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)
Jump to: [1 Introduction] – [2 Tool to design variable stiffness laminates for] – [2.1 Modelling of continuous fibre paths] – [2.2 Modelling of manufacture compliant fibre paths] – [3 Analysis of manufacturing features of variable stiffness] – [3.1 Analysis of gaps and overlaps] – [4.1 Design of flat square plate with a hole] – [4.2 Design of a windshield front fairing] and [5 Conclusions]
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.
Did you find this useful? Give us your feedback
Figures (12)
Figure 9. Flat square plate with a hole: reference paths optimised for structures and paths optimised for manufacturing with gap and overlap analysis for each ply (green: gap and blue: overlap) 
Figure 2. Curve smoothing approach to comply with minimum turning radius constraint 
Table 2. Analysis of results of ply 4 of flat square plate with a hole showing angle deviations, gaps and overlaps, and tow-drops that would be needed to remove the overlaps 
Table 3. Analysis of results for the design of reference (Ref) and manufacturing (Mfg) fibre paths of windshield front fairing Case study Windshield front fairing Ply orientation (deg) 0 45 90 Description Ref. 
Figure 1. Approach for fibre path modelling for manufacturing, including for each step (boxes): input and output variables (left and right side of boxes), conditions and constraints applicable (in bold at top side of boxes), and enablers and algorithms used (in italic at bottom side of boxes). 
Figure 3. (a) Case study used and representation of modelled curves; (b) graph of the effect of refinement of interpolation on computation time; (c) graph of the effect of refinement on average angle deviation 
Figure 11. Tow modelling of different design solutions with tow-dropping (coverage = 10% overlap; MCL= 80 mm) for ply 4 of flat square plate with a hole 
Figure 4. Generation of two reference curves on a plate with a hole with course width = 25.4mm and different input values for gap/overlap proportion (coverage) 
Figure 5. Process rationale to create fibre paths for manufacturing approaching reference curves 
Figure 13. Definition of case study for windshield front fairing: dimensions, design and manufacturing constraints 
Figure 8. Definition of case study for flat square plate with a hole: dimensions, design and manufacturing constraints 
Figure 7. Geometrical interpretation of curvature of a curve at point P
Citations
More filters
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
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
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
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
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
TL;DR: In this article, the problem of tailoring for the pressure pillowing problem of a fuselage panel bounded by two frames and two stringers is addressed using tow-placed steered fibers.
Abstract: The introduction of advanced tow-placement machines has made it possible to fabricate novel variable-stiffness composite structures where the fiber orientation angle varies continuously within each ply and throughout the structure. This manufacturing capability allows designers of composites to use the fiber orientation angle as design variable in their analysis, not only for each ply as with conventional composites, but at each point within a ply. Consequently, beyond the improvements that can be accomplished with traditional composites with straight fibers, the directional material properties of composites can be fully exploited to improve the laminate performance. In this paper, design tailoring for the pressure pillowing problem of a fuselage panel bounded by two frames and two stringers is addressed using tow-placed steered fibers. The panel is modeled as a two-dimensional plate loaded by out-of-plane pressure and in-plane loads. A Python-ABAQUS script is developed to perform the linear and geometrically nonlinear finite element analyses of variable-stiffness panels. The design objective is to determine the optimal fiber paths within each ply of the laminate for maximum load carrying capacity and for maximum buckling capacity. Simulated-annealing algorithm is used to solve the optimization problems. Optimal designs are obtained for different loading cases and boundary conditions. As a basis ofcomparison, a practical constant-stiffness quasi-isotropic design is used. Numerical results indicate that by placing the fibers in their optimal spatial orientations within each ply, the load carrying capacity and the buckling load of the structure can be substantially improved compared with traditional straight fiber designs. It is shown that laminates optimized for maximum failure load have buckling loads that are higher than those for quasi-isotropic laminates. On the other hand, laminates optimized for maximum buckling load fail at load levels lower than laminates optimized for maximum failure load. However, the failure loads of those laminates may still be higher than those for their quasi-isotropic counterparts.
