Evaluation of Critical Buckling Loads of Short Fiber Reinforced Nanobeams According to Different Beam Theories

Öz

This study analyzed the buckling behavior of short fiber reinforced nanobeams within the framework of nonlocal elasticity theory using Euler-Bernoulli, Timoshenko, and Levinson beam theories. The nonlocal elasticity theory provides a more realistic modeling approach by considering the effects of surface interactions, atomic forces, and the characteristics of microstructures, allowing for an examination of the impact of these factors on the buckling behavior of nanoscale materials. The analyses, conducted under the framework of nonlocal elasticity theory, investigated the effects of essential parameters such as fiber volume fraction, fiber length-to-diameter ratio, elastic modulus ratio, and the nonlocal parameter on critical buckling loads. The results, presented graphically, reveal that an increase in the nonlocal parameter leads to a significant reduction in the critical buckling loads of the beams, indicating a decrease in rigidity. An increase in fiber volume fraction enhances the buckling resistance of the beams, resulting in higher critical buckling loads. Additionally, increasing the fiber length-to-diameter ratio further strengthens the buckling resistance, particularly in beams with long and slender fibers. The increase in the elastic modulus ratio also leads to higher critical buckling loads, particularly highlighting the significant contribution of highly rigid fibers to structural performance. This study provides important insights into the design of composite nano-beams for micro- and nano-scale applications and provides an important basis for future research.

Anahtar Kelimeler

• Short Fiber Reinforced Beams
• Critical Buckling Load
• Nonlocal Elasticity Theory
• Euler-Bernoulli Beam Theory
• Timoshenko Beam Theory
• Levinson Beam Theory

Farklı Kiriş Teorilerine Göre Kısa Fiber Takviyeli Nano Kirişlerin Kritik Burkulma Yüklerinin Değerlendirilmesi

Öz

Bu çalışmada, kısa fiber takviyeli nano kirişlerin burkulma davranışları, yerel olmayan elastisite teorisi çerçevesinde, Euler-Bernoulli, Timoshenko ve Levinson kiriş teorileri kullanılarak analiz edilmiştir. Yerel olmayan elastisite teorisi, nanoyapıların küçük ölçekli etkilerini dikkate alarak daha gerçekçi bir modelleme sunmakta ve nano ölçekteki malzemelerin yüzey etkileri, atomik kuvvetler ve mikro yapıların özelliklerinin burkulma davranışları üzerindeki etkilerinin incelenmesine olanak tanımaktadır. Yerel olmayan elastisite teorisi çerçevesinde gerçekleştirilen bu analizlerde, fiber hacim oranı, fiberin uzunluk/çap oranı, elastisite modülü oranı ve yerel olmayan parametre gibi önemli parametrelerin kritik burkulma yükleri üzerindeki etkileri incelenmiştir. Analizler sonucu ortaya çıkan sonuçlar grafiksel olarak sunulmuştur. Analizler, yerel olmayan parametrenin artışının, kirişlerin kritik burkulma yüklerinde belirgin bir düşüşe neden olduğunu göstermektedir. Fiber hacim oranının artması ise, kirişlerin burkulma direncini artırarak kritik burkulma yüklerinin yükselmesine neden olmaktadır. Ayrıca, fiber uzunluk/çap oranının artışı da burkulma direncini güçlendirmekte, özellikle uzun ve ince fiberlerin kullanıldığı yapılar daha yüksek burkulma yüklerine ulaşmaktadır. Elastisite modül oranı artışı ise, kirişlerin burkulma yüklerini daha da yükselterek, özellikle rijitliği yüksek fiberlerin yapısal performansa katkısını açıkça ortaya koymaktadır. Bu çalışma, mikro ve nano ölçekli uygulamalarda kullanılacak kompozit nano kirişlerin tasarımı ile ilgili önemli bilgiler sunmakta olup, gelecekteki araştırmalar için de önemli bir temel oluşturmaktadır.

