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An efficient reliability method for composite laminates with high-dimensional uncertainty variables

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Abstract

This paper develops an efficient reliability analysis method for composite structures with high-dimensional uncertain variables. The concept and mathematical definition of the approximate design point (ADP) and the approximate important direction (AID) are introduced. A fast calculation ADP/AID formula is proposed. A numerical line sampling (LS) strategy is devised, which is further combined with ADP/AID to form a novel reliability method, named AID-LS. An equivalent criterion is introduced to address the problems with the non-normal random variables. A stochastic mechanical model of composite structures with geometrical nonlinearity is established based on first-order shear deformation theory and implemented with finite element analysis (FEA). Numerical examples are given to demonstrate the validity of the proposed method. The results show that the proposed method can significantly reduce the number of FEA samples in the reliability analysis of composite structures.

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References

  1. Shchurova, C.I.: A methodology to design a 3D graphic editor for micro-modeling of fiber-reinforced composite parts. Adv. Eng. Softw. 90(C), 76–82 (2015)

    Article  Google Scholar 

  2. Mesogitis, T.S., Skordos, A.A., Long, A.C.: Uncertainty in the manufacturing of fibrous thermosetting composites: a review. Compos. Part A Appl. Sci. Manuf. 57, 67–75 (2014)

    Article  Google Scholar 

  3. Aoues, Younes, Chateauneuf, Alaa, Lemosse, Didier, El-Hami, Abdelkhalak: Optimal design under uncertainty of reinforced concrete structures using system reliability approach. Int. J. Uncertain. Quantif. 3(6), 487–498 (2013)

    Article  MathSciNet  Google Scholar 

  4. Lopez, R.H., Lemosse, D., Cursi, J.E.S.D., et al.: An approach for the reliability based design optimization of laminated composites. Eng. Optim. 43(10), 1079–1094 (2011)

    Article  MathSciNet  Google Scholar 

  5. Sriramula, S., Chryssanthopoulos, M.K.: Quantification of uncertainty modelling in stochastic analysis of FRP composites. Compos. Part A Appl. Sci. Manuf. 40(11), 1673–1684 (2009)

    Article  Google Scholar 

  6. Zhou, X.Y., Gosling, P.D., Ullah, Z.: Exploiting the benefits of multi-scale analysis in reliability analysis for composite structures. Compos. Struct. 155, 197–212 (2016)

    Article  Google Scholar 

  7. Potter, K.D., Campbell, M., Langer, C., Wisnom, M.R.: The generation of geometrical deformations due to tool/part interaction in the manufacture of composite components. Compos. Part A Appl. Sci. Manuf. 36(2), 301 (2005)

    Article  Google Scholar 

  8. Potter, K., Khan, B., Wisnom, M., Bell, T., Stevens, J.: Variability fibre waviness and misalignment in the determination of the properties of composite materials and structures. Compos. Part A 39(9), 1343 (2008)

    Article  Google Scholar 

  9. Chamis, S.: Probabilistic evaluation of fuselage-type composite structures. Probab. Eng. Mech. 14, 179 (1999)

    Article  Google Scholar 

  10. Vinckenroy, G.V., de Wilde, W.P.: The use of Monte Carlo techniques in statistical finite element methods for the determination of the structural behaviour of composite materials structural components. Compos. Struct. 32, 247 (1995)

    Article  Google Scholar 

  11. Ostoja-Starzewski, M., Sheng, P.Y., Jasiuk, I.: Influence of random geometry on effective properties and damage formation in composite materials. J. Eng. Mater. Technol. 116(3), 384–391 (1994)

    Article  Google Scholar 

  12. Low, B.K.: FORM, SORM, and spatial modeling in geotechnical engineering. Struct. Saf. 49, 56–64 (2014)

    Article  Google Scholar 

  13. Lopes, P.A.M., Gomes, H.M., Awruch, A.M.: Reliability analysis of laminated composite structures using finite elements and neural networks. Compos. Struct. 92(7), 1603–1613 (2010)

    Article  Google Scholar 

  14. Zhao, Libin, Shan, Meijuan, Liu, Fengrui, Zhang, Jianyu: A probabilistic model for strength analysis of composite double-lap single-bolt joints. Compos. Struct. 161, 419–427 (2017)

    Article  Google Scholar 

  15. Guilleminot, J., Soize, C., Kondo, B.D.C.: Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: experimental identification and numerical aspects. Mech. Mater. 41(12), 1309–1322 (2009)

    Article  Google Scholar 

  16. SchuLler, G.I., Pradlwarter, H.J.: Benchmark study on reliability estimation in higher dimensions of structural systems: an overview. Struct. Saf. 29(3), 167–182 (2007)

    Article  Google Scholar 

  17. Mesogitis, T.S., Skordos, A.A., Long, A.C.: Uncertainty in the manufacturing of fibrous thermosetting composites: a review. Compos. Part A Appl. Sci. Manuf. 57, 67–75 (2014)

