Reliability Analysis of Composite-Nanofluid Tube Using Finite-Based Armijo Method
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
The reliable performance of composite tubes conveying nanofluid is an essential issue for robust design under dynamic loads. Further, the frequency failure mode of these structures is a considerable performance function to provide a balance between mass and stiffness of the structure. The ability of the first-order reliability method (FORM)-based finite-step adaptive length (FAL) is discussed for reliability analysis of composite tubes under frequency failure mode. The performances for efficiency and robustness to evaluate the failure probability FORM formulas are discussed. Therefore, the capability of FAL using the steepest descent sensitivity vector is compared with three FORM formulations that are extended by the steepest descent search direction for nanocomposite tubes conveying nanofluid. In this current work, the Navier scheme is employed for calculating the frequency failure mode. Furthermore, the robustness and efficiency related to the steepest descent FORM formulas of HL-RF, directional stability transformation method (DSTM), and finite-step length (FSL) are compared with FAL. Based on this discussion, FAL contains efficient formula in comparison with other FORM formulas. Moreover, it is found that FSL formulas as well as FAL formulas are more robust than HL-RF and DSTM. This structure’s failure probability rises as the fluid velocity and pipe diameter increase.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
List of available data, models, or code:
•
Data within tables.
•
Data within figures.
•
Iterative FORM algorithms utilizing steepest descent search direction of the finite-step length-based Armijo rule.
Acknowledgments
This research was supported by: University of Zabol (Iran) under Grant Nos. UOZ-GR-9618-1 and UOZ-GR-9719-1; University of Sistan and Baluchestan (Iran); CONSTRUCT–Instituto de I&D em Estruturas e Construções (FEUP, Portugal) that is funded by base funding—UIDB/04708/2020 and programmatic funding–UIDP/04708/2020 provided by national funds through the FCT/MCTES (PIDDAC) and Duy Tan University (Vietnam).
References
Al-Furjan, M. S. H., A. Farrokhian, B. Keshtegar, R. Kolahchi, and N.-T. Trung. 2021a. “Dynamic stability control of viscoelastic nanocomposite piezoelectric sandwich beams resting on Kerr foundation based on exponential piezoelasticity theory.” Eur. J. Mech. A Solids 86 (Mar): 104169. https://doi.org/10.1016/j.euromechsol.2020.104169.
Al-Furjan, M. S. H., A. Farrokhian, S. R. Mahmoud, and R. Kolahchi. 2021b. “Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact.” Thin-Walled Struct. 163 (Jun): 107706. https://doi.org/10.1016/j.tws.2021.107706.
Anish, W., J. Sunil, and S. K. Kumar. 2020. “Viscosity of -water nanofluids.” Mater. Today. Proc. 21: 681–683. https://doi.org/10.1016/j.matpr.2019.06.738.
Au, S.-K., and J. L. Beck. 2001. “Estimation of small failure probabilities in high dimensions by subset simulation.” Probab. Eng. Mech. 16 (4): 263–277. https://doi.org/10.1016/S0266-8920(01)00019-4.
Bacciocchi, M. 2020. “Buckling analysis of three-phase CNT/polymer/fiber functionally graded orthotropic plates: Influence of the non-uniform distribution of the oriented fibers on the critical load.” Eng. Struct. 223 (Nov): 111176. https://doi.org/10.1016/j.engstruct.2020.111176.
Bahaadini, R., A. R. Saidi, and M. Hosseini. 2018. “Dynamic stability of fluid-conveying thin-walled rotating pipes reinforced with functionally graded carbon nanotubes.” Acta Mech. 229 (12): 5013–5029. https://doi.org/10.1007/s00707-018-2286-0.
Ben Seghier, M. E. A., B. Keshtegar, and B. Elahmoune. 2018. “Reliability analysis of low, mid and high-grade strength corroded pipes based on plastic flow theory using adaptive nonlinear conjugate map.” Eng. Fail. Anal. 90 (Aug): 245–261. https://doi.org/10.1016/j.engfailanal.2018.03.029.
Bragaglia, M., L. Paleari, F. R. Lamastra, D. Puglia, F. Fabbrocino, and F. Nanni. 2021. “Graphene nanoplatelet, multiwall carbon nanotube, and hybrid multiwall carbon nanotube–graphene nanoplatelet epoxy nanocomposites as strain sensing coatings.” J. Reinf. Plast. Compos. 0731684421994324. https://doi.org/10.1177/0731684421994324.
Burke, A. D., D. H. Stover, and F. P. Dawson. 2002. “Magnetic nanocomposites: Preparation and characterization of polymer-coated Iron nanoparticles.” Chem. Mater. 14 (11): 4752–4761. https://doi.org/10.1021/cm020126q.
