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.
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.
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.
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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
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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.
Abstract: In this study, we optimized the curved fiber trajectories to realize variable fiber volume fraction and stiffness composites (VVfSC) using a continuous fiber composite 3D printer. During optimization, the fiber orientation was maintained along the principal stress direction based on preliminary stress field calculations, and the fiber trajectories were subsequently obtained. The fiber volume fraction was calculated from the obtained fiber trajectories; then, stress field calculations and redetermination of the fiber trajectories were performed. Optimization was achieved by repeating this sequence until convergence was obtained. Based on the optimization result, the specimens were molded using a continuous carbon fiber 3D printer and evaluated with bolt joint tensile tests. It was demonstrated that the stiffness and strength per unit weight of the optimized VVfSC were 9.4 and 1.6 times greater than those of conventional linear laminates, respectively.
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.
Abstract: Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.
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.
Abstract: The advent of novel robot-assisted composite manufacturing techniques has enabled steering of fibre paths in the plane of the lamina, leading to the emergence of the so-called variable angle tow (VAT) composite laminates. These laminates, with spatially varying fibre angle orientations, provide the designer with the ability to tailor the point-wise stiffness properties of VAT composites with substantially more efficient structural performance over conventional straight fibre laminates. As the application of fibre-steered composite laminates has reached an unprecedented scale in both academia and industry in recent years, a reflection upon the state-of-the-art advancements in the modelling, design, and analysis of these advanced structures becomes vital for successfully shaping the future landscape. Motivated by the gap and shortcomings in the available review works, in the present paper, we first summarize and discuss underlying fibre placement technologies including tailored fibre placement (TFP), continuous tow shearing (CTS), and automated fibre placement (AFP). Afterwards, mathematical models of reference fibre path in fibre-steering technology will be reviewed, followed by a detailed discussion on the manufacturing limitations and constraints of the AFP process. Then, design considerations in constructing a ply with multiple courses are elaborated, and key techniques to fill the entire layer with several courses are reviewed. This review is then followed by an introduction to the continuity and smoothness of fibre paths. Furthermore, a description on the material and geometric uncertainties is elaborated. Last but not least, the plate and shell laminate theories, which serve as the fundamental core of the modelling and design of VAT composite structures, are discussed.
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.
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.
18 citations
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