Abstract
The aerospace industry is constantly looking to integrate advanced materials and manufacturing methods into their airframes to achieve new breakthroughs in lightweight design. Enabling these advancements are new computational methods such as multi-material topology optimization. While this field has expanded in recent years, the current state-of-the-art typically focuses on academic-level examples and is usually restricted to isotropic-only or anisotropic-only studies. To address this gap, this paper presents practical examples of multi-material topology optimization for the aerospace industry, including the first application of both isotropic and orthotropic material models simultaneously in the same 3D design space. Here, the structural legs and seatback for a passenger aircraft seat are considered at the conceptual level and focuses on the use of single- and multi-material designs to determine the optimum utilization of a new aerospace-grade composite alongside aluminum and magnesium. Designs are discussed and compared with preliminary considerations on performance and cost, with the inclusion of various alternative manufacturing-based constraints. Ultimately, this paper seeks to demonstrate the practical capability of multi-material topology optimization, and review methods and perspectives for evaluating various single- and multi-material design combinations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim 43:1–16. https://doi.org/10.1007/s00158-010-0594-7
Bell D, Hall P, Passari R (2019) Lightweight aircraft passenger seat assembly. US Patent Application 075,028
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202. https://doi.org/10.1007/BF01650949
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224. https://doi.org/10.1016/0045-7825(88)90086-2
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654. https://doi.org/10.1007/s004190050248
Bendsøe MP, Sigmund O (2004) Topology optimization: theory, methods and applications. Springer-Verlag, Berlin. https://doi.org/10.1007/978-3-662-05086-6
Bushnell D, Rankin C (2005) Optimum design of stiffened panels with substiffeners. In: 46th AIAA Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics. doi:https://doi.org/10.2514/6.2005-1932
Chickermane H, Gea HC (1997) Design of multi-component structural systems for optimal layout topology and joint locations. Eng Comput 13:235–243. https://doi.org/10.1007/BF01200050
Dima G, Balcu I, Zamfir M (2015) Method for lightweight optimization for aerospace milled parts – case study for a helicopter pilot lightweight crashworthy seat side struts. Procedia Technol 19:161–168. https://doi.org/10.1016/j.protcy.2015.02.024
Florea V, Pamwar M, Sangha B, Kim IY (2020) Simultaneous single-loop multimaterial and multijoint topology optimization. Int J Numer Methods Eng 121:1558–1594. https://doi.org/10.1002/nme.6279
Gibiansky LV, Sigmund O (2000) Multiphase composites with extremal bulk modulus. J Mech Phys Solids 48:461–498. https://doi.org/10.1016/S0022-5096(99)00043-5
Guida M, Manzoni A, Zuppardi A, Caputo F, Marulo F, De Luca A (2018) Development of a multibody system for crashworthiness certification of aircraft seat. Multibody Syst Dyn 44:191–221. https://doi.org/10.1007/s11044-018-9612-0
Hvejsel CF, Lund E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43:811–825. https://doi.org/10.1007/s00158-011-0625-z
Kismarton M, Barmichev S (2011) Composite seatback structure for a lightweight aircraft seat assembly. US Patent 8,016,361
Kismarton M, Fullerton J (2013) Composite seat pan structure for a lightweight aircraft seat assembly. US Patent 8,550,564
Krog L, Tucker A, Kemp M, Boyd R (2004a) Topology optimisation of aircraft wing box ribs. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics. doi:https://doi.org/10.2514/6.2004-4481
Krog L, Tucker A, Rollema G (2004b) Application of Topology, Sizing and Shape Optimization Methods to Optimal Design of Aircraft Components. In: 3rd Altair UK HyperWorks Users Conference
Li C, Kim IY (2018) Multi-material topology optimization for automotive design problems. Proc Institut Mech Eng Part D: J Autom Eng 232:1950–1969. https://doi.org/10.1177/0954407017737901
Li D, Kim IY (2020) Modified element stacking method for multi-material topology optimization with anisotropic materials. Struct Multidiscip Optim 61:525–541. https://doi.org/10.1007/s00158-019-02372-x
Liu K, Tovar A (2014) An efficient 3D topology optimization code written in Matlab. Struct Multidiscip Optim 50:1175–1196. https://doi.org/10.1007/s00158-014-1107-x
