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Journal ArticleDOI

A design algorithm to model fibre paths for manufacturing of structurally optimised composite laminates

15 Nov 2018-Composite Structures (Elsevier)-Vol. 204, pp 882-895

TL;DR: This work develops a design for manufacturing (DFM) tool for the introduction in design of the manufacturing requirements and limitations derived from the fibre placement technology, which enables the automatic generation of continuous fibre paths for manufacturing.

AbstractFibre steering is involved in the development of non-conventional variable stiffness laminates (VSL) with curvilinear paths as well as in the lay-up of conventional laminates with complex shapes. Manufacturability is generally overlooked in design and, as a result, industrial applications do not take advantage of the potential of composite materials. This work develops a design for manufacturing (DFM) tool for the introduction in design of the manufacturing requirements and limitations derived from the fibre placement technology. This tool enables the automatic generation of continuous fibre paths for manufacturing. Results from its application to a plate with a central hole and an aircraft structure – a windshield front fairing – are presented, showing good correlation of resulting manufacturable paths to initial fibre trajectories. The effect of manufacturing constraints is assessed to elucidate the extent to which the structurally optimal design can be reached while conforming to existing manufacturing specifications.

Summary (3 min read)

1 Introduction

  • Fibre-reinforced composites are traditionally designed by stacking plies built with a discrete set of constant fibre orientation angles: 0°, ±45° and 90° [1].
  • Recently, a new manufacturing technology called continuous tow shearing (CTS) has been developed, avoiding gaps and overlaps at the expense of thickness variation [16,17].
  • In addition, to overcome this issue, many authors have employed a functional parametrisation to represent the fibre paths.
  • This method reduces the number of design variables an ease the consideration of manufacturing constraints while modelling continuous paths.
  • Hence, generic capabilities for the design of fibre-steered laminates and analysis of manufacturing features are required [89].

2 Tool to design variable stiffness laminates for

  • A software tool for manufacturing analysis and optimisation of fibre steering named FIPAM (Fibre Paths for Manufacturing) has been developed.
  • It provides 6 a post-processing of the design configurations from structural optimisation prior to manufacturing.
  • This tool enables the automatic generation of fibre paths (i.e., machine trajectories), imposing manufacturing requirements.
  • Structural approximations of the Finite Element (FE) response are used to reduce the required number of FE analyses [92].
  • The loading condition was shear force (1N) at the top and bottom edges.

2.1 Modelling of continuous fibre paths

  • The objective of this step is to generate continuous paths following the optimal discrete fibre orientations.
  • This process is repeated iteratively until the segments reach the boundary of the part or ply.
  • Assuming the orientation of a segment to be always equal to the interpolated orientation at the starting point of this section introduces some inaccuracy to the generated curve.
  • Measure minimum radius of curvature (section 3.2) and smooth the curve in case it does not comply with the minimum turning radius, also known as 8. Curve smoothing.
  • The selection of the starting points is done iteratively, by choosing first a point contained in a parallel curve to the previous reference with an offset equal to the course width.

2.2 Modelling of manufacture compliant fibre paths

  • In a second step, new fibre paths for manufacturing are modelled approaching the previously defined paths.
  • Choosing one curve as starting path, the method consists of defining a feasible region where the next path should be placed to comply with the specifications on course width, maximum gap and maximum overlap.
  • The feasible region where the fibre path must be contained to comply with the manufacturing constraints is defined by: a parallel curve to the current fibre path with a distance equal to the course width minus 12 the maximum overlap allowance, and a parallel offset of the course width plus the allowable gap .
  • Any coverage different from 100% will result in the appearance of triangular gaps in the ply.
  • When the contours of two adjacent courses intersect, tows will be dropped.

3 Analysis of manufacturing features of variable stiffness

  • For the implementation of manufacturing constraints in the algorithms discussed in section 2, tools to analyse these manufacturing features are required.
  • Specifically, methods to compute the gaps and overlaps of a particular fibre path design and to calculate the minimum curvature radius are presented.

3.1 Analysis of gaps and overlaps

  • Gaps and overlaps are automatically modelled in CATIA, which enables an evaluation of this design constraint and a visual representation in the model.
  • Select two adjacent paths to start 3. Compute edges of the fibre paths o Create parallel path: Distance = CourseWidth/2 17 o Extend and split parallel with curvature continuity to cover the surface 4. Compute intersection points of adjacent fibre path 5. Sort intersection points.
  • Identify whether area limited by intersection points and path boundaries represents a gap or an overlap (if there is no intersection, the whole area between the boundaries will be either a gap or an overlap) 7. Perform measures of the gap/overlap regions: area and maximum size.
  • For curves on surfaces, further measures of curvature can be defined: the geodesic curvature (]b), the normal curvature (]!), and the geodesic torsion (τr).
  • This induces a deflection of the fibres in the out-of-plane direction, which does not represent an issue.

