خمش غیرخطی تیرهای کامپوزیتی تقویت‌شده با پلاکت‌های‌گرافن با استفاده از روش مربعات دیفرانسیلی هارمونیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، دانشکدۀ فنی و مهندسی، دانشگاه خوارزمی، تهران.

2 گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه خوارزمی، تهران

چکیده

در این پژوهش تجزیه و تحلیل خمش غیرخطی یک تیر کامپوزیتی تقویت‌شده توسط پلاکت‌های گرافن با توزیع غیر یکنواخت در راستای ضخامت، بررسی و ارائه شده است. معادلات دیفرانسیل غیرخطی حاکم در این پژوهش بر اساس نظریه تغییر شکل برشی مرتبه اول و اصل حداقل انرژی پتانسیل، استخراج شده و با استفاده از روش مربعات دیفرانسیلی هارمونیک حل شده است. خواص مکانیکی و مدول الاستیک موثر کامپوزیت تقویت‌شده با پلاکت گرافن با استفاده از مدل میکرومکانیکی هالپین- تسای اصلاح‌شده محاسبه شده است. همچنین، از قاعده اختلاط برای تعیین نسبت پواسون موثر استفاده شده است. ابتدا، مطالعات مقایسه‌ای بین تیرهای استاندارد کامپوزیتی مدرج تابعی و تیرهای تقویت‌شده با پلاکت‌های گرافن، ارائه شده است و سپس اثرات شرایط مرزی، کسر وزنی و الگوی توزیع پلاکت‌های گرافن و تعداد کل لایه‌ها بر ویژگی‌های خمش غیرخطی تیرهای کامپوزیتی مورد مطالعه قرار گرفته است. نتایج این پژوهش نشان‌دهنده قابلیت بالای روش پیشنهادی برای حل مسائل غیرخطی و بدست آوردن رفتار خمشی تیرهای کامپوزیتی تقویت شده، می‌باشد. همچنین مطالعات پارامتری نشان می‌دهد با افزایش کسر وزنی پلاکت‌های گرافن، استحکام خمشی تیر بهبود یافته و خیز تیر کاهش می‌یابد. علاوه بر این، افزایش تعداد کل لایه‌های کامپوزیت تقویت‌شده با پلاکت گرافن، سبب می‌شود که توزیع تنش در راستای ضخامت تیر هموارتر شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Nonlinear Bending Analysis of Nanocomposite Beams Reinforced by Graphene Platelets using Harmonic Differential Quadrature Method

نویسندگان [English]

  • Hassan Shokrollahi 1
  • Reza Beigpour 2
1 Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran.
2 Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
چکیده [English]

The nonlinear bending analysis of a composite beam reinforced by graphene platelets (GPL) nanofillers having nonuniform distribution through the thickness, is presented. Governing nonlinear differential equations are derived based on the first order shear deformation theory with the aid of minimum potential energy principle. The nonlinear differential equations are solved using harmonic differential quadrature method (HDQM). The modified Halpin-Tsai model is implemented to determine the effective Young’s modulus of graphene platelet reinforced composite (GPLRC) beams. Moreover, the rule of mixture is used for definition of the effective Poisson’s ratio. At first, conventional nanocomposite beams are studied for evaluation of the applicability of the proposed method for nonlinear bending analyses. Then for the beams reinforced by graphene platelets, the effects of some parameters including boundary conditions, number of layers, weight fraction and distribution pattern of graphene platelet on the nonlinear bending characteristics of the GPLRC beams, are investigated. This study shows the capability of the proposed method to solve the nonlinear problems and to get the beams behavior under bending loading. In addition, by increasing the weight fraction of graphene platelets in the beam, the bending strength of the beam improves and the beam deflection decreases. Moreover, increasing the number of layers for GPLRC tends to smoother variation of stress through the beam thickness.

کلیدواژه‌ها [English]

  • Beam nonlinear analysis
  • bending analysis
  • nanocomposite beams
  • graphene platelets
  • harmonic differential quadrature method

