DOI QR코드

DOI QR Code

On bending of cutout nanobeams based on nonlocal strain gradient elasticity theory

  • Alazwari, Mashhour A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
  • 투고 : 2020.01.23
  • 심사 : 2022.04.18
  • 발행 : 2022.06.25

초록

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.

키워드

과제정보

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-747-135-1443). The authors, therefore, acknowledge with thanks DSR technical and financial support.

참고문헌

  1. Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A. M. and Hendi, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  2. Abdelrahman, A.A., Mohamed, N.A. and Eltaher, M. A. (2020a), "Static bending of perforated nanobeams including surface energy and microstructure effects", Eng. Comput., 1-21. https://doi.org/10.1007/s00366-020-01149-x.
  3. Abdelrahman, A.A., Abd El Mottaleb, H.E. and Eltaher, M.A. (2020b), "On bending analysis of perforated microbeams including the microstructure effects", Struct. Eng. Mech., 76(6), 765-779. https://doi.org/10.12989/sem.2020.76.6.765.
  4. Abdelrahman, A.A., Esen, I. and Eltaher, M.A. (2021a), "Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment", Appl. Mathem. Comput., 407, 126307. https://doi.org/10.1016/j.amc.2021.126307.
  5. Abdelrahman, A.A., Esen, I., Ozarpa, C., Shaltout, R., Eltaher, M. A. and Assie, A.E. (2021b), "Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory", Smart Struct. Syst., 28(4), 515-533. https://doi.org/10.12989/sss.2021.28.4.515.
  6. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389.
  7. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.
  8. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020a), "Influence of the perforation configuration on dynamic behaviors of multilayered beam structure", Structures, 28, 1413-1426. https://doi.org/10.1016/j.istruc.2020.09.055.
  9. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020b), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35(4), 555-566. https://doi.org/10.12989/scs.2020.35.4.555.
  10. Ansari, R. and Sahmani, S. (2011), "Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories", Int. J. Eng. Sci., 49(11), 1244-1255. https://doi.org/10.1016/j.ijengsci.2011.01.007.
  11. Arefi, M., Pourjamshidian, M. and Arani, A.G. (2019), "Dynamic instability region analysis of sandwich piezoelectric nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal strain gradient theory", Steel Compos. Struct., 32(2), 157-171. https://doi.org/10.12989/scs.2019.32.2.151.
  12. Assie, A., Akbas, S.D., Bashiri, A.H., Abdelrahman, A.A. and Eltaher, M.A. (2021), "Vibration response of perforated thick beam under moving load", Europ. Phys. J. Plus, 136(3), 1-15. https://doi.org/10.1140/epjp/s13360-021-01224-2.
  13. Babaei, H. and Eslami, M.R. (2021), "Study on nonlinear vibrations of temperature-and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory", Europ. Phys. J. Plus, 136(1), 1-28. https://doi.org/10.1140/epjp/s13360-020-00959-8.
  14. Bourouina, H., Yahiaoui, R., Sahar, A. and Benamar, M.E.A. (2016), "Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads", Physica E, 75, 163-168. https://doi.org/10.1016/j.physe.2015.09.014.
  15. Bourouina, H., Yahiaoui, R., Kerid, R., Ghoumid, K., Lajoie, I., Picaud, F. and Herlem, G. (2020), "The influence of hole networks on the adsorption-induced frequency shift of a perforated nanobeam using non-local elasticity theory", J. Phys. Chemistry Solids, 136, 109201. https://doi.org/10.1016/j.jpcs.2019.109201.
  16. Chan, J., Eichenfield, M., Camacho, R. and Painter, O. (2009), "Optical and mechanical design of a "zipper" photonic crystal optomechanical cavity", Optics Express, 17(5), 3802-3817. https://doi.org/10.1364/OE.17.003802.
  17. Chen, S.X., Sahmani, S. and Safaei, B. (2021), "Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling", Eng. Comput., 37(2), 1657-1678. https://doi.org/10.1007/s00366-021-01303-z.
  18. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36(6), 643-656. https://doi.org/10.12989/scs.2020.36.6.643.
  19. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11(7), 3250. https://doi.org/10.3390/app11073250.
  20. Diyaroglu, C., Madenci, E. and Phan, N.D. (2020), "Peridynamic modeling of perforated structures in a finite element framework", In AIAA Scitech., 0967.
