Abstract
In the context of more electrical aircraft, electromechanical de-icing systems provide a low-energy solution to protect aircraft’s surfaces from ice buildup. Such systems produce deformation of the protected surface leading to a stress production within the ice and, ultimately, to ice shedding thanks to fracture. However, these systems may show limitations when it comes to completely protect a given surface. Ice delamination is often restricted to a part of the surface and the remaining ice either requires more energy to be removed or is just impossible to remove. In this paper, topology optimization of the substrate covered by ice is thus investigated to increase fracture propagation and ice shedding. For that purpose, an optimization problem, involving the energy release rate but also the mass and the substrate stress, is formulated. The numerical results show how the delamination efficiency of mechanical based ice protection systems can be improved through the topology modification of the substrate.
Similar content being viewed by others
References
Ahrens J, Geveci B, Law C (2005) Paraview: an end-user tool for large data visualization. The visualization handbook 717:8
Aircraft Icing Handbook. Civil Aviation Authority (2000)
Akl W, El-Sabbagh A, Al-Mitani K, Baz A (2009) Topology optimization of a plate coupled with acoustic cavity. Int J Solids Struct 46(10):2060–2074. https://doi.org/10.1016/j.ijsolstr.2008.05.034 (Special Issue in Honor of Professor Liviu Librescu)
Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393. https://doi.org/10.1016/j.jcp.2003.09.032
Amir O (2013) A topology optimization procedure for reinforced concrete structures. Comput Struct 114–115:46–58. https://doi.org/10.1016/j.compstruc.2012.10.011
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidisc Optim 43(1):1–16
Bennani L, Villedieu P, Salaun M (2016) A mixed adhesion-brittle fracture model and its application to the numerical study of ice shedding mechanisms. Eng Fract Mech 158:59–80. https://doi.org/10.1016/j.engfracmech.2016.02.050
Budinger M, Pommier-Budinger V, Napias G, Costa da Silva A (2016) Ultrasonic ice protection systems: analytical and numerical models for architecture tradeoff. J Aircraft 680–690. https://doi.org/10.2514/1.C033625
Budinger M, Pommier-Budinger V, Bennani L, Rouset P, Bonaccurso E, Dezitter F (2018) Electromechanical resonant ice protection systems: analysis of fracture propagation mechanisms. AIAA J 56(11):4412–4422. https://doi.org/10.2514/1.J056663
Budinger M, Pommier-Budinger V, Reysset A, Palanque V (2021) Electromechanical resonant ice protection systems: energetic and power considerations. AIAA J 59(7):2590–2602. https://doi.org/10.2514/1.J060008
Cao Y, Tan W, Wu Z (2018) Aircraft icing: an ongoing threat to aviation safety. Aerospace Sci Technol 75:353–385. https://doi.org/10.1016/j.ast.2017.12.028
Da D (2019). Topology optimization design of heterogeneous materials and structures. https://doi.org/10.1002/9781119687252
Da D, Yvonnet J (2020) Topology optimization for maximizing the fracture resistance of periodic quasi-brittle composites structures. Materials 13:15. https://doi.org/10.3390/ma13153279
Da D, Yvonnet J, Xia L, Li G (2018) Topology optimization of particle-matrix composites for optimal fracture resistance taking into account interfacial damage. Int J Numer Methods Eng 115(5):604–626
Dondl PW, Bhattacharya K (2016) Effective behavior of an interface propagating through a periodic elastic medium. Interfaces Free Boundaries 18(1):91–113
Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8):1453–1478
Frémond M (1987) Adhérence des solides. J Méc Théor Appl 6(3):383–407
Geuzaine C, Remacle J-F (2009) Gmsh: a 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331
Griffith AA (1921) Vi the phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A 221(582–593):163–198. https://doi.org/10.1098/rsta.1921.0006
Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidisc Optim 48(1):33–47
Hsueh C-J, Bhattacharya K (2018) Optimizing microstructure for toughness: the model problem of peeling. Struct Multidisc Optim 58(3):1067–1080
Huang X, Xie Y-M (2010) A further review of eso type methods for topology optimization. Struct Multidisc Optim 41(5):671–683
Huang X, Zuo ZH, Xie YM (2010) Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput Struct 88(5):357–364. https://doi.org/10.1016/j.compstruc.2009.11.011
Huang X, Tepylo N, Pommier-Budinger V, Budinger M, Bonaccurso E, Villedieu P, Bennani L (2019) A survey of icephobic coatings and their potential use in a hybrid coating/active ice protection system for aerospace applications. Progr Aerospace Sci 105:74–97. https://doi.org/10.1016/j.paerosci.2019.01.002