4.1 Design of flat square plate with a hole

  • The variable stiffness design of a plate with a circular cut-out loaded in tension and optimised for strength has been undertaken.
  • Initially, tow-dropping is not allowed and a constraint to limit the maximum allowable angle deviation from optimal has not been imposed.
  • The resulting maximum angle deviation is lower than 22° for all plies and the average angle deviation is inferior to 8°.
  • For comparison, it includes the results for the reference paths (that correspond to a 0° maximum deviation constraint) and the optimal paths when the constraint is not imposed.
  • The gaps and overlaps of each design are modelled in Figure 10.

4.2 Design of a windshield front fairing

  • This structure has a double curved shape with reinforcement areas.
  • It is an aircraft component designed with conventional straight orientations (0°, ±45° and 90°).
  • The objective is to provide a fibre path design complying with all the manufacturing constraints.
  • For the 90° ply, the reference paths do not yield large overlaps and they can be completely eliminated with angle deviations below 3°.
  • The gap area increases as a result of the objective to minimise overlaps, although in a much inferior proportion than the overlap area reduction, and, in every case, respecting the maximum allowable gap size constraint.

5 Conclusions

  • The potential of fibre steering is limited by current manufacturing constraints of fibre placement technologies and design specifications.
  • A novel approach to automatically model fibre paths based on structurally optimised fibre angle distributions and considering manufacturing requirements is proposed.
  • This approach enables to design variable stiffness laminates with curvilinear paths as well as conventional complex structures that require fibre steering.
  • The algorithms are designed to minimise gaps, overlaps and angle deviation.
  • As the manufacturing variables are captured in the design process, variance between designed and manufactured parts can be reduced.

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This is a repository copy of A design algorithm to model fibre paths for manufacturing of
structurally optimised composite laminates.
White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/137073/
Version: Accepted Version
Article:
Lozano, G.G., Tiwari, A. and Turner, C. (2018) A design algorithm to model fibre paths for
manufacturing of structurally optimised composite laminates. Composite Structures, 204.
pp. 882-895. ISSN 0263-8223
https://doi.org/10.1016/j.compstruct.2018.07.088
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Accepted Manuscript
A design algorithm to model fibre paths for manufacturing of structurally opti-
mised composite laminates
G. Gonzalez Lozano, A. Tiwari, C. Turner
PII: S0263-8223(17)32552-7
DOI:
https://doi.org/10.1016/j.compstruct.2018.07.088
Reference: COST 10006
To appear in:
Composite Structures
Received Date: 10 July 2017
Revised Date: 12 June 2018
Accepted Date: 26 July 2018
Please cite this article as: Lozano, G.G., Tiwari, A., Turner, C., A design algorithm to model fibre paths for
manufacturing of structurally optimised composite laminates, Composite Structures (2018), doi:
https://doi.org/
10.1016/j.compstruct.2018.07.088
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers
we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and
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*Corresponding author: Gustavo Gonzalez Lozano, Airbus Group Innovations, Building 20A1,
Golf Course Lane, Filton, Bristol, BS34 7QW, UK. Email: g.gonzalezlozano@cranfield.ac.uk
Phone: +44(0)755 3737075
Ashutosh Tiwari, Automatic Control and Systems Engineering department, Amy Johnson
Building, The University of Sheffield, Portobello Street, Sheffield, S1 3JD, UK. Email:
a.tiwari@sheffield.ac.uk Phone: +44 (0)114 2225624
Christopher Turner, Manufacturing department, SATM, Cranfield University, Building 50,
Cranfield, Bedfordshire, MK43 0AL, UK. Email: c.j.turner@cranfield.ac.uk Phone: +44 (0) 1234
755264
A design algorithm to model fibre paths for manufacturing of
structurally optimised composite laminates
G. Gonzalez Lozano
a,b*
,
A. Tiwari
c
, C. Turner
a
a
Manufacturing and Materials department, School of Aerospace, Transport and Manufacturing
(SATM), Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK
b
Airbus Group, Innovations, Building 20A1, Golf Course Lane, Filton, Bristol, BS34 7QW, UK
c
Automatic Control and Systems Engineering department, Amy Johnson Building, The
University of Sheffield, Portobello Street, Sheffield, S1 3JD, UK
Abstract
Fibre steering is involved in the development of non-conventional variable
stiffness laminates (VSL) with curvilinear paths as well as in the lay-up of
conventional laminates with complex shapes. Manufacturability is generally
overlooked in design and, as a result, industrial applications do not take
advantage of the potential of composite materials. This work develops a design
for manufacturing (DFM) tool for the introduction in design of the manufacturing
requirements and limitations derived from the fibre placement technology. This
tool enables the automatic generation of continuous fibre paths for
manufacturing. Results from its application to a plate with a central hole and an
aircraft structure – a windshield front fairing are presented, showing good
correlation of resulting manufacturable paths to initial fibre trajectories. The
effect of manufacturing constraints is assessed to elucidate the extent to which
the structurally optimal design can be reached while conforming to existing
manufacturing specifications.