Civalek, O., S. Dastjerdi, S. D. Akbaş, and B. Akgöz. 2020. “Vibration analysis of carbon nanotube-reinforced composite microbeams.” Math. Methods Appl. Sci. https://doi.org/10.1002/mma.7069.
Curtin, W. 1991. “Theory of mechanical properties of ceramic-matrix composites.” J. Am. Ceram. Soc. 74 (11): 2837–2845. https://doi.org/10.1111/j.1151-2916.1991.tb06852.x.
Deng, J., Y. Liu, and W. Liu. 2017. “Size-dependent vibration analysis of multi-span functionally graded material micropipes conveying fluid using a hybrid method.” Microfluid. Nanofluid. 21 (8): 1–15. https://doi.org/10.1007/s10404-017-1967-7.
Dey, A., and S. Mahadevan. 1998. “Ductile structural system reliability analysis using adaptive importance sampling.” Struct. Saf. 20 (2): 137–154. https://doi.org/10.1016/S0167-4730(97)00033-7.
Dong, Y., A. P. Teixeira, and C. Guedes Soares. 2018. “Time-variant fatigue reliability assessment of welded joints based on the phi2 and response surface methods.” Reliab. Eng. Syst. Saf. 177 (Sep): 120–130. https://doi.org/10.1016/j.ress.2018.05.005.
El Amine Ben Seghier, M., B. Keshtegar, J. A. F. O. Correia, G. Lesiuk, and A. M. P. De Jesus. 2019. “Reliability analysis based on hybrid algorithm of M5 model tree and Monte Carlo simulation for corroded pipelines: Case of study X60 steel grade pipes.” Eng. Fail. Anal. 97 (Mar): 793–803. https://doi.org/10.1016/j.engfailanal.2019.01.061.
Engelund, S., and R. Rackwitz. 1993. “A benchmark study on importance sampling techniques in structural reliability.” Struct. Saf. 12 (4): 255–276. https://doi.org/10.1016/0167-4730(93)90056-7.
Fakhr, M. H., A. Fakhr, and H. Tabatabaei. 2019. “Analysis of critical fluid velocity and heat transfer in temperature-dependent nanocomposite pipes conveying nanofluid subjected to heat generation, conduction, convection and magnetic field.” Steel Compos. Struct. 30 (3): 281–292. https://doi.org/10.12989/scs.2019.30.3.281.
Fantuzzi, N., M. Bacciocchi, J. Agnelli, and D. Benedetti. 2020. “Three-phase homogenization procedure for woven fabric composites reinforced by carbon nanotubes in thermal environment.” Compos. Struct. 254 (Dec): 112840. https://doi.org/10.1016/j.compstruct.2020.112840.
Ghohani Arab, H., M. Rashki, M. Rostamian, A. Ghavidel, H. Shahraki, and B. Keshtegar. 2018. “Refined first-order reliability method using cross-entropy optimization method.” Eng. Comput. 35 (4): 1507–1519. https://doi.org/10.1007/s00366-018-0680-9.
Gong, J.-X., and P. Yi. 2011. “A robust iterative algorithm for structural reliability analysis.” Struct. Multidiscip. Optim. 43 (4): 519–527. https://doi.org/10.1007/s00158-010-0582-y.
Goswami, S., S. Ghosh, and S. Chakraborty. 2016. “Reliability analysis of structures by iterative improved response surface method.” Struct. Saf. 60 (May): 56–66. https://doi.org/10.1016/j.strusafe.2016.02.002.
Green, D. K. 2017. “Efficient Markov chain Monte Carlo for combined subset simulation and nonlinear finite element analysis.” Comput. Methods Appl. Mech. Eng. 313 (Jan): 337–361. https://doi.org/10.1016/j.cma.2016.10.012.
Hamzehkolaei, N. S., M. Miri, and M. Rashki. 2018. “New simulation-based frameworks for multi-objective reliability-based design optimization of structures.” Appl. Math. Modell. 62 (Oct): 1–20. https://doi.org/10.1016/j.apm.2018.05.015.
Hao, P., B. Wang, G. Li, Z. Meng, and L. Wang. 2015. “Hybrid framework for reliability-based design optimization of imperfect stiffened shells.” AIAA J. 53 (10): 2878–2889. https://doi.org/10.2514/1.J053816.
Huang, J., and D. Griffiths. 2011. “Observations on form in a simple geomechanics example.” Struct. Saf. 33 (1): 115–119. https://doi.org/10.1016/j.strusafe.2010.10.001.