Johnson SG (2014) The NLopt nonlinear-optimization package. https://github.com/stevengj/nlopt
Kalkowski MK, Waters TP, Rustighi E (2015) Removing surface accretions with piezo-excited high-frequency structural waves. In: Active and Passive Smart Structures and Integrated Systems 2015, vol 9431, p 94311 . https://doi.org/10.1117/12.2087048. International Society for Optics and Photonics. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/9431/94311T/Removing-surface-accretions-with-piezo-excited-high-frequency-structural-waves/10.1117/12.2087048.short
Kang Z, Pai L, Li M (2017) Topology optimization considering fracture mechanics behaviors at specified locations. Struct Multidisc Optim 55(5):1847–1864
Klarbring A, Torstenfelt B, Edlund U, Schmidt P, Simonsson K, Ansell H (2018) Minimizing crack energy release rate by topology optimization. Struct Multidisc Optim 58(4):1695–1703
Lazarov BS, Sigmund O (2011) Filters in topology optimization based on Helmholtz-type differential equations. Int J Numer Methods Eng 86(6):765–781
Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidisc Optim 41(4):605–620
Leary WM (2002) We freeze to please: a history of NASA’s icing research tunnel and the quest for flight safety. Technical report. https://trid.trb.org/view/725075
Liu P, Luo Y, Kang Z (2016) Multi-material topology optimization considering interface behavior via xfem and level set method. Comput Methods Appl Mech Eng 308:113–133. https://doi.org/10.1016/j.cma.2016.05.016
Marbœuf A, Bennani L, Budinger M, Pommier-Budinger V (2020) Electromechanical resonant ice protection systems: numerical investigation through a phase-field mixed adhesive/brittle fracture model. Eng Fract Mech 230:106926. https://doi.org/10.1016/j.engfracmech.2020.106926
Martin E, Vandellos T, Leguillon D, Carrère N (2016) Initiation of edge debonding: coupled criterion versus cohesive zone model. Int J Fract 199(2):157–168
Mergel JC, Sauer RA, Saxena A (2014) Computational optimization of adhesive microstructures based on a nonlinear beam formulation. Struct Multidisc Optim 50:1001–1017
Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45):2765–2778. https://doi.org/10.1016/j.cma.2010.04.011
Nguyen TT, Yvonnet J, Zhu Q-Z, Bornert M, Chateau C (2016) A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography. Comput Methods Appl Mech Eng 312:567–595.
Niemann H, Morlier J, Shahdin A, Gourinat Y (2010) Damage localization using experimental modal parameters and topology optimization. Mech Syst Signal Process 24(3):636–652. https://doi.org/10.1016/j.ymssp.2009.10.022
Nishiwaki S, Frecker MI, Min S, Kikuchi N (1998) Topology optimization of compliant mechanisms using the homogenization method. Int J Numer Methods Eng 42(3):535–559
Overmeyer A, Palacios JL, Smith EC, Royer R (2011) Rotating testing of a low-power, non-thermal ultrasonic de-icing system for helicopter rotor blades. Technical report, SAE Technical Paper. https://www.sae.org/publications/technical-papers/content/2011-38-0098/
Overmeyer A, Palacios J, Smith E (2012) Actuator bonding optimization and system control of a rotor blade ultrasonic deicing system. In: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, p 1476. https://doi.org/10.2514/6.2012-1476
Palacios JL (2008) Design, fabrication, and testing of an ultrasonic de-icing system for helicopter rotor blades. PhD thesis, Pennsylvania State University, State College
Palacios J, Smith E (2005) Dynamic analysis and experimental testing of thin-walled structures driven by shear tube actuators. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, p 2112 . https://doi.org/10.2514/6.2005-2112
Palacios J, Smith E, Rose J et al (2008) Investigation of an ultrasonic ice protection system for helicopter rotor blades. In: Annual forum Proceedings-American Helicopter Society, vol 64, p 609. American Helicopter Society, Inc
Palacios J, Smith E, Rose J, Royer R (2011) Instantaneous de-icing of freezer ice via ultrasonic actuation. AIAA J 49(6):1158–1167. https://doi.org/10.2514/1.J050143
Palacios J, Smith E, Rose J, Royer R (2011) Ultrasonic de-icing of wind-tunnel impact icing. J Aircraft 48(3):1020–1027. https://doi.org/10.2514/1.C031201
Palanque V, Marbæuf A, Budinger M, Pommier-Budinger V, Bennani L (2021) Improving mechanical ice protection systems with substrate thickness and topology optimization. In preparation
Parks DM (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract 10(4):487–502
Pommier-Budinger V, Budinger M, Rouset P, Dezitter F, Huet F, Wetterwald M, Bonaccurso E (2018) Electromechanical resonant ice protection systems: initiation of fractures with piezoelectric actuators. AIAA J 56(11):4400–4411. https://doi.org/10.2514/1.J056662