2
Keywords: A. Laminates, B. Defects, C. Computational modelling, D. Lay-up
(automated), Variable Stiffness
1 Introduction
Fibre-reinforced composites are traditionally designed by stacking plies built
with a discrete set of constant fibre orientation angles: 0°, ±4 and 90° [1].
These designs do not take full advantage of the potential of composite materials
[1–3]. Performance improvements can be driven by the lay-up of curvilinear
fibres [4,5], which benefits from a better stress distribution and an expanded
design space [6,7]. Automated Fibre Placement (AFP) offers the capability of
steering individual fibre tows over the surface of a laminate [1,5,8–10]. Due to
the variation of stiffness properties associated with the continuous change in
fibre orientation of a layer, these structures were termed as variable stiffness
laminates (VSL) [11].
Design and manufacturing of composite structures are interdependent [12]. AFP
presents a set of limitations that will affect the manufacturability and quality of
designed variable stiffness laminates, such as minimum steering radius
(smallest radius of the fibres that can be laid without significant defects, like
local fibre buckling or ply wrinkling), minimum cut length (shortest length a tow
can be laid in a controlled manner), and gaps and overlaps (defects introduced
when a course, set of tows laid up in one machine pass, is not laid parallel to an
adjacent one). For instance, tow kinking and wrinkling is noticed in the cylinders
manufactured by Blom et al. [13] and Wu et al. [14]. Gaps and overlaps are
observed in the cylindrical shells manufactured by Wu et al. [14] and the flat

3
plates manufactured by Tatting and Gürdal [15]. Recently, a new manufacturing
technology called continuous tow shearing (CTS) has been developed, avoiding
gaps and overlaps at the expense of thickness variation [16,17].
This type of non-conventional laminates shows an increasing interest from the
specialised literature. An extensive review on design optimisation methods can
be found in Ghiasi et al. [18] and Sabido et al. [19]. Design approaches include
aligning the fibres with the principal stress trajectories and load paths [4,20–24]
and using lamination parameters to find the optimal stiffness distribution [6,25–
40], which is followed by a retrieval of fibre orientations step [6,31,32]. These
methods result in an optimal fibre angle distribution, where continuity of the
distribution is not guaranteed and manufacturing constraints are difficult to
impose. Discontinuities between neighbouring elements are noticed in the
optimal fibre orientations in the work of [6,41,42]. The manufacturing of such
designs with curvilinear fibres is not possible [42], and post-processing would
be required [43]. For instance, introducing constraints to ensure continuity of
fibre orientations could alleviate this issue [28,42,44,45].
In addition, to overcome this issue, many authors have employed a functional
parametrisation to represent the fibre paths. This approach typically consists of
optimising a reference path, and then, a ply is created by replicating this path,
either by shifting the reference path in a specified direction (usually x- or y- axis)
or by placing adjacent courses parallel to one another. The former leads to the
occurrence of gaps and overlaps between adjacent courses, which may affect
the performance of the laminate [46]; while the latter will likely result in kinks as
the radius of the tows decreases to remain parallel to the reference path.

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TL;DR: The state of the art in modelling gaps and overlaps and assessing their influence on mechanical properties is presented and the research gaps and remaining issues are identified.
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Abstract: In the present study, the gap-overlap and curvature constraints on fiber tows are considered in the design optimization of variable stiffness laminates. The optimization problem is formulated in a framework proposed in our previous studies in which the fiber angle arrangement of a laminate is described by a continuous function constructed through the Shepard interpolation. In order to deal with the gap-overlap constraint, a gap-overlap-free rectangle is defined for each finite element. The fiber angles of the elements within this rectangle are constrained to be equal to each other, thus ensuring the fiber tows that pass through this rectangle are parallel. In order to control the curvature, a curvature-constrained rectangle is defined for each finite element. Within this rectangle the differences between fiber angles of the elements are constrained to be smaller than a user-specified upper bound. The compliance minimization with manufacturability constraints is considered, and it is solved with the MMA optimization algorithm. The results of numerical examples prove that the proposed method is effective.

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