Steel and Composite Structures

  • 제46권1호
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  • Pages.143-152
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  • 2023
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Application of computer algorithms for modelling and numerical solution of dynamic bending

  • 투고 : 2022.02.20
  • 심사 : 2023.01.02
  • 발행 : 2023.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, static and dynamic bending of nanocomposite micro beam armed with CNTs considering agglomeration effect is studied. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The micro beam is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the static and dynamic deflections are decreased. In addition, enhancing the nonlocal parameter yields to higher static and dynamic deflections.

키워드

참고문헌

  1. Al-Furjan, M.S.H., Farrokhian, A., Keshtegar, B., Kolahchi, R. and Trung, N.T. (2020), "Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones", Aerosp. Sci. Technol., 107, 106259.
  2. Al-Furjan, M.S.H., Farrokhian, A., Keshtegar, B., Kolahchi, R. and Trung, N.T. (2021a), "Dynamic stability control of viscoelastic nanocomposite piezoelectric sandwich beams resting on Kerr foundation based on exponential piezoelasticity theory", Europ. J. Mech. / A Solids, 86, 104169.
  3. Al-Furjan, M.S.H., Farrokhian, A., Mahmoud, S.R. and Kolahchi, R. (2021b), "Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact", ThinWall. Struct, 163, 107706. https://doi.org/10.1016/j.tws.2021.107706.
  4. Al-Furjan, M.S.H., Farrokhian, A., Keshtegar, B., Kolahchi, R. and Trung, N.T. (2021c), "Dynamic stability control of viscoelastic nanocomposite piezoelectric sandwich beams resting on Kerr foundation based on exponential piezoelasticity theory", Europ. J. Mech. / A Solids, 86, 104-169. https://doi.org/10.1016/j.euromechsol.2020.104169
  5. Abdulrazzaq, M.A., Fenjan Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct, 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.
  6. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  7. Thai, H.T. and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Math. Model. 37, 3269-3281. https://doi.org/10.1016/j.apm.2012.08.008
  8. Civalek, O., Uzun, B. and M. Yayli O., (2020), "Frequency, bendingand buckling loads of nanobeams with different cross sections", Adv. Nano Res., 9(2), 91-104, https://doi.org/10.12989/anr.2020.9.2.091.
  9. Farrokhian, A. (2020), "Buckling response of smart plates reinforced by nanoparticles utilizing analytical method", Steel Compos. Struct., 35(1), 1-12. https://doi.org/10.12989/scs.2020.35.1.001.
  10. Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2020), "Nonlinear static and dynamic hygrothermal buckling analysis of imperfect functionally graded porous cylindrical shells", Appl. Math. Model., 77, 539-553., https://doi.org/10.1016/j.apm.2019.07.062.
  11. Ghiasian, S.E., Kiani, Y. and Eslami, M.R. (2013), "Dynamic buckling of suddenly heated or compressed FGM beams resting on nonlinear elastic foundation", Compos. Struct., 106, 225-234. https://doi.org/10.1016/j.compstruct.2013.06.01.
  12. Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21, 431-440. https://doi.org/10.12989/cac.2018.21.4.431.
  13. Jiao, P., Chen, Z., Li, Y., Ma, H. and Wu, J. (2019), "Dynamic buckling analyses of functionally graded carbon nano tubes reinforced composite (FG-CNTRC) cylindrical shell under axial power-law time-varying displacement load", Compos. Struct., 220, 784-797., https://doi.org/10.1016/j.compstruct.2019.04.048.
  14. Hajmohammad, M.H., Azizkhani, M.B. and Kolahchi, R. (2018), "Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis", Int. J. Mech. Sci., 137, 205-213. https://doi.org/10.1016/j.ijmecsci.2018.01.026 .
  15. Hajmohammad, M.H., Nouri, A.H., Zarei, M.S. and Kolahchi, R. (2019), "A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal", Eng. Comput., 35(4), 1141-1157. https://doi.org/10.1007/s00366-018-0655-x.
  16. Hussain, M., Naeem, M.N., Asghar, S. and Tounsi, A. (2020), "Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT", Comput. Concrete, 25(4), 343-354. https://doi.org/10.12989/CAC.2020.25.4.343
  17. Hussain, M., Naeem, M.N. and Tounsi, A. (2020), "Numerical Study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Construct., 9(3), 301-312. https://doi.org/10.12989/acc.2020.9.3.301.
  18. Hussain, M., Naeem, M.N., Shahzad, A., Taj, M., Asghar, S., Fatahi-Vajari, A. and Tounsi, A. (2020), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled functionally graded cylindrical shell", Adv. Comput. Des., 5(4), 363-380. https://doi.org/10.12989/acd.2020.5.4.363.
  19. Hussain, M. and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathem. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  20. Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C. 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095
  21. Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C. 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095
  22. Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B. Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144
  23. Hussain, M., Naeem, M.N. and Isvandzibaei, M. (2018c), "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(24), 4564-4577. https://doi.org/10.1177/0954406217753459
  24. Hussain, M., Naeem, M.N., Shahzad A, He, M. and Habib, S. (2018b), "Vibrations of rotating cylindrical shells with FGM using wave propagation approach", IMechE Part C: J. Mech. Eng. Sci., 232(23), 4342-4356. https://doi.org/10.1177/0954406218802320
  25. Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B. Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144
  26. Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C. 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095