López C et al (2020) Model-based, multi-material topology optimization taking into account cost and manufacturability. Struct Multidiscip Optim 62:2951–2973. https://doi.org/10.1007/s00158-020-02641-0
Lund E, Stegmann J (2005) On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy 8:109–124. https://doi.org/10.1002/we.132
Remouchamps A, Bruyneel M, Fleury C, Grihon S (2011) Application of a bi-level scheme including topology optimization to the design of an aircraft pylon. Struct Multidiscip Optim 44:739–750. https://doi.org/10.1007/s00158-011-0682-3
Roper S, Li D, Florea V, Woischwill C, Kim IY (2018) Multi-material topology optimization: a practical approach and application. In: WCX SAE World Congress Experience. SAE International doi:https://doi.org/10.4271/2018-01-0110
Roper S, Vierhout G, Li D, Sangha B, Pamwar M, Kim IY (2019) Multi-material topology optimization and multi-material selection in design. In: WCX SAE World Congress Experience. SAE International. doi:https://doi.org/10.4271/2019-01-0843
Rozvany GIN (2008) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37:217–237. https://doi.org/10.1007/s00158-007-0217-0
SAE (2015a) Analytical methods for aircraft seat design and evaluation. SAE International. doi:https://doi.org/10.4271/ARP5765A
SAE (2015b) Performance standard for seats in civil rotorcraft, transport aircraft, and general aviation aircraft. SAE International. doi:https://doi.org/10.4271/AS8049C
SAE (2018) Aircraft seat design guidance and clarifications. SAE International. doi:https://doi.org/10.4271/ARP5526E
SAE (2019) Magnesium alloys in aircraft seats - engineering design and fabrication recommended practices. SAE International. doi:https://doi.org/10.4271/ARP6256
Shah V, Kashanian K, Pamwar M, Sangha B, Kim IY (2020a) Multi-material topology optimization considering manufacturing constraints. In: WCX SAE World Congress Experience. SAE International. doi:https://doi.org/10.4271/2020-01-0628
Shah V, Pamwar M, Sangha B, Kim IY (2020b) Material interface control in multi-material topology optimization using pseudo-cost domain method. Int J Numer Methods Eng:1–28. https://doi.org/10.1002/nme.6545
Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21:120–127. https://doi.org/10.1007/s001580050176
Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48:1031–1055. https://doi.org/10.1007/s00158-013-0978-6
Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16:68–75. https://doi.org/10.1007/BF01214002
Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45:1037–1067. https://doi.org/10.1016/S0022-5096(96)00114-7
Stachel A, Steinmeyer K, Jussli Z (2020) Aircraft seat device including force transferring carrier element. US Patent 10,814,986
Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62:2009–2027. https://doi.org/10.1002/nme.1259
Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373. https://doi.org/10.1002/nme.1620240207
Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12:555–573. https://doi.org/10.1137/S1052623499362822
Thomas H, Zhou M, Schramm U (2002) Issues of commercial optimization software development. Struct Multidiscip Optim 23:97–110. https://doi.org/10.1007/s00158-002-0170-x
Trivers NC, Carrick CA, Kim IY (2020) Design optimization of a business aircraft seat considering static and dynamic certification loading and manufacturability. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-020-02650-z
Vanderplaats GN (2007) Multidiscipline Design Optimization. Vanderplaats Research & Development, California
Vierhout G, Roper S, Li D, Pamwar M, Sangha B, Kim IY (2019a) Multi-material topology optimization as a concept generation and design tool. In: WCX SAE World Congress Experience. SAE International. doi:https://doi.org/10.4271/2019-01-1095
Vierhout G, Roper S, Li D, Sangha B, Pamwar M, Kim IY (2019b) Multi-material topology optimization: a practical method for efficient material selection and design. In: WCX SAE World Congress Experience. SAE International. doi:https://doi.org/10.4271/2019-01-0809
Warwick BT, Mechefske CK, Kim IY (2019) Topology optimization of a pre-stiffened aircraft bulkhead. Struct Multidiscip Optim 60:1667–1685. https://doi.org/10.1007/s00158-019-02284-w
Wong J, Ryan L, Kim IY (2018) Design optimization of aircraft landing gear assembly under dynamic loading. Struct Multidiscip Optim 57:1357–1375. https://doi.org/10.1007/s00158-017-1817-y
