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Mixed reliability-oriented topology optimization for thermo-mechanical structures with multi-source uncertainties

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Abstract

With the rapid development of topology optimization methodology in engineering application, how to deal with the multi-source uncertainties incurs more and more attention. In this study, an efficient single-loop method is proposed for reliability-based topology optimization (RBTO) of coupled thermo-mechanical continuum structure under multi-source uncertainties. To this end, a novel coupled thermo-mechanical RBTO model composed of triple-nested loops is first constructed based on fuzzy and probability theories, which aims to deal with the multi-source uncertainty factors, such as temperature rise fluctuation, thermal load variation, material property uncertainty, and manufacture tolerance. Second, a new mixed RBTO approach with single-loop is adopted to eliminate the nested triple loops, which aims to promote computational efficiency. Finally, the effectiveness and high performance of the proposed method are validated through a cantilever beam, clamped beam, and three-dimensional structure.

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References

  1. Cui M, Luo C, Li G, Pan M (2021) The parameterized level set method for structural topology optimization with shape sensitivity constraint factor. Eng Comput 37(2):855–872

    Google Scholar 

  2. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224

    MathSciNet  MATH  Google Scholar 

  3. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120–127

    Google Scholar 

  4. Liu Y, Yang C, Wei P, Zhou PZ, Du JB (2021) An ODE-driven level-set density method for topology optimization. Comput Methods Appl Mech Eng 387:114159

    MathSciNet  MATH  Google Scholar 

  5. Huang X, Xie Y (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401

    MathSciNet  MATH  Google Scholar 

  6. Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246

    MathSciNet  MATH  Google Scholar 

  7. Guo X, Zhang WS, Zhong WL (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(8):081001

    Google Scholar 

  8. Liu C, Du Z, Zhu Y, Zhang W, Zhang X, Guo X (2020) Optimal design of shell-graded-infill structures by a hybrid MMC-MMV approach. Comput Methods Appl Mech Eng 369:113187

    MathSciNet  MATH  Google Scholar 

  9. Savsani V, Dave P, Raja BD, Patel V (2021) Topology optimization of an offshore jacket structure considering aerodynamic, hydrodynamic and structural forces. Eng Comput 37(4):2911–2930

    Google Scholar 

  10. Rodrigues H, Fernandes P (1995) A material based model for topology optimization of thermoelastic structures. Int J Numer Methods Eng 38(12):1951–1965

    MathSciNet  MATH  Google Scholar 

  11. Deng S, Suresh K (2017) Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set. Struct Multidiscip Optim 56(6):1413–1427

    MathSciNet  Google Scholar 

  12. Gao T, Zhang W (2010) Topology optimization involving thermo-elastic stress loads. Struct Multidiscip Optim 42(5):725–738

    MathSciNet  MATH  Google Scholar 

  13. Meng Q, Xu B, Wang C, Zhao L (2021) Thermo-elastic topology optimization with stress and temperature constraints. Int J Numer Methods Eng 122(12):2919–2944

    MathSciNet  Google Scholar 

  14. Zhu J, Li Y, Wang F, Zhang W (2020) Shape preserving design of thermo-elastic structures considering geometrical nonlinearity. Struct Multidiscip Optim 61(5):1787–1804

    MathSciNet  Google Scholar 

  15. 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(3):417–429

    MathSciNet  Google Scholar 

  16. Xu Z, Zhang W, Gao T, Zhu J (2020) A B-spline multi-parameterization method for multi-material topology optimization of thermoelastic structures. Struct Multidiscip Optim 61(3):923–942

    MathSciNet  Google Scholar 

  17. Deng S, Suresh K (2017) Topology optimization under thermo-elastic buckling. Struct Multidiscip Optim 55(5):1759–1772

    MathSciNet  Google Scholar 

  18. Li Q, Grant P, Steven Y, Xie M (2001) Thermoelastic topology optimization for problems with varying temperature fields. J Therm Stresses 24(4):347–366

    Google Scholar 

  19. 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(3):2329–2344

    Google Scholar 

  20. Maute K, Frangopol DM (2003) Reliability-based design of MEMS mechanisms by topology optimization. Comput Struct 81(8–11):813–824

    Google Scholar 

  21. Wang L, Ni B, Wang X, Li Z (2021) Reliability-based topology optimization for heterogeneous composite structures under interval and convex mixed uncertainties. Appl Math Model 99:628–652

    MathSciNet  MATH  Google Scholar 

  22. Zhang JH, Xiao M, Gao L (2021) A new local update-based method for reliability-based design optimization. Eng Comput 37:3591–3603

    Google Scholar 

  23. Ni BY, Elishakoff I, Jiang C, Fu CM, Han X (2016) Generalization of the super ellipsoid concept and its application in mechanics. Appl Math Model 40(21–22):9427–9444

    MathSciNet  MATH  Google Scholar 

  24. Wang L, Liang JX, Wu D (2018) A non-probabilistic reliability-based topology optimization (NRBTO) method of continuum structures with convex uncertainties. Struct Multidiscip Optim 58:2601–2620