  27. Hussain, M. and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Applied Mathematical Modeling, 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  28. Hussain, M., and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathem. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  29. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431
  30. Hajmohammad, H.M., Kolahchib, R., Sharif Zareic, M. and Malekia, M. (2018), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004.
  31. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. ttps://doi.org/10.1016/j.compstruct.2016.05.023.
  32. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of visco elastic sandwich nano plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci Technol., 66, 235-248. http://dx.doi.org/10.1016/j.ast.2017.03.016.
  33. Kolahchi, R., Hosseini, H., Esmailpour, M., (2016), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157(2016) 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032.
  34. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016.
  35. Kolahchi, R., Hosseini, H., Fakhar, M.H., Taherifar, R. and Mahmoudi, M. (2018), "A numerical method for magneto-hygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Comput. Mathemat. Applicat., 78(6), 2018-2034. https://doi.org/10.1016/j.camwa.2019.03.042.
  36. Kolahchi, R. and Kolahdouzan, F. (2021), "A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Appl. Math. Model., 91, 458-475. https://doi.org/10.1016/j.apm.2020.09.060.
  37. Kolahchi, R., Keshtegar, B. and Trung, N.T. (2021a), "Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions", Int. J. Sandw. Struct, https://doi.org/10.1177/10996362211020388.
  38. Li, X., Li, L., Hu, Y., Ding, Z. and Deng, W. (2017), "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory", Compos. Struct, 165, 250-265. https://doi.org/10.1016/j.compstruct.2017.01.032.
  39. Li, Y.H., Dong, Y.H., Qin, Y. and Lv, H.W. (2018), "Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam", Int. J. Mech. Sci., 138, 131-145. https://doi.org/10.1016/j.ijmecsci.01.041.
  40. Lei, Y., Adhikari, S. and Friswell, M.I. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004.
  41. Liu, D., Xu, W. and Xu, Y. (2012), "Dynamic responses of axially moving visco elastic beam under a randomly disordered periodicex citation", J. Sound Vib., 33, 14045-4056, https://doi.org/10.1016/j.jsv.2012.04.005.
  42. Magnucka-Blandzi, E. (2018), "Bending and buckling of a metal seven-layer beam with crosswise corrugated main core-comparative analysis with sandwich beam", Compos. Struct., 183, 35-41. https://doi.org/10.15632/jtam-pl.55.1.41.
  43. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermo elastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur J. Mech. A Solids ,65, 384e396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  44. Motezaker, M. and Kolahchi, R. (2017), "Seismic response of SiO2 nanoparticles-reinforced concrete pipes based on DQ and newmark methods", Comput. Concrete, 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745.
  45. Motezaker, M., Kolahchi, R., Rajak, D.K. and Mahmoud, S.R. (2021), "Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load", Polym. Compos, 31, https://doi.org/10.1002/pc.26118.
  46. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028.
  47. Nejati, M., Asanjarani, A., Dimitri, R. and Tornabene, F. (2017), "Static and free vibration analysis of functionaly graded conical shells reinforced by carbon nanotubes", Int. J. Mech. Sci, 130, 383-398. https://doi.org/10.1016/j.ijmecsci.2017.06.024.
  48. Qin, Y., Luo, K.R. and Yan, X. (2020), "Buckling analysis of steel plates in composite structures with novel shape function", Steel Compos. Struct., 35(3), 405-413. https://doi.org/10.12989/scs.2020.35.3.405.
  49. Ansari, R., Mohammadi, V., Shojaei, M.F., Gholami, R. and Rouhi, H. (2014), "Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory", Europ. J. Mech.-A/Solids, 45, 143-152. https://doi.org/10.1016/j.euromechsol.2013.11.002.
  50. Safaeia, B., Moradi-Dastjerdi, R. and Chu, F. (2018), "Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nano tube agglomerations", Compos. Struct, 192, 28-37. https://doi.org/10.1016/j.compstruct.2018.02.022.
  51. Shojaeian, M. and Zeighampour, H. (2016), "Size dependent pullin behavior of functionally graded sandwich nano bridges using higher order shear deformation theory", Compos. Struct., 143,117-129. https://doi.org/10.1016/j.compstruct.2016.02.008.
  52. Thai, H.T. and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Mathem. Model., 37(5), 3269-3281. https://doi.org/10.1016/j.apm.2012.08.008.
  53. Wadee, M.A., Yiatros, S. and Theofanous, M. (2010), "Comparative studies of localized buckling in sandwich struts with different core bending models", Int J Non Linear Mech., 45,111-120. https://doi.org/10.1016/j.ijnonlinmec.2009.10.001.
  54. Zeinedini, A., Shokrieh M.M. and Ebrahimi, A. (2018), "The effect of agglomeration on the fracture toughness of CNT-sreinforced nano composites", Theor. Appl. Fract. Mech, 94, 84-94, https://doi.org/10.1016/j.tafmec.2018.01.009.
  55. Hamed, E. (2012), "Bending and creep buckling response of viscoelastic functionally graded beam-columns", Compos. Struct., 94, 3043-3051. https://doi.org/10.1016/j.compstruct.2012.04.029.
  56. Simsek, M. and Reddy, J.N. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", Int. J. Eng. Sci, 64, 37-53. https://doi.org/10.1016/j.ijengsci.2012.12.002.
  57. Taherifar, R., Zareei, S.A., Rabani Bidgoli, M. and Kolahchi, R. (2021), "Application of differential quadrature and Newmark methods for dynamic response in pad concrete foundation covered by piezoelectric layer", J. Computat. Appl. Math., 382, 113075. https://doi.org/10.1016/j.cam.2020.113075.