    Article  Google Scholar 

  18. Chiachio, M., Chiachio, J., Rus, G.: Reliability in composites: a selective review and survey of current development. Compos. Part B Eng. 43(3), 902–913 (2012)

    Article  Google Scholar 

  19. Sokolowski, D., Kamiski, M.: Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects. Acta Mech. 229(9), 3727–3765 (2018)

    Article  MathSciNet  Google Scholar 

  20. Deng, Zhongmin, Guo, Zhaopu: Interval identification of structural parameters using interval overlap ratio and Monte Carlo simulation. Adv. Eng. Softw. 121, 120–130 (2018)

    Article  Google Scholar 

  21. Dubourg, V., Sudret, B.: Meta-model-based importance sampling for reliability sensitivity analysis. Struct. Saf. 49, 27–36 (2014)

    Article  Google Scholar 

  22. Shufang, S.O.N.G.: Structural reliability sensitivity analysis method based on Markov chain monte Carlo subset simulation. J. Mech. Eng. 45(4), 33–38 (2009)

    Article  Google Scholar 

  23. Sadik, L., Omairey, Peter, et al.: Influence of micro-scale uncertainties on the reliability of fibre-matrix composites. Compos. Struct. 203, 204–216 (2018)

    Article  Google Scholar 

  24. Thapa, M., Mulani, S.B., Walters, R.W.: Stochastic multi-scale modeling of carbon fiber reinforced composites with polynomial chaos. Compos. Struct. 213, 82–97 (2019)

    Article  Google Scholar 

  25. Zhao, Z., Duan, X., Wang, Z.: A novel global method for reliability analysis with Kriging. Int. J. Uncertain. Quantif. 6(5), 445–466 (2016)

    Article  MathSciNet  Google Scholar 

  26. Haeri, A., Fadaee, M.J.: Efficient reliability analysis of laminated composites using advanced Kriging surrogate model. Compos. Struct. 149, 26–32 (2016)

    Article  Google Scholar 

  27. Pradlwarter, H.J., SchuLler, G.I., Koutsourelakis, P.S., et al.: Application of line sampling simulation method to reliability benchmark problems. Struct. Saf. 29(3), 208–221 (2007)

    Article  Google Scholar 

  28. Depina, I., Le, T., Fenton, G., et al.: Reliability analysis with metamodel line sampling. Struct. Saf 60, 1–15 (2016)

    Article  Google Scholar 

  29. Dubourg, V., Sudret, B., Deheeger, F.: Metamodel-based importance sampling for structural reliability analysis. Probab. Eng. Mech. 33, 47–57 (2013)

    Article  Google Scholar 

  30. Schueller, G.I., Pradlwarter, H.J., Koutsourelakis, P.S.: A critical appraisal of reliability estimation procedures for high dimensions. Probab. Eng. Mech. 19(4), 463–474 (2004)

    Article  Google Scholar 

  31. Liu, Pei-Ling, Der Kiureghian, Armen: Optimization algorithms for structural reliability. Struct. Saf. 9(3), 161–177 (1991)

    Article  Google Scholar 

  32. Hasofer, A.M., Lind, N.C.: Exact and invariant second moment code format. J. Eng. Mech. Div. 100(EM1), 111–121 (1974)

    Article  Google Scholar 

  33. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells, second edn. CRC Press LLC, Florida (2004)

    MATH  Google Scholar 

  34. Kaw, A.K.: Mechanics of Composites Materials, 2nd edn, p. 457p. CRC Taylor and Francis Group, Boca Raton (2006)

    Google Scholar 

  35. Soden, P.D., Hinton, M.J., Kaddour, A.S.: Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates[J]. Compos. Sci. Technol. 58(7), 1011–1022 (1998)

    Article  Google Scholar 

  36. Almeida, F.S., Awruch, A.M.: Design optimization of composite laminated structures using genetic algorithms and finite element analysis. Compos. Struct. 88(3), 443–454 (2009)

    Article  Google Scholar 

  37. Zhang, J., Liu, F., Zhao, L.: A novel characteristic curve for failure prediction of multi-bolt composite joints. Compos. Struct. 108, 129–136 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (11772018).

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  1. School of Astronautics, Beihang University, 37 Xueyuan Road, Haidian, 100191, Beijing, China

    Benke Shi & Zhongmin Deng

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  1. Benke Shi
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  2. Zhongmin Deng
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Correspondence to Zhongmin Deng.

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Shi, B., Deng, Z. An efficient reliability method for composite laminates with high-dimensional uncertainty variables. Acta Mech 232, 3509–3527 (2021). https://doi.org/10.1007/s00707-021-03008-2

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  • DOI: https://doi.org/10.1007/s00707-021-03008-2

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