مراجع

  1. Hosseini Kordkheili, S. A., and Moshrefzadeh-Sani, H., "Mechanical Properties of Double-Layered Graphene Sheets", Computational Materials Science, Vol. 69, Pp. 335-343, (2013).
  2. Balandin, A. A., "Thermal Properties of Graphene and Nanostructured Carbon Materials", Nature Materials, Vol. 10, No. 8, Pp. 569-581, (2011).
  3. Murugan, A. V., Muraliganth, T., and Manthiram, A., "Rapid, Facile Microwave-Solvothermal Synthesis of Graphene Nanosheets and their Polyaniline Nanocomposites for Energy Strorage", Chemistery of Materials, Vol. 21, No. 21, Pp. 5004-5006, (2009).
  4. Kuila, T., Bose, S., Khanra, P., Mishra, A. K., Kim, N. H., and Lee, J. H., "Recent Advances in Graphene-Based Biosensors", Biosensors and Bioelectronics, Vol. 26, No. 12, Pp. 4637-4648, (2011).
  5. Kuilla, T., Bhadra, S., Yao, D., Kim, N. H., Bose, S., and Lee, J. H., "Recent Advances in Graphene Based Polymer Composites", Progress in Polymer Science, Vol. 35, No. 11, Pp. 1350-1375, (2010).
  6. Schwierz, F., "Graphene Transistors", Nature Nanotechnology, Vol. 5, No. 7, Pp. 487-496, (2010).
  7. Rafiee, M. A., Rafiee, J., Wang, Z., Song, H., Yu, Z. Z., and Koratkar, N., "Enhanced Mechanical Properties of Nanocomposites at Low Graphene Content", American Chemical Society Nano, Vol. 3, No. 12, Pp. 3884-3890, (2009).
  8. Hu, K., Kulkarni, D. D., Choi, I., and Tsukruk, V. V., "Graphene-Polymer Nanocomposites for Structural and Functional Applications", Progress in Polymer Science, Vol. 39, Pp. 1934-1972, (2014).
  9. Guo, Z., Song, L., Boay, C. G., Li, Z., Li, Y., and Wang, Z., "A New Multiscale Numerical Characterization of Mechanical Properties of Graphene-Reinforced Polymer-Matrix Composites", Composite Structures, Vol. 199, Pp. 1-9, (2018).
  10. Aminivida, H., Shokrollahi, H., and Beigpour, R., "Thermal Stress Analysis of the Carbon Nanotube Reinforced Composite Cylindrical Shells",Amirkabir Journal of Mechanical Engineering, Vol. 53, No. 10, Pp.14-14, (2021).
  11. King, J. A., Klimek, D. R., Miskioglu, I., and Odegard, G. M., "Mechanical Properties of Graphene Nanoplatelet/Epoxy Composites", Journal of Applied Polymer Science, Vol. 128, Pp. 4217-4223, (2013).
  12. Liang, J., Wang, Y., Huang, Y., Ma, Y., Liu, Z., and Cai, J., "Electromagnetic Interference Shielding of Graphene/Epoxy Composites", Carbon, Vol. 47, Pp. 922-925, (2008).
  13. Feng, C., Kitpornchai, S., and Yang, J., "Nonlinear Bending of Polymer Nanocomposite Beams Reinforced with Non-Uniformly Distributed Graphene Platelets (GPLs)", Composites Part B: Engineering, Vol. 110, Pp. 132-140, (2017).
  14. Barati, M. R., and Zenkour, A. M., "Analysis of Postbuckling of Graded Porous GPL-Reinforced Beams with Geometrical Imperfection", Mechanics of Advanced Materials and Structures, Vol. 26, No. 6, Pp. 503-511, (2019).
  15. Bidgoli, E. R., and Arefi, M., "Free Vibration Analysis of Micro Plate Reinforced with Functionally Graded Graphene Nanoplatelets Based on Modified Strain-Gradient Formulation", Journal of Sandwich Structures & Materials, DOI: 10.1177/1099636219839302, (2019).
  16. Yang, S.Y., Lin, W. N., Huang, Y. L., Tien, H. W., Wang, J. Y., Ma, C. C. M., et al., "Synergetic Effects of Graphene Platelets and Carbon Nanotubes on the Mechanical and Thermal Properties of Epoxy Composites", Carbon, Vol. 9, Pp. 793-803, (2011).
  17. Dong, Y. H., He, L. W., Wang, L., et al., "Buckling of Spinning Functionally Graded Graphene Reinforced Porous Nanocomposite Cylindrical Shells: An Analytical Study", Aerospace Science Technology, Vol. (82-83), Pp. 466-478, (2018).
  18. Barati, M. R., and Shahverdi, H., "Finite Element Forced Vibration Analysis of Refined Shear Deformable Nanocomposite Graphene Platelet-Reinforced Beams", Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42, Pp. 33, (2020).