  21. Dougherty, B.K. (1981), "Buckling of web posts in perforated beams", J. Struct. Div., 107(3), 507-519. https://doi.org/10.1061/JSDEAG.0005661.
  22. Duan, L., Zhao, J. and Zou, J. (2022), "Generalized beam theorybased advanced beam finite elements for linear buckling analyses of perforated thin-walled members", Comput. Struct., 259, 106683. https://doi.org/10.1016/j.compstruc.2021.106683.
  23. Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018a), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsyst. Technol., 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3.
  24. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018b), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.
  25. Eltaher, M.A. and Norhan A. Mohamed. (2020), "Vibration of nonlocal perforated nanobeams under general boundary conditions", Smart Struct. Syst., 25(4), 510-514. https://doi.org/10.12989/sss.2020.25.4.501.
  26. Eltaher, M.A. and Abdelrahman, A.A. (2020), "Bending behavior of squared cutout nanobeams incorporating surface stress effects", Steel Compos. Struct, 36(2), 143-161. https://doi.org/10.12989/scs.2020.36.2.143.
  27. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and A.E. Alshorbagy. (2020a), "Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts", Smart Struct. Syst., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219.
  28. Eltaher, M.A., Omar, F.A., Abdalla, W.S., Kabeel, M.A. and Alshorbagy, A.E. (2020b), "Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects", Struct. Eng. Mech., 76(1), 141-151. https://doi.org/10.12989/sem.2020.76.1.141.
  29. Eltaher, M.A., Mohamed, N. and Mohamed, S.A. (2020c), "Nonlinear buckling and free vibration of curved CNTs by doublet mechanics", Smart Struct. Syst., 26(2), 213-226. https://doi.org/10.12989/sss.2020.26.2.213.
  30. Eltaher, M.A., Abdelmoteleb, H.E., Daikh, A.A. and Abdelrahman, A.A. (2021a), "Vibrations and stress analysis of rotating perforated beams by using finite elements method", Steel Compos. Struct., 41(4), 505-520. https://doi.org/10.12989/scs.2021.41.4.505.
  31. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  32. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17(3), 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  33. Faraji Oskouie, M., Ansari, R. and Rouhi, H. (2021), "Bending analysis of nanoscopic beams based upon the strain-driven and stress-driven integral nonlocal strain gradient theories", J. Brazil. Soc. Mech. Sci. Eng., 43(3), 1-14. https://doi.org/10.1007/s40430-020-02782-9.
  34. Farrokhabadi, A., Mohebshahedin, A., Rach, R. and Duan, J.S. (2016), "An improved model for the cantilever NEMS actuator including the surface energy, fringing field and Casimir effects", Physica E: Low-Dimens. Syst. Nanostruct., 75, 202-209. https://doi.org/10.1016/j.physe.2015.09.033.
  35. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  36. Hamed, M.A., Mohamed, N. and Eltaher, M.A. (2022), "Stability buckling and bending of nanobeams including cutouts", Eng. Comput., 38, 209-230. https://doi.org/10.1007/s00366-020-01063-2.
  37. Hashemian, M., Foroutan, S. and Toghraie, D. (2019), "Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects", Mech. Mater., 139, 103209. https://doi.org/10.1016/j.mechmat.2019.103209.
  38. Hutchinson, J. and Fleck, N. (1997), "Strain gradient plasticity", Adv. Appl. Mech., 33, 295-361. https://doi.org/10.1016/S0065-2156(08)70388-0.
  39. Jeong, K.H. and Amabili, M. (2006), "Bending vibration of perforated beams in contact with a liquid", J. Sound Vib., 298(1-2), 404-419. https://doi.org/10.1016/j.jsv.2006.05.029.
  40. Kerid, R., Bourouina, H., Yahiaoui, R., Bounekhla, M. and Aissat, A. (2019), "Magnetic field effect on nonlocal resonance frequencies of structure-based filter with periodic square holes network", Physica E: Low-Dimen. Syst. Nanostruct., 105, 83-89. https://doi.org/10.1016/j.physe.2018.05.021.
  41. Kerid, R. and Bounnah, Y. (2021), "Effects of structure design on electrostatic pull-in voltage of perforated nanoswitch with intermolecular surface forces", J. Ultrafine Grained Nanostruct. Mater., 54(2), 219-227. https://doi.org/10.22059/JUFGNSM.2021.02.11.