85 citations
Dissertation•
05 Jun 1996
TL;DR: In this article, the in-plane responses of variable-stiffness laminates to either an applied uniform end shortening or inplane shear were determined, where subsequent paths are truly parallel to the reference fiber path.
Abstract: (Abstract) It is possible to create laminae that have spatially varying fiber orientation with a tow placement machine. A laminate which is composed of such plies will have stiffness properties which vary as a function of position. Previous work had modelled such variable-stiffness laminae by taking a reference fiber path and creating subsequent paths by shifting the reference path. This thesis introduces a method where subsequent paths are truly parallel to the reference fiber path. The primary manufacturing constraint considered in the analysis of variable-stiffness laminates was limits on fiber curvature which proved to be more restrictive for parallel fiber laminae than for shifted fiber. The in-plane responses of shifted and parallel fiber variable-stiffness laminates to either an applied uniform end shortening or in-plane shear were determined. Both shifted and parallel fiber variable-stiffness laminates can redistribute the applied load thereby increasing critical buckling loads compared to traditional straight fiber laminates. The primary differences between the two methods is that parallel fiber laminates are not able to redistribute the loading to the degree of the shifted fiber. This significantly reduces the increase in critical buckling load for parallel fiber variable-stiffness laminates over straight fiber laminates. Acknowledgements I would like to express gratitude to my advisor, Dr. Zafer Gürdal, and Dr. Calvin Ribbens for making the time to answer the seemingly endless line of questions I had during the past couple of years. I would also like to thank Dr Robert M. Jones for being on my advisory committee. Finally,
85 citations
TL;DR: In this article, the authors present an analytical method for determining natural frequencies and vibration modes of laminated plates having such curvilinear reinforcing fibers, and the results show that the natural frequencies obtained by the present method agree well with results from finite element analyses.
84 citations
"A design algorithm to model fibre p..." refers methods in this paper
...To overcome the reduced design space of a linear fibre path representation, non-linear variations of fibre angles have also been proposed, for example by means of Lagrangian polynomials [56–58], LobattoLegendre polynomials [59,60], Bezier curves [17,61,62], splines [63,64], Bsplines surfaces [41], NURBS (Non-Uniform Rational B-Splines) [65], and...
[...]
TL;DR: In this article, an optimisation strategy for the design of postbuckling behavior of VAT composite laminates under axial compression is presented, where a mathematical definition based on Lagrangian polynomials, which requires few design parameters, is used to define a general fiber angle distribution of the VAT plate.
84 citations
TL;DR: In this article, the problem of tailoring for the pressure-pillowing problem of a fuselage skin is addressed using steered fibers, where the problem is modeled as a two-dimensional plate using von Karman plate equations.
Abstract: Manufacturing of high-quality fiber-reinforced composite structures with spatially varying fiber orientation is possible using advanced tow-placement machines. Changing the fiber-orientation angle within a layer produces variable-stiffness properties. Contrary to traditional composites with straight fibers, this method allows the designer to fully benefit from the directional material properties of the composite to improve laminate performance by determining optimal fiber paths. In this paper, design tailoring for the pressure-pillowing problem of a fuselage skin is addressed using steered fibers. The problem is modeled as a two-dimensional plate using von Karman plate equations. The analysis is performed using the Rayleigh-Ritz method, and the nonlinear response is traced using a normal flow algorithm. The design objective is to determine the optimal fiber paths over the panel for maximum failure load. Different designs are obtained for different loading cases. The results indicate that by using steered fibers, the pressure-pillowing problem can be alleviated and the load-carrying capacity of the structure can be improved, compared with designs using straight fibers.
81 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]....
[...]
...To overcome the reduced design space of a linear fibre path representation, non-linear variations of fibre angles have also been proposed, for example by means of Lagrangian polynomials [56–58], LobattoLegendre polynomials [59,60], Bezier curves [17,61,62], splines [63,64], Bsplines surfaces [41], NURBS (Non-Uniform Rational B-Splines) [65], and...
[...]