Abstract
This study investigates a non-probabilistic thermo-elastic reliability-based topology optimization (NTE-RBTO) scheme for the lightweight design of composite laminates under thermo-elastic loads with unknown-but-bounded (UBB) parameters. The equivalent constitutive relation of composite laminates is first introduced, and the deterministic topology optimization formulation of composite laminates is derived. In view of the inevitability of multi-source uncertainties during the whole design optimization procedure, the interval model and interval parametric vertex theorem are proposed for the acquisition of the reasonable characterization of uncertain responses in every iterative layout configuration. For reasons of structural safety, an improved non-probabilistic reliability index, the optimization feature distance is adopted, and its design sensitivity with respect to each element pseudo-density under thermal–mechanical coupling loads is calculated. GCMMA, the globally convergent version of MMA (method of moving asymptotes), is employed as the optimization problem solver. The effectiveness and rationality of the proposed method are demonstrated by several numerical examples, eventually.
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Data availability statement
In this work, the basic codes for the topology optimization, the uncertainty response analysis, the reliability assessment, and the numerical results of composite structures presented are available from the author on reasonable request.
References
Renton W, Baron W, Batzer R, Olcott D, Roeseler W, Velicki A (2004) Future of flight vehicle structures (2000 to 2023). J Aircraft 41:986–998
Forster E, Clay S, Holzwarth R, Paul D Flight Vehicle Composite Structures, In: The 26th Congress of ICAS and 8th AIAA ATIO
Michell AGM (1904) The limits of economy of materials in frame structures. Phil Mag 6:589–597
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224
Rozvany GIN (2001) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Multidisc Optim. https://doi.org/10.1007/s001580050174
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654
Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4:250–252
Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33:401–424
Eom YS, Yoo KS, Park JY, Han SY (2011) Reliability-based topology optimization using a standard response surface method for three-dimensional structures. Struct Multidiscip Optim 43:287–295
Dijk NPV, Maute K, Langelaar M, Keulen FV (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48:437–472
Mei YL, Wang XM (2004) A level set method for structural topology optimization and its applications. Comput Methods Appl Mech Eng 35:415–441
Zhang WS, Li D, Yuan J, Song JF, Guo X (2017) A new three-dimensional topology optimization method based on moving morphable components (MMCs). Comput Mech 59:1–19
Zhang WS, Zhou JH, Zhu YC, Guo X (2017) Structural complexity control in topology optimization via moving morphable component (MMC) approach. Struct Multidiscip Optim 56:535–552
Bourdin B, Chambolle A (2003) Design-dependent loads in topology optimization. Esaim Control Optim Calc Var 9:19–48
Yin L, Ananthasuresh G (2001) Topology optimization of compliant mechanisms with multiple material using peak function material interpolation scheme. Struct Multidiscip Optim 23:49–62
Ren L, Yang R, Mi D, Guo D (2005) Topology optimization design for micro compliant mechanism with two materials, in: Proc. ICMIT 2005: Control Systems and Robotics, 60424A-60424A
Xu ZS, Huang QB, Zhao Z (2011) Topology optimization of composite material plate with respect to sound radiation. Eng Anal Boundary Elem 35:61–67
Li D, Zhang X, Guan Y, Zhang H (2010) Topology optimization of compliant mechanisms with anisotropic composite materials, 2010 IEEE International Conference on Mechatronics and Automation, ICMA 2010
Wang L, Wang XJ, Li YL, Hu JX (2019) A non-probabilistic time-variant reliable control method for structural vibration suppression problems with interval uncertainties. Mech Syst Signal Process 115:301–322
Wang L, Liu YR (2020) A novel method of distributed dynamic load identification for aircraft structure considering multi-source uncertainties. Struct Multidiscip Optim 61:1929–1952
Wu D, Pan B, Gao Z (2012) On the experimental simulation of ultra-high temperature, high heat flux and nonlinear aerodynamic heating environment and thermo-mechanical testing technique. J Exp Mech 27:255–271
Yu B, Kodur V (2014) Effect of high temperature on bond strength of near-surface mounted FRP reinforcement. Compos Struct 110:88–97
Zhang W, Yang J, Xu Y, Gao T (2014) Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization. Struct Multidiscip Optim 49:417–429
