Advertisement

Computational Mechanics

, Volume 64, Issue 3, pp 829–845 | Cite as

Non-probabilistic interval model-based system reliability assessment for composite laminates

  • Yujia Ma
  • Xiaojun WangEmail author
  • Lei Wang
  • Qiang Ren
Original Paper

Abstract

Composite materials have been widely applied to engineering fields by virtue of its superior mechanical properties. Therefore, the problem of composite laminates safety assessment has also been discussed. This paper develops the non-probabilistic interval model-based system reliability evaluation strategy based on the last ply failure criterion (LPF), which improves the rough reliability solution based on first ply failure criterion (FPF) for composite laminates, and overcomes the shortage of traditional LPF method based on the probabilistic reliability theory. Obviously, the probability density function (PDF) is difficult to be calculated due to the experimental cost and time. In the proposed method, considering the fiber failure and matrix failure (limit state functions) for composite laminates, the failure possibility of every single ply is evaluated by the non-probabilistic interval model method. Subsequently, the progressive damage method is combined with the branch-bound method (B&B) to search the significant failure paths of composite laminates, and then the whole system analysis process is completed based on LPF criterion. Finally, the system reliability model of composite laminates can be constructed by introducing non-probabilistic interval model. Furthermore, the correlation description for the non-probabilistic interval model among is applied to the failure modes, and the Cornell first-order bound theory is applied to achieve the system reliability of composite laminates. After the detailed analysis steps, the numerical example of laminated plate is presented to demonstrate the validity and reasonability of the developed methodology.

Keywords

Non-probabilistic interval model System reliability Last ply failure criterion Composite laminates Progressive damage analysis Failure sequence 

Notes

Acknowledgements

The authors would like to thank the National Key Research and Development Program (No. 2016YFB0200700), the National Nature Science Foundation of the P.R. China (No. 11872089, No. 11572024, No. 11432002), Defense Industrial Technology Development Programs (No. JCKY2016601B001, No. JCKY2016204B101, No. JCKY2017601B001), and the postgraduate innovation practice fund of Beihang University (No. YCSJ-01-2018-07) for the financial supports. Besides, the authors wish to express their many thanks to the reviewers for their useful and constructive comments.

