. Design and manufacture of elastically tailored tow placed plates. Technical report: NASA/CR-2002-211919, August 2002. Hampton, VA: NASA STI.

23.

Blom

Abdalla

Gürdal

. Optimization of course locations in fiber-placed panels for general fiber angle distributions. Compos Sci Technol 2010; 70(4): 564–570.

24.

Arian Nik

Fayazbakhsh

Pasini

. Surrogate-based multi-objective optimization of a composite laminate with curvilinear fibers. Compos Struct 2012; 94(8): 2306–2313.

25.

Weaver

Potter

Hazra

. Buckling of variable angle tow plates: from concept to experiment. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Palm Springs, CA, 4–7 May 2009, report no. 2009-2509, pp.1–10. Reston, VA: AIAA.

26.

Blom

Lopes

Kromwijk

. A theoretical model to study the influence of tow-drop areas on the stiffness and strength of variable-stiffness laminates. J Compos Mater 2009; 43(5): 403–425.

27.

Ghiasi

Fayazbakhsh

Pasini

. Optimum stacking sequence design of composite materials Part II: variable stiffness design. Compos Struct 2010; 93(1): 1–13.

28.

Setoodeh

Gürdal

Watson

. Design of variable-stiffness composite layers using cellular automata. Comput Method Appl M 2006; 195(9–12): 836–851.

29.

Sørensen

Kann

. Optimisation of composite structures using lamination parameters in a finite element application. MSc Thesis, Aalborg University, Aalborg, 2011.

30.

Waldhart

Gürdal

Ribbens

. Analysis of tow placed, parallel fiber, variable stiffness laminates. In: 37th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Salt Lake City, UT, 15–17 April 1996, pp.2210–2220. New York: AIAA.

31.

Pilaka

VKR

. Design of realistic variable stiffness laminates – a gradient-based optimizer for retrieving fiber orientation angles with average curvature constraints from lamination parameter distributions. MSc Thesis, Delft University of Technology, Delft, 2010.

32.

Van Campen

JMJF

Kassapoglou

Gürdal

. Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates. Compos Part B: Eng 2012; 43(2): 354–360.

33.

Blom

Tatting

Hol

JMAM

. Fiber path definitions for elastically tailored conical shells. Compos Part B: Eng 2009; 40(1): 77–84.

34.

Blom

Setoodeh

Hol

JMAM

. Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Comput Struct 2008; 86(9): 870–878.

35.

Haddadpour

Zamani

. Curvilinear fiber optimization tools for aeroelastic design of composite wings. J Fluids Struct 2012; 33: 180–190.

36.

Abdalla

Setoodeh

Gürdal

. Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Compos Struct 2007; 81(2): 283–291.

37.

Setoodeh

Gürdal

. Design of composite layers with curvilinear fiber paths using cellular automata. In: 44th AIAA/ASME/ASCE/AHS structures, structural dynamics, and materials conference, Norfolk, VA, 7–10 April 2003, pp.1–10. Reston, VA: AIAA.

38.

Setoodeh

Abdalla

Gürdal

. Design of variable-stiffness laminates using lamination parameters. Compos Part B: Eng 2006; 37(4–5): 301–309.

39.

Legrand

Kelly

Crosky

. Optimisation of fibre steering in composite laminates using a genetic algorithm. Compos Struct 2006; 75(1–4): 524–531.

40.

Khani

IJsselmuiden

Abdalla

. Design of variable stiffness panels for maximum strength using lamination parameters. Compos Part B: Eng 2011; 42(3): 546–552.

41.

Tatting

. Analysis and design of variable stiffness composite cylinders. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1998.

42.

Weaver

Raju

. Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Struct 2012; 60: 163–172.

43.

Dems

Wiśniewski

. Optimal design of fibre-reinforced composite disks. J Theor Appl Mech 2009; 47(3): 515–535.

44.

Parnas

Oral

Ceyhan

. Optimum design of composite structures with curved fiber courses. Compos Sci Technol 2003; 63(7): 1071–1082.

45.

Luraghi

. Surrogate-based shape optimization of fiber paths in tow-steered laminates for maximum buckling load. In: Ferreira

AJM

(ed.) 16th international conference on composite structures, Porto, 28–30 June 2011. Porto: FEUP.

46.

Zamani

Haddadpour

Ghazavi

. Curvilinear fiber optimization tools for design thin walled beams. Thin-Walled Struct 2011; 49(3): 448–454.