Kruijf N, Zhou S, Li Q, Mai YW (2007) Topological design of structures and composite materials with multiobjectives. Int J Solids Struct 44:7092–7109
Chen Y, Zhou S, Li Q (2010) Multiobjective topology optimization for finite periodic structures. Comput Struct 88:806–811
Wang XJ, Ren Q, Chen WP, Liu YS, Wang L, Ding XY (2019) Structural Design optimization based on the moving baseline strategy. Acta Mech Solida Sin. https://doi.org/10.1007/s10338-019-00144-0
Wang XJ, Shi QH, Fan WC, Wang RX, Wang L (2019) Comparison of the reliability-based and safety factor methods for structural design. Appl Math Model 72:68–84
Meng Z, Guo L, Wang X (2021) A general fidelity transformation framework for reliability-based design optimization with arbitrary precision. Struct Multidiscip Optim 65:14
Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscip Optim 26:295–307
Bae K, Wang S (2013) Reliability-based topology optimization In: Aiaa/issmo symposium on multidisciplinary analysis and optimization
Bobby S, Suksuwan A, Spence SMJ, Kareem A (2017) Reliability-based topology optimization of uncertain building systems subject to stochastic excitation. Struct Saf 66:1–16
Kim C, Wang S, Rae KR, Moon H, Choi KK (2006) Reliability-based topology optimization with uncertainties. J Mech Sci Technol 20:494–504
Jalalpour M, Guest JK, Igusa T (2013) Reliability-based topology optimization of trusses with stochastic stiffness. Struct Saf 43:41–49
Jung HS, Cho S (2004) Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties. Finite Elem Anal Des 41:311–331
Silva M, Tortorelli DA, Norato JA, Ha C, Bae HR (2010) Component and system reliability-based topology optimization using a single-loop method. Struct Multidiscip Optim 41:87–106
Ben-Haim Y, Elishakoff I (1995) Discussion on: a non-probabilistic concept of reliability. Struct Saf 17:195–199
Jiang C, Han X, Li D (2012) A new interval comparison relation and application in interval number programming for uncertain problems. Comput Mater Contin 27:275–303
Meng Z, Keshtegar B (2019) Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization. Comput Methods Appl Mech Eng 344:95–119
Kang Z, Luo YJ (2009) Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Methods Appl Mech Eng 198:3228–3238
Wang L, Liang JX, Zhang ZX, Yang YW (2019) Nonprobabilistic reliability oriented topological optimization for multi-material heat-transfer structures with interval uncertainties. Struct Multidiscip Optim 59:1599–1620
Meng Z, Pang Y, Pu Y, Wang X (2020) New hybrid reliability-based topology optimization method combining fuzzy and probabilistic models for handling epistemic and aleatory uncertainties. Comput Methods Appl Mech Eng 363:112886
Bendsøe BP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer Science and Business Media
Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12:555–573
Nguyen V, Strodiot JJ, Fleury C (1987) A mathematical convergence analysis of the convex linearization method for engineering design optimization. Eng Optim 11:195–216
Qiu ZP, Wang L (2016) The need for introduction of non-probabilistic interval conceptions into structural analysis and design. Sci China Phys Mech Astronomy 59:114632
Wang X, Qiu Z, Elishakoff I (2008) Non-probabilistic set-theoretic model for structural safety measure. Acta Mech 198:51–64
Wang L, Liu DL, Yang YW, Wang XJ, Qiu ZP (2017) A novel method of non-probabilistic reliability-based topology optimization corresponding to continuum structures with unknown but bounded uncertainties. Comput Methods Appl Mech Eng 326:573–595
Lam-Phat T, Ho-Huu V, Nguyen-Ngoc S, Nguyen-Hoai S, Nguyen-Thoi T (2021) Deterministic and reliability-based lightweight design of Timoshenko composite beams. Eng Comput 37:2329–2344
Meng Z, Wu Y, Wang X, Ren S, Yu B (2021) Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties. Int J Numer Meth Eng 122:2095–2111
Acknowledgements
This research is supported by the National Nature Science Foundation of China (Nos. 12072006, 11872089, 12072007, 12132001 and 52192632) and the Defense Industrial Technology Development Program (Nos. JCKY2019203A003, JCKY2019205A006 and JCKY2019209C004). In addition, the authors thank the reviewers for their valuable and constructive comments.
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Ni, B., Wang, X., Lv, T. et al. Non-probabilistic thermo-elastic reliability-based topology optimization (NTE-RBTO) of composite laminates with interval uncertainties. Engineering with Computers 38, 5713–5732 (2022). https://doi.org/10.1007/s00366-022-01761-z
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DOI: https://doi.org/10.1007/s00366-022-01761-z