References

  1. 1.
    Shaw A et al (2010) A critical reliability evaluation of fibre reinforced composite materials based on probabilistic micro and macro-mechanical analysis. Compos B Eng 41(6):446–453CrossRefGoogle Scholar
  2. 2.
    XiangYang WANGC, Jianqiao C, Cheng L (2004) Optimum design of the reliability for composite laminates based on genetic algorithm. J Huazhong Univ Sci Technol 32:10–12Google Scholar
  3. 3.
    Gomes HM, Awruch AM, Lopes PAM (2011) Reliability based optimization of laminated composite structures using genetic algorithms and Artificial Neural Networks. Struct Saf 33(3):186–195CrossRefGoogle Scholar
  4. 4.
    Soremekun G et al (2013) Improving genetic algorithm efficiency and reliability in the design and optimization of composite structures. In: Symposium on multidisciplinary analysis and optimizationGoogle Scholar
  5. 5.
    Liu PF, Zheng JY (2010) Strength reliability analysis of aluminium–carbon fiber/epoxy composite laminates. J Loss Prev Process Ind 23(3):421–427CrossRefGoogle Scholar
  6. 6.
    Yan FF, Deng KX (2014) Statistical analysis on safety factor of notched composite laminates. J Mech Strength 01:23–34Google Scholar
  7. 7.
    Nicholas PE, Padmanaban KP, Sofia AS (2012) Optimization of dispersed laminated composite plate for maximum safety factor using genetic algorithm and various failure criteria. Procedia Eng 38:1209–1217CrossRefGoogle Scholar
  8. 8.
    Zhu TL (1993) A reliability-based safety factor for aircraft composite structures. Comput Struct 48(4):745–748CrossRefGoogle Scholar
  9. 9.
    Yang L, Ma Z, Fu G (1991) Safety factor and reliability for composite laminates. Acta Aeronaut Et Astronaut Sin 12:B631–B634Google Scholar
  10. 10.
    Lin SC, Kam TY (2000) Probabilistic failure analysis of transversely loaded laminated composite plates using first-order second moment method. J Eng Mech 126(8):812–820CrossRefGoogle Scholar
  11. 11.
    Jeong HK, Shenoi RA (2000) Probabilistic strength analysis of rectangular FRP plates using Monte Carlo simulation. Comput Struct 76(1–3):219–235CrossRefGoogle Scholar
  12. 12.
    Venugopal SM (2003) Stochastic mechanics and reliability of composite laminates based on experimental investigation and stochastic FEM. Mech Ind Eng. Concordia UniversityGoogle Scholar
  13. 13.
    Cederbaum G, Elishakoff I, Librescu L (1989) Reliability of laminated plates via the first-order second-moment method. Compos Struct 15(2):161–167CrossRefGoogle Scholar
  14. 14.
    Liu WK et al (2016) Three reliability methods for fatigue crack growth. Eng Fract Mech 53(5):733–752CrossRefGoogle Scholar
  15. 15.
    Bostanabad R et al (2018) Uncertainty quantification in multiscale simulation of woven fiber composites. Comput Methods Appl Mech Eng 338:S0045782518302032MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mehrez L et al (2017) A PCE-based multiscale framework for the characterization of uncertainties in complex systems. Comput Mech 61(43–44):1–18MathSciNetGoogle Scholar
  17. 17.
    Liu W (1986) Probabilistic finite elements for nonlinear structural dynamics. Comput Methods Appl Mech Eng 56(1):61–81zbMATHCrossRefGoogle Scholar
  18. 18.
    Liu WK, Belytschko T, Mani A (2010) Random field finite elements. Int J Numer Methods Eng 23(10):1831–1845MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Bostanabad R et al (2017) Leveraging the nugget parameter for efficient Gaussian process modeling. Int J Numer Methods Eng 114:501–516MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ben-Haim Y et al (1990) Convex models of uncertainty in applied mechanics. Elsevier, AmsterdamzbMATHGoogle Scholar
  21. 21.
    Elishakoff I, Ohsaki M (2010) Optimization and anti-optimization of structures under uncertainty. Eng Struct 33(9):2724–2725zbMATHGoogle Scholar
  22. 22.
    Ben-Haim Y (1995) A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Struct Saf 17(2):91–109CrossRefGoogle Scholar
  23. 23.
    Ben-Haim Y (1994) A non-probabilistic concept of reliability. Struct Saf 14(4):227–245CrossRefGoogle Scholar
  24. 24.
    Elishakoff I, Li YW, Jr JHS (1994) A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures. Comput Methods Appl Mech Eng 111(1–2):155–167zbMATHCrossRefGoogle Scholar
  25. 25.
    Wang X, Chen J (2006) Probability and non-probabilistic model of laminated composite plate structures. J Huazhong Univ Sci Technol 12:14–23Google Scholar