47.

Croft

Lessard

Pasini

. Experimental study of the effect of automated fiber placement induced defects on performance of composite laminates. Compos Part A: Appl S 2011; 42(5): 484–491.

48.

Mills

Patel

Frost

. Resin transfer moulding of highly loaded carbon fibre composite aircraft spars using novel fabrics and tow placement techniques. Sampe J 2007; 43(3): 67–72.

49.

Fayazbakhsh

Arian Nik

Pasini

. Defect layer method to capture effect of gaps and overlaps in variable stiffness laminates made by automated fiber placement. Compos Struct 2013; 97: 245–251.

50.

Lopes

. Damage and failure of non-conventional composite laminates, PhD Thesis, Delft University of Technology, Delft, 2009.

51.

Schueler

Hale

. Object-oriented implementation of an integrated design and analysis tool for fiber placed structures. In: 43rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Denver, CO, 22–25 April 2002, pp.173–183. Reston, VA: AIAA.

52.

Kärger

Kling

. As-built FE simulation of advanced fibre placement structures based on manufacturing data. Compos Struct 2013; 100: 104–112.

53.

Debout

Chanal

Duc

. Tool path smoothing of a redundant machine: application to automated fiber placement. Comput Des 2011; 43(2): 122–132.

54.

Shirinzadeh

Alici

Foong

. Fabrication process of open surfaces by robotic fibre placement. Robot Comput Integr Manuf 2004; 20(1): 17–28.

55.

Tosh

Kelly

. Fibre steering for a composite C-beam. Compos Struct 2001; 53(2): 133–141.

56.

Tosh

Kelly

. On the design, manufacture and testing of trajectorial fibre steering for carbon fibre composite laminates. Compos Part A: Appl S 2000; 31(10): 1047–1060.

57.

Bruyneel

. A general and effective approach for the optimal design of fiber reinforced composite structures. Compos Sci Technol 2006; 66(10): 1303–1314.

58.

Muc

Ulatowska

. Design of plates with curved fibre format. Compos Struct 2010; 92(7): 1728–1733.

59.

Alhajahmad

Abdalla

Gürdal

. Optimal design of tow-placed fuselage panels for maximum strength with buckling considerations. AIAA J Aircr 2010; 47(3): 775–782.

60.

Hyer

Lee

. The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos Struct 1991; 18(3): 239–261.

61.

Hyer

Charette

. Use of curvilinear fiber format in composite structure design. AIAA J 1991; 29(6): 1011–1015.

62.

Setoodeh

Abdalla

Gürdal

. Combined topology and fiber path design of composite layers using cellular automata. Struct Multidiscip Optim 2005; 30(6): 413–421.

63.

Muc

Ulatowska

. Local fibre reinforcement of holes in composite multilayered plates. Compos Struct 2012; 94(4): 1413–1419.

64.

Stegmann

Lund

. Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 2005; 62(14): 2009–2027.

65.

Ijsselmuiden

Abdalla

Gürdal

. Optimization of variable-stiffness panels for maximum buckling load using lamination parameters. AIAA J 2010; 48(1): 134–143.

66.

Ijsselmuiden

Abdalla

Gúrdal

. Thickness tailoring of variable stiffness panels for maximum buckling load. In: Bank

Wisnom

(eds) 17th international conference on composite materials, Edinburgh, 27–31 July 2009, pp.1–10. London: British Composites Society.

67.

Ijsselmuiden

Abdalla

Gürdal

. Thermomechanical design optimization of variable stiffness composite panels for buckling. J Therm Stress 2010; 33(10): 977–992.

68.

Ijsselmuiden

Abdalla

Gürdal

. Maximising buckling loads of variable stiffness shells using lamination parameters. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Reston, VA; Palm Springs, CA, 4–7 May 2009, report no 2009–2556. Reston, VA: AIAA.

69.

Charan

Renault

Ogale

. Automated fiber reinforced composite prototypes. In: Proceedings of the 5th international conference rapid prototyping, Dayton, OH, 12–15 June 1994, pp. 91–97. Dayton: The University of Dayton.

A review on design for manufacture of variable stiffness composite laminates

Abstract

Keywords

Introduction

Manufacturing technologies of fibre placement

Design for manufacture of variable stiffness laminates

Discussion

Research opportunities

Design and analysis software tools

Impact of manufacturing features and defects on performance

Real case studies

Integration of different research areas in a systematic method or tool for design

Conclusion

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

References