Anahtar Kelimeler

• Kısa Fiber Takviyeli Kirişler
• Kritik Burkulma Yükü
• Yerel Olmayan Elastisite Teorisi
• Euler-Bernoulli Kiriş Teorisi
• Timoshenko Kiriş Teorisi
• Levinson Kiriş Teorisi

Kaynakça

1. Abdelrahman, A. A. ve Eltaher, M. A. (2022). On bending and buckling responses of perforated nanobeams including surface energy for different beams theories. Engineering with Computers, 38(3), 2385-2411. https://doi.org/10.1007/s00366-020-01211-8
2. Agarwal, B. D., Broutman, L. J., Agarwal, B. D. ve Broutman, L. J. (2006). Analysis and performance of fiber composites Third edition (Third.). John Wiley & Sons.
3. Akbaş, Ş. D. (2018). Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
4. Akgöz, B. ve Civalek, Ö. (2015). Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Composite Structures, 134, 294-301. https://doi.org/10.1016/j.compstruct.2015.08.095
5. Akpinar M. Uzun B. ve Yaylı, M. Ö. (2024a). On the thermo-mechanical vibration of an embedded short-fiber-reinforced nanobeam. Advances in nano research, 17(3), 197-211. doi:10.12989/ANR.2024.17.3.197
6. Akpınar, M., Uzun, B. ve Yaylı, M. Ö. (2024b). Stokes’ transform solution method for dynamics of a short-fiber-reinforced nanorod via second-order strain gradient theory. Mechanics Based Design of Structures and Machines, 1-21. doi:10.1080/15397734.2024.2404612
7. Arda, M. ve Aydogdu, M. (2018). Torsional vibration of double CNT system embedded in an elastic medium. Noise Theory Pract., 4, 15-27.
8. Aydogdu, M. ve Arda, M. (2016). Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity. International Journal of Mechanics and Materials in Design, 12(1), 71-84. https://doi.org/10.1007/s10999-014-9292-8