    MathSciNet  Google Scholar 

  25. Tang Z, Lu Z, Hu J (2014) An efficient approach for design optimization of structures involving fuzzy variables. Fuzzy Sets Syst 255:52–73

    MathSciNet  Google Scholar 

  26. Yin H, Yu DJ, Yin SW, Xia BZ (2018) Possibility-based robust design optimization for the structural-acoustic system with fuzzy parameters. Mech Syst Signal Process 102:329–345

    Google Scholar 

  27. Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscip Optim 26(5):295–307

    Google Scholar 

  28. Wang L, Liu D, Yang Y, Hu J (2019) Novel methodology of non-probabilistic reliability-based topology optimization (NRBTO) for multi-material layout design via interval and convex mixed uncertainties. Comput Methods Appl Mech Eng 346:550–573

    MathSciNet  MATH  Google Scholar 

  29. Wang L, Li ZS, Ni BW, Gu KX (2021) Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level-set method and interval mathematics. Comput Methods Appl Mech Eng 373:113477

    MathSciNet  MATH  Google Scholar 

  30. Yin H, Yu D, Xia B (2018) Reliability-based topology optimization for structures using fuzzy set model. Comput Methods Appl Mech Eng 333:197–217

    MathSciNet  MATH  Google Scholar 

  31. Luo YJ, Li A, Kang Z (2011) Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and non-probabilistic uncertainties. Eng Struct 33(7):2110–2119

    Google Scholar 

  32. Meng Z, Pang YS, Pu YX, 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

    MathSciNet  MATH  Google Scholar 

  33. Xia Q, Shi T, Xia L (2018) Topology optimization for heat conduction by combining level set method and BESO method. Int J Heat Mass Transf 127:200–209

    Google Scholar 

  34. Li Y, Wei P, Ma H (2017) Integrated optimization of heat-transfer systems consisting of discrete thermal conductors and solid material. Int J Heat Mass Transf 113:1059–1069

    Google Scholar 

  35. Zhu X, Zhao C, Wang X, Zhou Y, Hu P, Ma ZD (2019) Temperature-constrained topology optimization of thermo-mechanical coupled problems. Eng Optim 51(10):1687–1709

    MathSciNet  Google Scholar 

  36. Liu X, Wang C, Zhou Y (2014) Topology optimization of thermoelastic structures using the guide-weight method. Sci China Technol Sci 57(5):968–979

    Google Scholar 

  37. Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des 126:403–411

    Google Scholar 

  38. Jiang C, Qiu HB, Gao L, Cai XW, Li PG (2017) An adaptive hybrid single-loop method for reliability-based design optimization using iterative control strategy. Struct Multidiscip Optim 56(6):1271–1286

    MathSciNet  Google Scholar 

  39. Moens D, Vandepitte D (2005) A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Methods Appl Mech Eng 194(12):1527–1555

    MATH  Google Scholar 

  40. Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidiscip Optim 41(2):277–294

    MathSciNet  MATH  Google Scholar 

  41. Meng Z, Zhou H (2018) New target performance approach for a super parametric convex model of non-probabilistic reliability-based design optimization. Comput Methods Appl Mech Eng 339(9):644–662

    MathSciNet  MATH  Google Scholar 

  42. Jung Y, Cho H, Lee I (2020) Intelligent initial point selection for MPP search in reliability-based design optimization. Struct Multidiscip Optim 62(4):1809–1820

    MathSciNet  Google Scholar 

  43. Zuo ZH, Xie YM (2014) Evolutionary topology optimization of continuum structures with a global displacement control. Comput Aided Des 56:58–67

    Google Scholar 

  44. Sigmund O, Maute K (2012) Sensitivity filtering from a continuum mechanics perspective. Struct Multidiscip Optim 46(4):471–475

    MathSciNet  MATH  Google Scholar 

  45. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The support of the National Natural Science Foundation of China (Grant no. 11972143), the Fundamental Research Funds for the Central Universities of China (Grant nos. JZ2020HGPA0112, JZ2020HGTA0080), State Key Laboratory of Reliability and Intelligence of Electrical Equipment (Grant no. EERI_KF2020002) and the Natural Science Foundation of Anhui Province (Grant no. 2008085QA21) are much appreciated.

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Authors and Affiliations

  1. Institute of Applied Mechanics, School of Civil Engineering, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Zeng Meng, Liangbing Guo & Xuan Wang

  2. Department of Mechanical Engineering, State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin, 300401, People’s Republic of China

    Zeng Meng

  3. Department of Automotive Engineering, Uludağ University, Görükle, Bursa, Turkey

    Ali Rıza Yıldız

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  1. Zeng Meng
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  2. Liangbing Guo
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  4. Xuan Wang
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Correspondence to Xuan Wang.

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Meng, Z., Guo, L., Yıldız, A.R. et al. Mixed reliability-oriented topology optimization for thermo-mechanical structures with multi-source uncertainties. Engineering with Computers 38, 5489–5505 (2022). https://doi.org/10.1007/s00366-022-01662-1

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