SpringerLink
Log in

Buckling optimization of variable stiffness composite wing boxes with manufacturing defects

  • Research
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Composite structures can achieve greater performance through variable stiffness design. In consideration of inevitable manufacturing defects introduced by the Automatic Fiber Placement machine, modified models are established to calculate equivalent properties for materials with gaps or overlaps. A modeling method for variable stiffness structures with defects is proposed based on the modified models. This approach significantly reduces the dependence on mesh size for analysis accuracy, thereby improving modeling and calculation efficiency. Upon validation of the proposed modeling method, a Hierarchical Kriging surrogate modeling is employed to optimize the buckling performance of a variable stiffness wing box with defects. The impact of different manufacturing strategies on optimization results is also investigated. The findings demonstrate that the variable stiffness design improves the wing box buckling performance under a combined torsion-bending condition. Finally, the potential of utilizing overlaps without cut-restart is analyzed for weight reduction in the design of variable stiffness wing boxes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  • Alhajahmad A, Mittelstedt C (2020) Design tailoring of curvilinearly grid-stiffened variable-stiffness composite cylindrically curved panels for maximum buckling capacity. Thin-Walled Struct 157:107132

    Article  Google Scholar 

  • Alhajahmad A, Mittelstedt C (2021) Minimum weight design of curvilinearly grid-stiffened variable-stiffness composite fuselage panels considering buckling and manufacturing constraints. Thin-Walled Struct 161:107526

    Article  Google Scholar 

  • Aragh B, Farahani EB, Xu BX, Ghasemnejad H, Mansur WJ (2021) Manufacturable insight into modelling and design considerations in fibre-steered composite laminates: state of the art and perspective. Comput Methods Appl Mech Eng 379:113752

    Article  MathSciNet  Google Scholar 

  • Bakhshi N, Hojjati M (2018) An experimental and simulative study on the defects appeared during tow steering in automated fiber placement. Compos A 113:122–131

    Article  Google Scholar 

  • Blom A, Lopes C, Kromwijk P, Gürdal Z, Camanho P (2009) A theoretical model to study the influence of tow-drop areas on the stiffness and strength of variable-stiffness laminates. J Compos Mater 43:403–425

    Article  Google Scholar 

  • Brooks T, Martins J (2018) On manufacturing constraints for tow-steered composite design optimization. Compos Struct 204:548–559

    Article  Google Scholar 

  • Brooks T, Martins J, Kennedy G (2019) High-fidelity aerostructural optimization of tow-steered composite wings. J Fluids Struct 88:122–147

    Article  Google Scholar 

  • Brooks T, Martins J, Kennedy G (2020) Aerostructural tradeoffs for tow-steered composite wings. J Aircr 57:787–799

    Article  Google Scholar 

  • Cao Z, Dong M, Shi Q, Han Z, Qiu R (2022) Research on buckling characteristics and placement processability of variable stiffness open-hole laminates. Composites C 7:100233

    Google Scholar 

  • Coburn BH, Wu Z, Weaver PM (2014) Buckling analysis of stiffened variable angle tow panels. Compos Struct 111:259–270

    Article  Google Scholar 

  • Falcó O, Mayugo JA, Lopes CS, Gascons N, Turon A, Costa J (2014) Variable-stiffness composite panels: as-manufactured modeling and its influence on the failure behavior. Compos B 56:660–669

    Article  Google Scholar 

  • Fayazbakhsh K, Nik M, Pasini D, Lessard L (2013) Defect layer method to capture effect of gaps and overlaps in variable stiffness laminates made by Automated Fiber Placement. Compos Struct 97:245–251

    Article  Google Scholar 

  • Forrester A, Sóbester A, Keane A (2008) Engineering design via surrogate modelling: a practical guide. Wiley, New York

    Book  Google Scholar 

  • Gruber M, Lamontia M, Waibel B (2001) Automated fabrication processes for large composite aerospace structures: A trade study. In: 46th International SAMPE Symposium and Exhibition. Long Beach, 1987–1997.

  • Guo Q, Hang J, Wang S, Hui W, **e S (2021) Design optimization of variable stiffness composites by using multi-fidelity surrogate models. Struct Multidisc Optim 63:439–461

    Article  MathSciNet  Google Scholar 

  • Gürdal Z, Olmedo R (1993a) In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J 31:751–758

    Article  Google Scholar 

  • Gürdal Z, Olmedo R (1993b) Composite laminates with spatially varying fiber orientations: Variable Stiffness panel concept. AIAA J 31:751–758

    Article  Google Scholar 

  • Han Z, Stefan G (2012) Hierarchical kriging model for variable-fidelity surrogate modeling. AIAA J 50:1885–1896

    Article  Google Scholar 

  • Hao P, Liu C, Yuan X, Wang B, Li G, Zhu T, Niu F (2017) Buckling optimization of variable-stiffness composite panels based on flow field function. Compos Struct 181:240–255

    Article  Google Scholar 

  • Irisarri F, Lasseigne A, Leroy F, Riche R (2014) Optimal design of laminated composite structures with ply drops using stacking sequence tables. Compos Struct 107:559–569

    Article  Google Scholar 

  • Jegley D, Tatting B, Gürdal Z (2003) Optimization of elastically tailored tow-placed plates with holes. In: 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Norfolk, 1420.