9. Borjalilou, V., Taati, E. ve Ahmadian, M. T. (2019). Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions. SN Applied Sciences, 1(11), 1323. doi:10.1007/s42452-019-1359-6
10. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2020). Frequency, bending and buckling loads of nanobeams with different cross sections. Advances in Nano Research, 9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091
11. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2022a). Nonlocal Free Vibration of Embedded Short-Fiber-Reinforced Nano-/Micro-Rods with Deformable Boundary Conditions. Materials, 15(19), 6803. doi:10.3390/ma15196803
12. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2022b). Torsional vibrations of functionally graded restrained nanotubes. European Physical Journal Plus, 137(1). https://doi.org/10.1140/epjp/s13360-021-02309-8
13. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2022c). An effective analytical method for buckling solutions of a restrained FGM nonlocal beam. Computational and Applied Mathematics, 41(2), 67. https://doi.org/10.1007/s40314-022-01761-1
14. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2023a). Torsional static and free vibration analysis of noncircular short‐fiber‐reinforced microwires with arbitrary boundary conditions. Polymer Composites. doi:10.1002/pc.27321
15. Civalek, Ö., Uzun, B. ve Yaylı, M. Ö. (2023b). Thermal buckling analysis of a saturated porous thick nanobeam with arbitrary boundary conditions. Journal of Thermal Stresses, 46(1), 1-21. https://doi.org/10.1080/01495739.2022.2145401
16. Daikh A. A., Drai A., Belarbi M. O., Houari Mohammed S. A., Benoumer A., Eltaher M. A. ve Mohamed N. A. (2024). Static bending response of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. Advances in nano research, 16(3), 289-301. doi:10.12989/ANR.2024.16.3.289
17. Dong, M., Zhang, H., Tzounis, L., Santagiuliana, G., Bilotti, E. ve Papageorgiou, D. G. (2021). Multifunctional epoxy nanocomposites reinforced by two-dimensional materials: A review. Carbon, 185, 57-81. doi:10.1016/j.carbon.2021.09.009
18. Dubina, D., Ungureanu, V. ve Crisan, A. (2013). Experimental Evidence of Erosion of Critical Load in Interactive Buckling. Journal of Structural Engineering, 139(5), 705-716. doi:10.1061/(ASCE)ST.1943-541X.0000789
19. Eringen, A. C. (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54(9), 4703-4710. doi:10.1063/1.332803
20. Eringen, A. C. ve Edelen, D. G. B. (1972). On nonlocal elasticity. International Journal of Engineering Science, 10(3), 233-248. doi:10.1016/0020-7225(72)90039-0
21. Esen, I., Daikh, A. A. ve Eltaher, M. A. (2021). Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load. The European Physical Journal Plus, 136(4), 458. doi:10.1140/epjp/s13360-021-01419-7
22. Gul, U. ve Aydogdu, M. (2023). On the Axial Vibration of Viscously Damped Short-Fiber-Reinforced Nano/Micro-composite Rods. Journal of Vibration Engineering & Technologies, 11(3), 1327-1341. doi:10.1007/s42417-022-00643-4
23. Haddouch, I., Mouallif, I., Benhamou, M., Zhouri, O., Abdellaoui, H., Hachim, A., El Maani, R., Radi, B. ve Mouallif, Z. (2024). Effect of plant short fibers on the mechanical properties of carbon fiber reinforced epoxy matrix by using FEM based numerical homogenization technique. International Journal of Nanoelectronics and Materials (IJNeaM), 17(1), 52-65. doi:10.58915/ijneam.v17i1.462
24. Hosseini, S. B. (2017). A Review: Nanomaterials as a Filler in Natural Fiber Reinforced Composites. Journal of Natural Fibers, 14(3), 311-325. doi:10.1080/15440478.2016.1212765
25. I-Ling. (2011). Structural Instability of Carbon Nanotube. Carbon Nanotubes - Synthesis, Characterization, Applications içinde . InTech. doi:10.5772/17946
26. Kafkas, U., Ünal, Y., Yaylı, M. Ö. ve Uzun, B. (2023). Buckling analysis of perforated nano/microbeams with deformable boundary conditions via nonlocal strain gradient elasticity. Advances in Nano Research, 15(4), 339-353. https://doi.org/10.12989/anr.2023.15.4.339
27. Khadem, S. ve Euler, J. (1992). Dynamic stability of flexible spinning missiles. II - Vibration and stability analysis of a structurally damped controlled free-free Bernoulli-Euler beam, as a model for flexible missiles. 33rd Structures, Structural Dynamics and Materials Conference içinde . Reston, Virigina: American Institute of Aeronautics and Astronautics. doi:10.2514/6.1992-2211
28. Levinson, M. (1981). A new rectangular beam theory. Journal of Sound and Vibration, 74(1), 81-87. doi:10.1016/0022-460X(81)90493-4
29. Lim, C. W., Zhang, G. ve Reddy, J. N. (2015). A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78, 298-313. doi:10.1016/j.jmps.2015.02.001
30. Mindlin, R. D. (1964). Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16, 51-78. doi:10.1007/BF00248490
31. Mindlin, R. D. (1965). Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures, 1(4), 417-438. doi:10.1016/0020-7683(65)90006-5
