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Journal ArticleDOI

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

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.
About: This article is published in Composite Structures.The article was published on 2018-11-15 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Design for manufacturability & Composite laminates.

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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Figures (12)
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, the authors optimized the curved fiber trajectories to realize variable fiber volume fraction and stiffness composites (VVfSC) using a continuous fiber composite 3D printer.

111 citations

Journal ArticleDOI
02 Jun 2019
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.
Abstract: The automated fiber placement process (AFP) enables the manufacturing of large and geometrical complex fiber composite structures with high quality at low cycle times. Although the AFP process is highly accurate and reproducible, manufacturing induced imperfections in the produced composite structure occur. This review summarizes and classifies typical AFP-related manufacturing defects. Several methodologies for evaluating the effects of such manufacturing defects from the literature are reviewed. This review paper presents recent scientific contributions and discusses proposed experimental and simulation-based methodologies. Among the identified ten defect classes, gaps and overlaps are predominant. This paper focuses then on methods for modelling and assessing gaps and overlaps. The state of the art in modelling gaps and overlaps and assessing their influence on mechanical properties is presented. Finally, research gaps and remaining issues are identified.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical model was proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates with curvilinear fiber paths.

25 citations

Journal ArticleDOI
TL;DR: In this article, the authors summarize and discuss underlying fiber placement technologies including tailored fiber placement (TFP), continuous tow shearing (CTS), and automated fibre placement (AFP), followed by a detailed discussion on the manufacturing limitations and constraints of the AFP process.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the gap-overlap and curvature constraints on fiber tows are considered in the design optimization of variable stiffness laminates, and the problem of compliance minimization with manufacturability constraints is solved with the MMA optimization algorithm.

18 citations

References
More filters
Journal ArticleDOI
TL;DR: In this article, a method for optimizing ply drop locations in composite laminates is developed using ideas from topology optimization, which is parametrized using a fiber angle and fictitious density distribution for each ply.
Abstract: A method for optimizing ply drop locations in composite laminates is developed using ideas from topology optimization. The design is parametrized using a fiber angle and fictitious density distribution for each ply. The solution proceeds using a successive conservative convex approximations strategy. Starting from a feasible point, the algorithm converges to a local minimum. The structural responses are approximated separately in terms of the angle and fictitious density distributions of each ply. Explicit penalization of intermediate densities is used to force the densities to either one for ply coverage or zero for no coverage. Ply drop locations are identified as the boundary between regions having densities near one and those near zero. The ply drop optimization is combined with fiber angle optimization by alternating the optimization between the corresponding sets of variables. Optimized variable-stiffness variable-thickness composite laminates, with a prespecified ply drop order, are obtained. Initi...

18 citations


"A design algorithm to model fibre p..." refers methods in this paper

  • ...[68,74,90,91] and comprises an optimisation of the stiffness distribution using lamination parameters [12] and a...

    [...]

  • ...posterior fibre angle retrieval and optimisation [68,74,90,91]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a bend-free shell is a specially designed structure, in which the external loading results in a zero bending stress resultant and a zero change in curvature, and the possibility of creating such states in composite shells by steering the fibre-tows, and hence tailoring the local orthotropy.

18 citations

Proceedings ArticleDOI
04 Apr 2011
TL;DR: In this article, the authors proposed a method to convert variable stiffness (VS) laminate designs using LPs into fiber angle designs, including a constraint on in-plane curvature, a manufacturing constraint related to AFP, and the amount of thickness build-up that results from the obtained fiber angles designs is discussed as a function of the constraint on fiber curvature.
Abstract: Mechanical properties of fiber-reinforced laminated composite materials are directionally dependent. Contemporary laminated composite design aims to make effective use of these directional properties by means of stacking sequence design, selecting the fiber orientation angle of each ply from a predefined set. Automated fiber-placement (AFP) technology can be used to improve the efficacy of composite materials by means of fiber steering. The variation of fiber orientation angles per ply of the laminate yields a variable stiffness (VS) laminate. For optimization purposes it is attractive to design such laminates in terms of lamination parameters (LP), as the number of design variables per point in the structure can be reduced to as little as four dimensionless variables considering balanced symmetric layups, and because many lay-up optimization problems can be made convex by describing them in terms of LPs. VS laminate design in terms of LP requires the obtained LP distribution to be converted into an actual fiber angle design. In a previous study the authors proposed a method to convert VS laminate designs using LPs into fiber angle designs. This method includes a constraint on in-plane curvature, a manufacturing constraint related to AFP. Thickness build-up will occur due to fiber steering. The amount of thickness build-up that results from the obtained fiber angle designs is discussed here as a function of the constraint on fiber curvature. The streamline analogy is used to obtain an estimate for thickness build-up and to determine fiber paths. A square plate loaded in biaxial compression is used to demonstrate the effect of the in-plane curvature constraint on thickness build-up, and several fiber angle designs, thickness distributions and fiber paths are given for this structure.

17 citations


"A design algorithm to model fibre p..." refers methods in this paper

  • ...A streamline analogy, also known as a fluid flow analogy, has been employed to compute continuous fibre paths from discrete fibre angles [4,21,23,31,59,69,70]....

    [...]

  • ...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]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the As-built Feedback Method has been used to transform manufacturing data of advanced fiber placement (AFP) structures to as-built FE-models by suitably considering the realised fibre orientations as well as special fibre features like tight fibre curves.

16 citations

Proceedings ArticleDOI
07 Apr 2003
TL;DR: In this article, the displacement update rules are derived using a finite element model governing the equilibrium of the cell neighborhood and fiber angles are locally optimized based on a minimum strain energy criterion.
Abstract: The anisotropic advantageous properties of fiber reinforced composites may not be fully exploited unless the fibers are properly placed in their optimal spatial orientations. This paper investigates application of Cellular Automata (CA) for curvilinear fiber design of composite laminae for in-plane responses. CA use local rules to update both field and design variables in an iterative scheme till convergence. In the present study, displacement update rules are derived using a finite element model governing the equilibrium of the cell neighborhood and fiber angles are locally optimized based on a minimum strain energy criterion. A manufacturing improvement is applied on top of the local optimum orientation wherever this angle is not consistent with the cell neighborhood orientation trend. Numerical studies showed convergency of the local update rules and considerable improvements in the stiffness properties for a cantilever bending test and a square plate with a cutout.

15 citations