  • Jegley D, Tatting B, Gürdal Z (2005) Tow-steered panels with holes subjected to compression or shear loading. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2081.

  • Langley P (1999) Finite element modeling of tow-placed variable-stiffness composite laminates. Virginia Polytechnic Institute and State University, Virginia

    Google Scholar 

  • Liguori F, Zucco G, Madeo A, Magisano D, Leonetti L, Garcea G, Weaver P (2019) Postbuckling optimisation of a variable angle tow composite wingbox using a multi-modal Koiter approach. Thin-Walled Struct 138:183–198

    Article  Google Scholar 

  • Lopes C, Camanho P, Gürdal Z, Tatting B (2007) Progressive failure analysis of tow-placed, variable-stiffness composite panels. Int J Solids Struct 44:8493–8516

    Article  Google Scholar 

  • Marouene A, Boukhili R, Chen J, Yousefpour A (2016a) Buckling behavior of variable-stiffness composite laminates manufactured by the tow-drop method. Compos Struct 139:243–253

    Article  Google Scholar 

  • Marouene A, Boukhili R, Chen J, Yousefpour A (2016b) Effects of gaps and overlaps on the buckling behavior of an optimally designed variable-stiffness composite laminates: a numerical and experimental study. Compos Struct 140:556–566

    Article  Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    MathSciNet  Google Scholar 

  • Meng L, Zhang J, Hou Y, Breitkopf P, Zhu J, Zhang W (2023) Revisiting the Fibonacci spiral pattern for stiffening rib design. Int J Mech Sci 246:108131

    Article  Google Scholar 

  • Oliveri V, Zucco G, Peeters D, Clancy G, Telford R, Rouhi M, McHale C, O’Higgins R, Young T, Weaver P (2019) Design, manufacture and test of an in-situ consolidated thermoplastic variable-stiffness wingbox. AIAA J 57:1671–1683

    Article  Google Scholar 

  • Oromiehie E, Prusty B, Compston P, Rajan G (2019) Automated fibre placement based composite structures: Review on the defects, impacts and inspections techniques. Compos Struct 224:110987

    Article  Google Scholar 

  • Punera D, Mukherjee P (2022) Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites. J Reinf Plast Compos 41:917–945

    Article  Google Scholar 

  • Singh K, Kapania R (2019) Buckling load maximization of curvilinearly stiffened tow-steered laminates. J Aircraft 56:2272–2284

    Article  Google Scholar 

  • Stodieck O, Cooper J, Weaver P, Kealy P (2017) Aeroelastic tailoring of a representative wing box using tow-steered composites. AIAA J 55:1425–1439

    Article  Google Scholar 

  • Sun CT, Vaidya RS (1996) Prediction of composite properties from a representative volume element. Compos Sci Technol 56:171–179

    Article  Google Scholar 

  • Tatting B, Gürdal Z (2003) Automated finite element analysis of elastically-tailored plates: NASA/CR-2003-212679. Hampton: NASA Langley Research Center.

  • Tatting BF, Gürdal Z, Jegley D (2002) Design and manufacture of elastically tailored tow placed plates. Hampton: National Aeronautics and Space Administration Langley Research Center, 211919.

  • Woigk W, Hallett S, Jones M, Kuhtz M, Hornig A, Gude M (2018) Experimental investigation of the effect of defects in automated fibre placement produced composite laminates. Compos Struct 201:1004–1017

    Article  Google Scholar 

  • Wu K, Gürdal Z, Starnes J (2002) Structural response of compression-loaded, tow-placed, variable stiffness panels. In: 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, 1512.

  • **a Z, Zhou C, Yong Q, Wang X (2006) On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites. Int J Solids Struct 43:266–278

    Article  MathSciNet  Google Scholar 

  • Zhao W, Kapania R (2022) Buckling analysis and optimization of stiffened variable angle tow laminates with a cutout considering manufacturing constraints. J Compos Sci 6:80

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China [Grant Number 12272358].

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nan**g University of Aeronautics and Astronautics, Nan**g, 210016, China

    Yan Huang & Puhui Chen

  2. School of Aeronautic Science and Engineering, Beihang University, Bei**g, 100083, China

    Zhe Wang

  3. National Key Laboratory of Strength and Structural Integrity, Aircraft Strength Research Institute of China, **’an, 710065, China

    Zhe Wang

Authors
  1. Yan Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhe Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Puhui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y. H.: Conceptualization, Investigation, Validation, Visualization, Writing - Original Draft, Methodology. Z. W.: Supervision, Project administration, Resources, Software, Writing - Review & Editing. P. C.: Resources, Supervision, Writing - Review & Editing.

Corresponding author

Correspondence to Puhui Chen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

We state that the results presented in this paper can be reproduced by the values of the related parameters provided by the authors.

Additional information

Responsible Editor: ** Du

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Y., Wang, Z. & Chen, P. Buckling optimization of variable stiffness composite wing boxes with manufacturing defects. Struct Multidisc Optim 67, 109 (2024). https://doi.org/10.1007/s00158-024-03809-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00158-024-03809-8

Keywords

Search

Navigation