Ramanathan S, Varadan VV, Varadan VK (2000) Deicing of helicopter blades using piezoelectric actuators. In: Smart Structures and Materials 2000: Smart Electronics and MEMS, vol 3990, pp 281–293. https://doi.org/10.1117/12.388906. International Society for Optics and Photonics. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/3990/0000/Deicing-of-helicopter-blades-using-piezoelectric-actuators/10.1117/12.388906.short?SSO=1
Russ JB, Waisman H (2019) Topology optimization for brittle fracture resistance. Comput Methods Appl Mech Eng 347:238–263. https://doi.org/10.1016/j.cma.2018.12.031
Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidisc Optim 21(2):120–127
Sih G, Rice J (1965) Plane problems of cracks in dissimilar materials. J Appl Mech 32:418–423
Strobl T, Storm S, Thompson D, Hornung M, Thielecke F (2015) Feasibility study of a hybrid ice protection system. J Aircraft 52(6):2064–2076. https://doi.org/10.2514/1.C033161
Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373
Sylves K, Maute K, Dunn M (2009) Adhesive surface design using topology optimization. Struct Multidisc Optim 38:455–468
Venna SV, Lin Y- (2006) Mechatronic development of self-actuating in-flight deicing structures. IEEE/ASME Trans Mechatron 11(5):585–592. https://doi.org/10.1109/TMECH.2006.882990
Venna S, Lin Y-J, Botura G (2007) Piezoelectric transducer actuated leading edge de-icing with simultaneous shear and impulse forces. J Aircraft 44(2):509–515. https://doi.org/10.2514/1.23996
Venna S, Lin Y (2003) Development of self-actuating in-flight de-icing structures with power consumption considerations. In: Proceedings of the American Society of Mechanical Engineers International Mechanical Engineering Congress and Exposition, pp 45–53. ASME Washington, DC
Villeneuve E, Harvey D, Zimcik D, Aubert R, Perron J (2015) Piezoelectric deicing system for rotorcraft. J Am Helicop Soc 60(4):1–12. https://doi.org/10.4050/JAHS.60.042001
Waisman H (2010) An analytical stiffness derivative extended finite element technique for extraction of crack tip strain energy release rates. Eng Fract Mech 77(16):3204–3215. https://doi.org/10.1016/j.engfracmech.2010.08.015
Work A, Lian Y (2018) A critical review of the measurement of ice adhesion to solid substrates. Progr Aerospace Sci 98:1–26. https://doi.org/10.1016/j.paerosci.2018.03.001
Wu J-Y (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99. https://doi.org/10.1016/j.jmps.2017.03.015
Wu J-Y, Nguyen VP (2018) A length scale insensitive phase-field damage model for brittle fracture. J Mech Phys Solids 119:20–42. https://doi.org/10.1016/j.jmps.2018.06.006
Xia L, Da D, Yvonnet J (2018) Topology optimization for maximizing the fracture resistance of quasi-brittle composites. Comput Methods Appl Mech Eng 332:234–254. https://doi.org/10.1016/j.cma.2017.12.021
Xia SM, Ponson L, Ravichandran G, Bhattacharya K (2015) Adhesion of heterogeneous thin films ii: Adhesive heterogeneity. J Mech Phys Solids 83:88–103. https://doi.org/10.1016/j.jmps.2015.06.010
Zargham S, Ward TA, Ramli R, Badruddin IA (2016) Topology optimization: a review for structural designs under vibration problems. Struct Multidisc Optim 53(6):1157–1177
Zhang Z, Chen B, Lu C, Wu H, Wu H, Jiang S, Chai G (2017) A novel thermo-mechanical anti-icing/de-icing system using bi-stable laminate composite structures with superhydrophobic surface. Compos Struct 180:933–943. https://doi.org/10.1016/j.compstruct.2017.08.068
Acknowledgements
This work has been partially funded by STAE foundation through the ReMOVEICE project and by ISAE-SUPAERO.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Replication of results
The algorithm is described in this paper together with numerical parameters. Numerical results are obtained with a 2D sequential code writing in Python and starting from scratch. The code implements mesh reading and writing, \({\mathbb {P}}_1\) finite element solver, filtering, objective and constraints evaluations, and sensitivities’ computation. The external Python package nlopt (Johnson 2014) is used for updating densities with MMA. Mesh generation is done with gmsh (Geuzaine and Remacle 2009) which provides MSH files to the code. Results are written in the VTK file format and are visualized with Paraview (Ahrens et al. 2005).
Additional information
Responsible Editor: Emilio Carlos Nelli Silva
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Marbœuf, A., Budinger, M., Pommier-Budinger, V. et al. Improving mechanical ice protection systems with topology optimization. Struct Multidisc Optim 65, 147 (2022). https://doi.org/10.1007/s00158-022-03235-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00158-022-03235-8