  19. Arefi, M., Bidgoli, E. M. R., Dimitri, R., Bacciocchi, M., and Tornabene, F., "Nonlocal Bending Analysis of Curved Nanobeams Reinforced by Graphene Nanoplatelets", Composites Part B: Engineering, Vol. 166, Pp. 1-12, (2019).
  20. Ziaee, S., "Free Vibration of Heterostructures of Graphene and Boron Nitride in Thermal Environment Via Aifantis Theory with Velocity Gradients and Ritz Method", Amirkabir Journal of Mechanical Engineering, Vol. 50, No. 5, Pp. 1061-1078, (2018).
  21. Varzandian, Gh., Ziaee, S., and Farid, M., "Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet", Amirkabir Journal of Mechanical Engineering, Vol. 52, No. 8, Pp. 2177-2194 (2020).
  22. Bahrami, M. A., Heshmati, M., and Feli, S., "A Study on the Synergistic Influence of Reduced Graphene Oxide and MWCNTs on the Mechanical Properties of Epoxy Nanocomposite", Amirkabir Journal of Mechanical Engineering, Vol. 53, No. 6 (Special Issue), Pp. 13-13, (2021).
  23. Wang, Y., Feng, C., Santiuste, C., et al., "Buckling and Postbuckling of Dielectric Composite Beam Reinforced with Graphene Platelets (GPLs)", Aerospace Science Technology, Vol. 91, Pp. 208-218, (2019).
  24. Choi, J., Shin, H., Yang, S. and Cho, M., "The Influence of Nanoparticle Size on the Mechanical Properties of Polymer Nanocomposites and the Associated Interphase Region: A Multiscale Approach", Composite Structures, Vol. 119, Pp. 365-376, (2015).
  25. Aluko, O., Gowtham, S., and Odegard, G. M., "The Development of Multiscale Models for Predicting the Mechanical Response of GNP Reinforced Composite Plate", Composite Structures, Vol. 206, Pp. 526-534, (2018).
  26. Shokrieh, M. M., Ghoreishi, S. M., and Esmkhani, M., "Toughening Mechanisms of Nanoparticle-Reinforced Polymers. In: Toughening Mechanisms in Composite Materials", Woodhead Publishing, Pp. 295-320, (2015).
  27. Shokrieh, M. M., Esmkhani, M., Shahverdi, H. R., and Vahedi, F., "Effect of Graphene Nanosheets (GNS) and Graphite Nanoplatelets (GNP) on the Mechanical Properties of Epoxy Nanocomposites", Science of Advanced Materials, Vol. 5, Pp. 260-266, (2013).
  28. Civalek, Ö., and Ülker, M., "Harmonic Differential Quadrature (HDQ) for Axisymmetric Bending Analysis of Thin Isotropic Circular Plates", Structural Engineering and Mechanics, Vol. 17, No. 1, Pp. 1-14, (2004).
  29. Reddy, J., El-Borgi, S., and Romanoff, J., "Non-Linear Analysis of Functionally Graded Microbeams Using Eringen ׳s Non-Local Differential Model", International Journal of Non-Linear Mechanics, Vol. 67, Pp. 308-318, (2014).
  30. Liu, F., Ming, P., and Li, J., "Ab Initio Calculation of Ideal Strength and Phonon Instability of Graphene under Tension", Physical Review B, Vol. 76, No. 6, 064120, (2007).
  31. Shokrieh, M. M., Esmkhani, M., and Haghighatkhah, A. R., "Mechanical Properties of Graphene/Epoxy Nanocomposites under Static and Flexural Fatigue Loadings", Mechanics of Advanced Composite Structures, Vol. 1, Pp. 1-7, (2014).
  32. Zegeye, E., Ghamsari, A.K. and Woldesenbet, E., "Mechanical Properties of Graphene Platelets Reinforced Syntactic Foams", Composites Part B: Engineering, Vol. 60, Pp. 268-273, (2014).
  33. Nagar, S., Sharma, K., Kukreja, N., and Shukla, M. K., "Micromechanical and Experimental Analysis of Mechanical Properties of Graphene/CNT Epoxy Composites", Materials Today: Proceedings, Vol. 26, Pp. 1855-1863, (2020).
  34. Mishra, B. P., Mishra, D., Panda, P., and Maharana, A., "An Experimental Investigation of the Effects of Reinforcement of Graphene Fillers on Mechanical Properties of Bi-Directional Glass/Epoxy Composite", Materials Today: Proceedings, Vol. 33, Pp. 5429-5441, (2020).
  35. Wang, J., Wang, X., Xu, C., Zhang, M., and Shang, X., "Preparation of Graphene/Poly (Vinyl Alcohol) Nanocomposites with Enhanced Mechanical Properties and Water Resistance", Polymer International, Vol. 60, Pp. 816-822, (2011).

 

 

ارسال نظر در مورد این مقاله
CAPTCHA Image

فایل ها

هم رسانی

ارجاع به این مقاله

آمار