Huang, X., Y. Li, Y. Zhang, and X. Zhang. 2018. “A new direct second-order reliability analysis method.” Appl. Math. Modell. 55 (Mar): 68–80. https://doi.org/10.1016/j.apm.2017.10.026.
Jalaei, M., and O. Civalek. 2019. “On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam.” Int. J. Eng. Sci. 143 (Oct): 14–32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
Jian, W., S. Zhili, Y. Qiang, and L. Rui. 2017. “Two accuracy measures of the Kriging model for structural reliability analysis.” Reliab. Eng. Syst. Saf. 167 (Nov): 494–505. https://doi.org/10.1016/j.ress.2017.06.028.
Keshtegar, B. 2016. “Chaotic conjugate stability transformation method for structural reliability analysis.” Comput. Methods Appl. Mech. Eng. 310 (Oct): 866–885. https://doi.org/10.1016/j.cma.2016.07.046.
Keshtegar, B. 2018. “Enriched FR conjugate search directions for robust and efficient structural reliability analysis.” Eng. Comput. 34 (1): 117–128. https://doi.org/10.1007/s00366-017-0524-z.
Keshtegar, B., and M. Bagheri. 2018. “Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map.” Nonlinear Dyn. 91 (3): 1443–1459. https://doi.org/10.1007/s11071-017-3957-4.
Keshtegar, B., and S. Chakraborty. 2018a. “An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search.” Reliab. Eng. Syst. Saf. 172 (Apr): 195–206. https://doi.org/10.1016/j.ress.2017.12.014.
Keshtegar, B., and S. Chakraborty. 2018b. “A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis.” Appl. Math. Modell. 53 (Jan): 319–332. https://doi.org/10.1016/j.apm.2017.09.017.
Keshtegar, B., and P. Hao. 2018. “Enriched self-adjusted performance measure approach for reliability-based design optimization of complex engineering problems.” Appl. Math. Modell. 57 (May): 37–51. https://doi.org/10.1016/j.apm.2017.12.030.
Keshtegar, B., P. Hao, and Z. Meng. 2016. “A self-adaptive modified chaos control method for reliability-based design optimization.” Struct. Multidiscip. Optim. 55 (1): 63–75.
Keshtegar, B., and I. Lee. 2016. “Relaxed performance measure approach for reliability-based design optimization.” Struct. Multidiscip. Optim. 54 (6): 1439–1454. https://doi.org/10.1007/s00158-016-1561-8.
Keshtegar, B., and Z. Meng. 2017. “A hybrid relaxed first-order reliability method for efficient structural reliability analysis.” Struct. Saf. 66 (May): 84–93. https://doi.org/10.1016/j.strusafe.2017.02.005.
Keshtegar, B., and S.-P. Zhu. 2019. “Three-term conjugate approach for structural reliability analysis.” Appl. Math. Modell. 76 (Dec): 428–442. https://doi.org/10.1016/j.apm.2019.06.022.
Kolahchi, R. 2017. “A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods.” Aerosp. Sci. Tech. 66 (Jul): 235–248. https://doi.org/10.1016/j.ast.2017.03.016.
Li, D.-Q., Z.-Y. Yang, Z.-J. Cao, S.-K. Au, and K.-K. Phoon. 2017. “System reliability analysis of slope stability using generalized subset simulation.” Appl. Math. Modell. 46 (Jun): 650–664. https://doi.org/10.1016/j.apm.2017.01.047.
Li, X., Y. Yang, and X. Cheng. 2004. “Ultrasonic-assisted fabrication of metal matrix nanocomposites.” J. Mater. Sci. 39 (9): 3211–3212. https://doi.org/10.1023/B:JMSC.0000025862.23609.6f.
Liu, P.-L., and A. Der Kiureghian. 1991. “Optimization algorithms for structural reliability.” Struct. Saf. 9 (3): 161–177. https://doi.org/10.1016/0167-4730(91)90041-7.
Meng, Z., and B. Keshtegar. 2019. “Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization.” Comput. Methods Appl. Mech. Eng. 344 (Feb): 95–119. https://doi.org/10.1016/j.cma.2018.10.009.
Meng, Z., G. Li, B. P. Wang, and P. Hao. 2015. “A hybrid chaos control approach of the performance measure functions for reliability-based design optimization.” Comput. Struct. 146 (Jan): 32–43. https://doi.org/10.1016/j.compstruc.2014.08.011.
Meng, Z., G. Li, D. Yang, and L. Zhan. 2017. “A new directional stability transformation method of chaos control for first order reliability analysis.” Struct. Multidiscip. Optim. 55 (2): 601–612. https://doi.org/10.1007/s00158-016-1525-z.
