the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Dec 2025
A Multi-Parametric Composite Approach for the Optimization of Wind Turbine Blades using Double-Double Laminates
Abstract. As wind turbines scale to meet growing energy demands, blade structures face increasingly demanding performance requirements. This work addresses this challenge by extending the design space of composite blades through the substitution of traditional triaxial laminates with Double-Double (DD) laminates. While triaxial laminates are widely used due to their convenient layup and manufacturability, they are rarely scrutinized in literature and often lead to suboptimal structural performance. To enable this substitution, a multi-parametric composite modeling approach is developed and integrated into a gradient-based optimization framework. This architecture enables the coexistence of discrete and continuous laminate formulations within a single panel, allowing for detailed, skin-wise optimization of sandwich structures. The approach is applied to a modified blade design of the IEA-15-240 Reference Wind Turbine. Results demonstrate that DD laminates provide a more effective buckling-oriented design, resulting in significant mass savings in the shell structure.
- Preprint
(2996 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 13 Feb 2026)
-
CC1: 'Comment on wes-2025-285', Alexander Krimmer, 18 Jan 2026
reply
-
AC1: 'Reply on CC1', Edgar Werthen, 20 Jan 2026
reply
Dear Dr. Krimmer,
thank you very much for taking the time to review our paper. We would like to address your two main concerns here to encourage you to continue the review. We will then, of course, respond to your valuable comments in detail.
Unfortunately, the conversion of the table with the material properties into LaTeX format was faulty. We sincerely apologise for this. The material properties were taken directly from this source and were also used correctly for the simulations in this paper. The correct table can be found in the appendix.
Below the table you find a picture which shows that Tsai’s criterion for homogenization is fulfilled for both Triax and our optimised DD laminates in case of four resp. two repetitions r. Since a DD laminate is defined by two angles (±φ, ±ψ), a Triax fabric is already a DD laminate: [+0,-0,+45,-45] = one repetition. The fulfilment of the Tsai criterion depends only on the number of repetitions and not on the individual ply thickness, as the criterion works with ABD* matrices normed by the laminate thickness. We have also created a small Excel tool which you can use to perform the calculations yourself.
According to our understanding of the literature on rotor blade optimisation, predefined layups are used and their thickness distribution is optimised, e.g. that of the shell and the main spar cap. The overall idea of this paper is to enlarge the design space by integrating the layer angles of the shell fabric into the optimization (optimization with DD laminates). Of course, this leads to fabrics that do not currently exist on the market, which in turn would be part of further research but we don’t increase the complexity of already established manufacturing processes.
We hope we have encouraged you to continue your review and thank you very much for your efforts. We would be very pleased to receive your full review and would like to work through the valuable comments and integrate them into the revised manuscript.
Kind regards,
Edgar Werthen
- On behalf of all authors –
-
AC1: 'Reply on CC1', Edgar Werthen, 20 Jan 2026
reply
-
RC1: 'Comment on wes-2025-285', Anonymous Referee #1, 21 Jan 2026
reply
Comments on wes-2025-285
Title: A Multi-Parametric Composite Approach for the Optimization of Wind Turbine Blades using Double-Double Laminates
The manuscript presents a comprehensive methodological framework for expanding the composite design space of large wind turbine blades by replacing conventional triaxial glass laminates with Double–Double laminates.
The paper is technically complete, well structured, and addresses a relevant and timely problem in large-scale wind turbine blade design. The reviewer suggests just some minor comments:
- While tapering advantages of DD laminates are mentioned, could the authors discuss the practical manufacturability of Double–Double laminates at full blade scale?
- The authors may consider citing ”Riccio A., Caprio F.D., Tsai S.W., Russo A., Sellitto A. Optimization of composite aeronautical components by Re-designing with double-double laminates (2024) Aerospace Science and Technology, 151, art. no. 109304” in the Introduction, as it presents a recent optimization-driven application of Double–Double laminates that is closely related to the present work.
- Could the authors briefly comment on whether ply-by-ply failure checks were considered in selected critical regions to assess potential conservativeness? Additionally, how are interlaminar failure modes, such as delamination or debonding, considered?
- Given the extensive use of symbols and analytical expressions throughout the manuscript, the authors may consider adding a short Nomenclature section.
- A short clarification on the criteria used to select the PreDoCS discretization shown in Figure 15 would be helpful.
- The Appendix contains several analytical expressions whose symbols are not fully defined. For completeness and reproducibility, all terms should be clearly introduced when first used.
Citation: https://doi.org/10.5194/wes-2025-285-RC1 -
RC2: 'Comment on wes-2025-285', Anonymous Referee #2, 27 Jan 2026
reply
Dear Authors,
thank you for the effort put into this paper. With the updated material properties I proceeded with my review. I understand that available information on blade design is limited. Anyhow, the main design driver for rotor blades today is fatigue. Since this aspect is not taken into account, the optimization especially using criteria as per Tsai's double-double (DD) work completely lacks practical relevance. Further, using DD ply drop rules for DD laminates and not for the established triaxials is distorting the results since ply drop rules from aircraft industry are not used in rotor blade design. We happily apply non-symmetric laminates all over the blade.
The use of the optimization framework is questionable from my point of view. DD is to my understanding not meant to result in laminates with only two fiber directions. This results in very unstable laminates, especially in the case of matrix damaging. An according design would lack robustness and is therefore to be avoided. Anyhow, this is the supperior optimization result in this study with +/-48°. What would be the result if at least three fiber angles would be required? This would be much more realistic with respect to required robustness under field conditions.
(line 255) it would be preferrable if the reference plane for laminates through laminate optimization would coincide with the aerodynamic surface of the blade.
In my opinion, the whole work could significantly be shortened if the details on classical laminated plate theory would be referenced from established literature such as VDI2014 or comparable.