  26. 26.
    Mu HS, Gao L (2014) Finite element study of settlement of cement mixing composite foundation and non-probabilistic reliability analysis. Appl Mech Mater 638–640:675–679CrossRefGoogle Scholar
  27. 27.
    Kang Z, Luo Y (2009) Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Methods Appl Mech Eng 198(41):3228–3238MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Luo Y, 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):2110–2119CrossRefGoogle Scholar
  29. 29.
    Qiu Z, Elishakoff I (1998) Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis. Comput Methods Appl Mech Eng 152(3):361–372zbMATHCrossRefGoogle Scholar
  30. 30.
    Qiu Z, Yang D, Elishakoff I (2008) Probabilistic interval reliability of structural systems. Int J Solids Struct 45(10):2850–2860zbMATHCrossRefGoogle Scholar
  31. 31.
    Qiu Z (2003) Comparison of static response of structures using convex models and interval analysis method. Int J Numer Meth Eng 56(12):1735–1753zbMATHCrossRefGoogle Scholar
  32. 32.
    Jiang C, Han X, Liu GR (2007) Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput Methods Appl Mech Eng 196(49–52):4791–4800zbMATHCrossRefGoogle Scholar
  33. 33.
    Peng WJ, Huang XX, Ge R (2013) The analysis and optimization of the reliability of laminates based on probabilistic and non-probabilistic hybrid model. Adv Mater Res 629:752–756CrossRefGoogle Scholar
  34. 34.
    Yangjun KZL et al (2006) On structural optimization for non-probabilistic reliability based on convex models. Chin J Theor Appl Mech 38(6):807–815Google Scholar
  35. 35.
    Lin SC, Kam TY (2007) Reliability analysis of composite laminates subject to buckling and first-ply failure. Comput Aided Des Compos Technol V 35(13):84–96Google Scholar
  36. 36.
    Lopes CS, Gürdal Z, Camanho PP (2008) Variable-stiffness composite panels: buckling and first-ply failure improvements over straight-fibre laminates. Comput Struct 86(9):897–907CrossRefGoogle Scholar
  37. 37.
    Shao S, Miki M, Murotsu Y (2015) Optimum fiber orientation angle of multiaxially laminated compositesbased on reliability. AIAA J 31(5):919–920CrossRefGoogle Scholar
  38. 38.
    Soliman HE, Kapania RK (2015) Probability of failure of composite cylinders subjected to axisymmetric loading. AIAA J 43(6):1342–1348CrossRefGoogle Scholar
  39. 39.
    Yang L (1988) Reliability of composite laminates. Mech Based Des Struct Mach 16(4):523–536CrossRefGoogle Scholar
  40. 40.
    Wetherhold RC, Thomas DJ (1991) Reliability analysis of composite laminates with load sharing. J Compos Mater 25(11):1459–1475CrossRefGoogle Scholar
  41. 41.
    Zhao H, Gao Z (1995) Reliability analysis of composite laminates by enumerating significant failure modes. J Reinf Plast Compos 14(14):427–444CrossRefGoogle Scholar
  42. 42.
    Wang X, Z Li (2009) Reliability-based robust of symmetric laminated plates subject to last-ply failure. In: International conference on industrial mechatronics and automationGoogle Scholar
  43. 43.
    Mahadevan S, Raghothamachar P (2000) Adaptive simulation for system reliability analysis of large structures. Comput Struct 77(6):725–734CrossRefGoogle Scholar
  44. 44.
    Mahadevan S, Liu X, Xiao Q (1997) A probabilistic progressive failure model of composite laminates. J Reinf Plast Compos 16(11):1020–1038CrossRefGoogle Scholar
  45. 45.
    Zhang X, X Chang (2008) A probabilistic progressive failure model for reliability of composite laminates. In: 2008 National academic symposium for Ph.D. candidates and tri-university workshop on aero-structural mechanics & aerospace engineeringGoogle Scholar
  46. 46.
    Tan SC, Perez J (1993) Progressive failure of laminated composites with a hole under compressive loading. J Reinf Plast Compos 12(10):1043–1057CrossRefGoogle Scholar
  47. 47.
    Morrison DR et al (2016) Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning. Discrete Optim 19:79–102MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Ditlevsen O (1979) Narrow reliability bounds for structural systems. Mech Based Des Struct Mach 7(4):453–472CrossRefGoogle Scholar
  49. 49.
    Cornell CA (1967) Bounds on the reliability of structural systems. Cadernos De Saúde Pública 8(3):254–261Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Solid Mechanics, School of Aeronautical Science and EngineeringBeihang UniversityBeijingChina

Personalised recommendations