Meng, Z., Y. Pu, and H. Zhou. 2018a. “Adaptive stability transformation method of chaos control for first order reliability method.” Eng. Comput. 34 (4): 671–683. https://doi.org/10.1007/s00366-017-0566-2.
Meng, Z., D. Zhang, G. Li, and B. Yu. 2018b. “An importance learning method for non-probabilistic reliability analysis and optimization.” Struct. Multidiscip. Optim. 59 (4): 1255–1271. https://doi.org/10.1007/s00158-018-2128-7.
Nie, J., and B. R. Ellingwood. 2000. “Directional methods for structural reliability analysis.” Struct. Saf. 22 (3): 233–249. https://doi.org/10.1016/S0167-4730(00)00014-X.
Ovid’ko, I. A. 2013. “Enhanced mechanical properties of polymer- matrix nanocomposites reinforced by graphene inclusions: A review.” Rev. Adv. Mater. Sci. 34 (1): 19–25.
Periçaro, G., S. Santos, A. Ribeiro, and L. Matioli. 2015. “HLRF–BFGS optimization algorithm for structural reliability.” Appl. Math. Modell. 39 (7): 2025–2035. https://doi.org/10.1016/j.apm.2014.10.024.
Rashki, M., M. Miri, and M. A. Moghaddam. 2012. “A new efficient simulation method to approximate the probability of failure and most probable point.” Struct. Saf. 39 (Nov): 22–29. https://doi.org/10.1016/j.strusafe.2012.06.003.
Rashki, M., M. Miri, and M. A. Moghaddam. 2014. “A simulation-based method for reliability based design optimization problems with highly nonlinear constraints.” Autom. Constr. 47 (Nov): 24–36. https://doi.org/10.1016/j.autcon.2014.07.004.
Reddy, J. N. 2003. Mechanics of laminated composite plates and shells. 2nd ed. Boca Raton, FL: CRC Press.
Roudak, M. A., M. A. Shayanfar, M. A. Barkhordari, and M. Karamloo. 2017. “A robust approximation method for nonlinear cases of structural reliability analysis.” Int. J. Mech. Sci. 133 (Nov): 11–20. https://doi.org/10.1016/j.ijmecsci.2017.08.038.
Santosh, T., R. Saraf, A. Ghosh, and H. Kushwaha. 2006. “Optimum step length selection rule in modified HL–RF method for structural reliability.” Int. J. Press. Vessels Pip. 83 (10): 742–748. https://doi.org/10.1016/j.ijpvp.2006.07.004.
Sunder, L. S., G. Otero-Irurueta, M. K. Singh, and A. C. M. Sousa. 2016. “Heat transfer and friction factor of multi-walled carbon nanotubes– nanocomposite nanofluids flow in a tube with/without longitudinal strip inserts.” Int. J. Heat Mass Transfer 100 (Sep): 691–703. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.065.
Yang, D. 2010. “Chaos control for numerical instability of first order reliability method.” Commun. Nonlinear Sci. Numer. Simul. 15 (10): 3131–3141. https://doi.org/10.1016/j.cnsns.2009.10.018.
Zhang, Z., C. Jiang, G. Wang, and X. Han. 2015. “First and second order approximate reliability analysis methods using evidence theory.” Reliab. Eng. Syst. Saf. 137 (May): 40–49. https://doi.org/10.1016/j.ress.2014.12.011.
Zhao, Y. G., and A. H. Ang. 2003. “System reliability assessment by method of moments.” J. Struct. Eng. 129 (10): 1341–1349. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1341).
Zhao, Y. G., and T. Ono. 2004. “On the problems of the fourth moment method.” Struct. Saf. 26 (3): 343–347. https://doi.org/10.1016/j.strusafe.2003.10.001.
Zhu, S. P., Q. Liu, J. Zhou, and Z. Y. Yu. 2018. “Fatigue reliability assessment of turbine discs under multi-source uncertainties.” Fatigue Fract. Eng. Mater. Struct. 41 (6): 1291–1305. https://doi.org/10.1111/ffe.12772.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Feb 13, 2021
Accepted: May 20, 2021
Published online: Aug 11, 2021
Published in print: Dec 1, 2021
Discussion open until: Jan 11, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Hanshu Chen, Guohai Chen, Zeng Meng, Dixiong Yang, Stochastic bifurcation and dynamic reliability analyses of nonlinear MDOF vehicle system with generalized fractional damping via DPIM, Nonlinear Dynamics, 10.1007/s11071-024-09313-4, 112, 7, (5291-5316), (2024).