32. Moses, F. (1982). System reliability developments in structural engineering. Structural Safety, 1(1), 3-13. doi:10.1016/0167-4730(82)90011-X
33. Nunes, F., Silvestre, N. ve Correia, J. R. (2016). Structural behaviour of hybrid FRP pultruded columns. Part 2: Numerical study. Composite Structures, 139, 304-319. doi:10.1016/j.compstruct.2015.12.059
34. Pakravan, H. R., Latifi, M. ve Jamshidi, M. (2017). Hybrid short fiber reinforcement system in concrete: A review. Construction and Building Materials, 142, 280-294. doi:10.1016/j.conbuildmat.2017.03.059
35. Pervaiz, S., Qureshi, T. A., Kashwani, G. ve Kannan, S. (2021). 3D Printing of Fiber-Reinforced Plastic Composites Using Fused Deposition Modeling: A Status Review. Materials, 14(16), 4520. doi:10.3390/ma14164520
36. Ramu, P., Jaya Kumar, C. V. ve Palanikumar, K. (2019). Mechanical Characteristics and Terminological Behavior Study on Natural Fiber Nano reinforced Polymer Composite – A Review. Materials Today: Proceedings, 16, 1287-1296. doi:10.1016/j.matpr.2019.05.226
37. Reddy, J. N. (2007). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2-8), 288-307. doi:10.1016/J.IJENGSCI.2007.04.004
38. Salehipour, H., Shahmohammadi, M. A., Folkow, P. D. ve Civalek, O. (2024). An analytical solution for vibration response of CNT/GPL/fibre/polymer hybrid composite micro/nanoplates. Mechanics of Advanced Materials and Structures, 31(10), 2094-2114. doi:10.1080/15376494.2022.2150916
39. Serna, M. A., López, A., Puente, I. ve Yong, D. J. (2006). Equivalent uniform moment factors for lateral–torsional buckling of steel members. Journal of Constructional Steel Research, 62(6), 566-580. doi:10.1016/j.jcsr.2005.09.001
40. Silvestre, N., Faria, B. ve Canongia Lopes, J. N. (2014). Compressive behavior of CNT-reinforced aluminum composites using molecular dynamics. Composites Science and Technology, 90, 16-24. doi:10.1016/j.compscitech.2013.09.027
41. Şimşek, M. (2019). Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory. Composite Structures, 224, 111041. doi:10.1016/j.compstruct.2019.111041
42. T Kaneko. (1975). On Timoshenko’s correction for shear in vibrating beams. Journal of Physics D: Applied Physics, 8(16), 1927-1936. doi:10.1088/0022-3727/8/16/003
43. Togun, N. ve Bağdatlı, S. (2016a). Nonlinear Vibration of a Nanobeam on a Pasternak Elastic Foundation Based on Non-Local Euler-Bernoulli Beam Theory. Mathematical and Computational Applications, 21(1), 3. https://doi.org/10.3390/mca21010003
44. Togun, N. ve Bağdatlı, S. M. (2016b). Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255-262. https://doi.org/10.1016/j.compositesb.2016.04.074
45. Toupin, R. (1962). Elastic materials with couple-stresses. Archive for rational mechanics and analysis, 11(1), 385-414. doi:10.1007/BF00253945
46. Wang, Y., Wang, Z. ve Zhu, L. (2022). A Short Review of Recent Progress in Improving the Fracture Toughness of FRP Composites Using Short Fibers. Sustainability, 14(10), 6215. doi:10.3390/su14106215
47. Yang, F., Chong, A. C. M., Lam, D. C. C. ve Tong, P. (2002). Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10), 2731-2743. doi:10.1016/S0020-7683(02)00152-X
48. Yaylı, M. Ö. (2013). Torsion of Nonlocal Bars with Equilateral Triangle Cross Sections. Journal of Computational and Theoretical Nanoscience, 10(2), 376-379. https://doi.org/10.1166/jctn.2013.2707
49. Yaylı, M. Ö. (2017). A compact analytical method for vibration of micro-sized beams with different boundary conditions. Mechanics of Advanced Materials and Structures, 24(6), 496-508. https://doi.org/10.1080/15376494.2016.1143989
50. Yaylı, M. Ö. (2018a). Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material. Micro & Nano Letters, 13(7), 1031-1035. https://doi.org/10.1049/mnl.2018.0181
51. Yaylı, M. Ö. (2018b). On the torsional vibrations of restrained nanotubes embedded in an elastic medium. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(9), 419. https://doi.org/10.1007/s40430-018-1346-7
52. Yaylı, M. Ö. (2018c). Torsional vibration analysis of nanorods with elastic torsional restraints using non‐local elasticity theory. Micro & Nano Letters, 13(5), 595-599. https://doi.org/10.1049/mnl.2017.0751
53. Yaylı, M. Ö. (2018d). Torsional vibrations of restrained nanotubes using modified couple stress theory. Microsystem Technologies, 24(8), 3425-3435. https://doi.org/10.1007/s00542-018-3735-3
54. Yaylı, M. Ö. (2019a). Stability analysis of a rotationally restrained microbar embedded in an elastic matrix using strain gradient elasticity. Curved and Layered Structures, 6(1), 1-10. doi:10.1515/cls-2019-0001
55. Yaylı, M. Ö. (2019). Free vibration analysis of a rotationally restrained (FG) nanotube. Microsystem Technologies, 25(10), 3723-3734. https://doi.org/10.1007/s00542-019-04307-4
56. Yaylı, M. Ö. (2020). Axial vibration analysis of a Rayleigh nanorod with deformable boundaries. Microsystem Technologies, 26(8), 2661-2671. https://doi.org/10.1007/s00542-020-04808-7