(table 2) definition of coordinate systems is not in line with established literature. Please adapt. Further, please correct material properties as per your prior comment.
(line 337) How is convergence defined?
(line 343) The number of cross-sections seems to be very low. What would be the result of a convergence analysis with regard to element size?
(equation 25) It seems that through thickness shear is neglected throughout buckling analysis. Is that true? In reality this is significantly driving the buckling behavior of rotor blade structures. Please comment/adapt.
(line 388) The chamfer ratio seems very steep. Has applicability been validated for heavy fabrics as applied in wind blades (around 1200 gsm)? This seems to be the main driver for mass reduction in the root area and therefor should be validated.
(line 464) The minimum allowable thickness for DD laminates is different from that for triaxials. This distorts the results in favor of DD laminates since in many of the outboard areas only one layer is necessary. Please use comparable assumptions here.
(line 479) Please use more concise terms or explain/define.
(line 510) How is resin uptake of core material taken into account? Such optimization usually leads to an increase in core material thickness trading off laminate materials. When resin uptake of core materials as dead mass is neglected, the results are not comparable anymore. Please comment/include.
(line 542) What is meant by "upper skin" please define.
Further, please see my comments in attached *.pdf document.
Thanks again and best, Alex
-
RC3: 'Comment on wes-2025-285', Anonymous Referee #3, 02 Feb 2026
reply
Dear Authors,
Thanks for submitting a well-written, technically detailed manuscript that addresses an important topic in composite structural optimization for wind turbine blades. The paper presents a mathematically elegant framework and a thorough theoretical development. The following comments are intended to be constructive and to clarify the scope, assumptions, and practical relevance of the proposed approach, particularly regarding its applicability to real wind turbine blade structures.
Optimizing the blade mass should be put in the context of a multi-parameter optimization (e.g., fatigue resistance, total blade deflection, root requirements for stiffness for optimal load transition to the pitch bearing and the bolted connections etc.), rather than only on the buckling resistance and static strength of composite panels.
Should the presented optimization be only an example case, then it must be made implementing the appropriate mechanics, i.e., considering the out-of-plane shear stiffness, which dominates the stability of large sandwich panels. The analyses are valid within the framework of classical laminate theory for thin plates. However, the core assumptions are not representative of wind turbine blade panels, where transverse shear, core compliance, and face–core interaction govern both stiffness and stability behavior.
From the material volume point of view, it is not profitable for a fabric manufacturer to set up the machines for a limited amount of material production. The wind turbine blade industry serves a cost-driven market. Standardization of fabrics reduces the manufacturing cost and effort, while enhancing alternatives in terms of supply.
Moreover, the drapability of the fabric is not to be underestimated. The dry fabric must be laid in the mold and follow the difficult contours. Thus, an arbitrary fiber selection which folds due to its nature, or is “stiff” might be inappropriate for manufacturing purposes.
If “tapering” is meant only as a thickness variation, then this comment is not valid. If through “tapering” an angle variation along the blade length, then another counter side of the analysis is that it neglects the increase in the blade manufacturing complexity, which again speaks for increased costs.
Finally, substituting the Triax with a DD material not only affects stiffness, but it also affects the failure mode, which changes from fiber-dominated to matrix-dominated. That increases the risk of a brittle catastrophic failure even with a single crack initiation.
(around line 50) Concerning your literature survey, what were the optimization criteria behind the referenced papers? For example, does the other research consider major design drivers, like fatigue, to optimize their stacking sequence? A more critical review of the literature should be presented, rather than a list presentation. I cannot imagine designing a blade with 5.8° off-axis spars without having severe fatigue issues.
(line 227) The proposed Kirchhoff-Love plate theory does not account for transverse shear, which is the instability driver for thick-composite sandwich structures. How are you coping with that?
(line 275) By implementing a higher-order shear theory, would your approach still be valid?
(Table 7) In what you presented, the multi-parametric framework allows wind blade skins (only thin) to be treated like aerospace composite structures, and when applied to a large blade it naturally converges to slightly off-axis DD laminates that soften the structure in shear and compression, reducing mass by ~10%; in this particular case the optimal solution might remain manufacturable because it collapses to a simple repeated building block. Would this always be the case, or might we end up with variable angles all over blade segments, which makes manufacturing a lot more complicated if not impractical?
(Table 7) When substituting Triax plies with DD laminates, how will you cope with the risk of a brittle matrix crack? The whole root will be in severe danger.
In summary, the paper presents an elegant and mathematically rigorous framework for composite panel optimization and introduces interesting methodological concepts with clear potential value for structural design. These might be relevant for more automated manufacturing procedures, like in the aerospace industry, where, additionally, composite structures are substantially thinner. At the same time, these structural assumptions limit its direct applicability to real wind turbine blades, particularly with respect to thick sandwich mechanics, fatigue performance, damage risk, and manufacturing constraints. Addressing these aspects more explicitly and moderating claims regarding industrial relevance would significantly strengthen the paper and clarify its contribution to the wind energy community.
Kind regards,
Alexandros
Citation: https://doi.org/10.5194/wes-2025-285-RC3
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 263 | 112 | 24 | 399 | 19 | 21 |
- HTML: 263
- PDF: 112
- XML: 24
- Total: 399
- BibTeX: 19
- EndNote: 21
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Dear Authors,
thank you for the huge effort you took to write this paper. Unfortunately, some of the leading assumptions to my knowledge are not fitting rotor blade design procedures. I stopped my review at page 18 where the material properties used for the optimization and comparison are given. These are completely unrealistic and should not be used to assess one or the other design method. Please establish realistic material assumptions prior to re-evaluating the calculations. With the given values the research is irrelevant.
Best regards,
Alexander Krimmer