Yoon GH, Park YK, Kim YY (2007) Element stacking method for topology optimization with material-dependent boundary and loading conditions. J Mech Mater Struct 2:883–895. https://doi.org/10.2140/jomms.2007.2.883
Zhou M, Rozvany GIN (1991) The COC algorithm, Part II: Topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336. https://doi.org/10.1016/0045-7825(91)90046-9
Zhu JH, Zhang WH (2010) Integrated layout design of supports and structures. Comput Methods Appl Mech Eng 199:557–569. https://doi.org/10.1016/j.cma.2009.10.011
Zhu J-H, Hou J, Zhang W-H, Li Y (2014) Structural topology optimization with constraints on multi-fastener joint loads. Struct Multidiscip Optim 50:561–571. https://doi.org/10.1007/s00158-014-1071-5
Zhu J-H, Li Y, Zhang W-H, Hou J (2016a) Shape preserving design with structural topology optimization. Struct Multidiscip Optim 53:893–906. https://doi.org/10.1007/s00158-015-1364-3
Zhu J-H, Zhang W-H, Xia L (2016b) Topology optimization in aircraft and aerospace structures design. Arch Comput Meth Eng 23:595–622. https://doi.org/10.1007/s11831-015-9151-2
Funding
This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Korea Institute of Carbon Convergence Technology (KCTECH).
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
Sufficient information for replicating results is provided throughout the manuscript. Of key importance is the inclusion of material properties for this application, which are provided in Table 1. Additional modeling details are provided in Appendix 1 and Appendix 2. Appropriate references are specified for aspects not immediately within the scope of this paper (e.g., sensitivity analysis for the element stacking method).
Additional information
Responsible Editor: Ren-Jye Yang
Replication of results
Sufficient information for replicating results is provided throughout the manuscript. Of key importance is the inclusion of material properties for this application, which are provided in Table 1. Additional modeling details are provided in Appendix 1 and Appendix 2. Appropriate references are specified for aspects not immediately within the scope of this paper (e.g., sensitivity analysis for the element stacking method).
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix 1. Seat leg finite element model
Finite element model for the aircraft seat leg study. Note the MMTO design space features a 3D mesh discretization. In addition to various optimization-based benefits discussed in Section 3.1, a 3D discretization was implemented here since the seat leg structure does not represent not a plane stress or plane strain condition
Loadcases (LC) for the aircraft seat leg study. These loadcases are linear static simplifications of the certification loads outlined in SAE aerospace recommended practices (SAE 2015a; SAE 2015b), based on accelerations to a 77-kg anthropomorphic test device (ATD). Loads are applied directly to ATD body blocks connected to the seat structure using rigid (RBE2) and load distribution elements (RBE3). a LC 1.1 ultimate load, forward; b LC 1.2 ultimate load, side (left); c LC 1.3 ultimate load, side (right); d LC 1.4 ultimate load, up; e LC 1.5 ultimate load, down; f LC 1. 6 ultimate load, aft; g LC 2.1 impact load, forward (left); h LC 2.2 impact load, forward (right); i LC 2.3 impact load, down
Appendix 2. Seatback finite element model
Finite element model for the aircraft seatback study. This design space is complimentary to the aircraft seat leg/lower assembly in Appendix 1. Like the seat leg study, the MMTO design space for the seatback features a 3D mesh discretization
Loadcases (LC) for the aircraft seatback study. These loadcases are linear static simplifications of seat secondary structure abuse loads outlined in SAE aerospace recommended practices (SAE 2018). Loads are applied directly to the seatback design space or surrounding non-designable features (e.g., armrests). a LC 1.1 abuse load, backward; b LC 1.2 abuse load, forward; c LC 1.3 abuse load, twist; d LC 1.4 abuse load, armrest (down); e LC 1.5 abuse load, armrest (lateral); f LC 2.1 distributed load, seatback
Rights and permissions
About this article
Cite this article
Roper, S.W.K., Lee, H., Huh, M. et al. Simultaneous isotropic and anisotropic multi-material topology optimization for conceptual-level design of aerospace components. Struct Multidisc Optim 64, 441–456 (2021). https://doi.org/10.1007/s00158-021-02893-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-021-02893-4