  42. Keivani, M., Koochi, A., Sedighi, H.M., Abadyan, M., Farrokhabadi, A. and Shahedin, A.M. (2016), "Effect of surface layer on electromechanical stability of tweezers and cantilevers fabricated from conductive cylindrical nanowires", Surface Rev. Lett., 23(02), 1550101. https://doi.org/10.1142/S0218625X15501012.
  43. Kim, J.H., Jeon, J.H., Park, J.S., Seo, H.D., Ahn, H.J. and Lee, J. M. (2015), "Effect of reinforcement on buckling and ultimate strength of perforated plates", Int. J. Mech. Sci., 92, 194-205. https://doi.org/10.1016/j.ijmecsci.2014.12.016
  44. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013.
  45. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.
  46. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021.
  47. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation" J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  48. Lu, L., Guo, X. and Zhao, J. (2017), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006.
  49. Luschi, L. and Pieri, F. (2014), "An analytical model for the determination of resonance frequencies of perforated beams", J. Micromech. Microeng., 24(5), 055004. https://doi.org/10.1088/0960-1317/24/5/055004.
  50. Luschi, L. and Pieri, F. (2016), "An analytical model for the resonance frequency of square perforated Lame-mode resonators", Sensors Actuators B: Chemical, 222, 1233-1239. https://doi.org/10.1016/j.snb.2015.07.085.
  51. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022), "Free vibration of FGCNTRCs nano-plates/shells with temperature-dependent Properties", Mathematics, 10(4), 583. https://doi.org/10.3390/math10040583.
  52. Merzouki, T., Ahmed, H.M.S., Bessaim, A., Haboussi, M., Dimitri, R. and Tornabene, F. (2022), "Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory", Mathem. Mech. Solids, 27(1), 66-92. https://doi.org/10.1177/10812865211011759.
  53. Mohebshahedin, A. and Farrokhabadi, A. (2015), "The influence of the surface energy on the instability behavior of NEMS structures in presence of intermolecular attractions", Int. J. Mech. Sci., 101, 437-448. https://doi.org/10.1016/j.ijmecsci.2015.08.017.
  54. Rashidpour, P., Ghadiri, M. and Zajkani, A. (2021), "The response of viscoelastic composite laminated microplate under lowvelocity impact based on nonlocal strain gradient theory for different boundary conditions", Steel Compos. Struct., 41(3), 335-351. https://doi.org/10.12989/scs.2021.41.3.335
  55. Sahmani, S. and Safaei, B. (2019), "Nonlocal strain gradient nonlinear resonance of bi-directional functionally graded composite micro/nano-beams under periodic soft excitation", Thin-Wall. Struct., 143, 106226. https://doi.org/10.1016/j.tws.2019.106226.
  56. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082.
  57. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179.
  58. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin-Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  59. Simsek, M. (2019)., "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Structures, 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.
  60. Smith, F.H. and Moen, C.D. (2014), "Finite strip elastic buckling solutions for thin-walled metal columns with perforation patterns", Thin-Wall. Struct., 79, 187-201. https://doi.org/10.1016/j.tws.2014.02.009.
  61. Staszak, N., Gajewski, T. and Garbowski, T. (2022), "Shell-toBeam Numerical Homogenization of 3D Thin-Walled Perforated Beams", Materials, 15(5), 1827. https://doi.org/10.3390/ma15051827.
  62. Toupin, R. (1962), "Elastic materials with couple-stresses", Archive Rational Mech. Anal., 11(1), 385-414. https://doi.org/10.1007/BF00253945.
  63. Tsavdaridis, K.D. and D'Mello, C. (2011), "Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes", J. Construct. steel Res., 67(10), 1605-1620. https://doi.org/10.1016/j.jcsr.2011.04.004.
  64. Tsavdaridis, K.D., Lau, C.K. and Alonso-Rodriguez, A. (2021), "Experimental behaviour of non-seismical RWS connections with perforated beams under cyclic actions", J. Construct. Steel Res., 183, 106756. https://doi.org/10.1016/j.jcsr.2021.106756.
  65. Wang, A.J. and Chung, K.F. (2008), "Advanced finite element modelling of perforated composite beams with flexible shear connectors", Eng. Struct., 30(10), 2724-2738. https://doi.org/10.1016/j.engstruct.2008.03.001.
  66. Wang, S., Kang, W., Yang, W., Zhang, Z., Li, Q., Liu, M. and Wang, X. (2022), "Hygrothermal effects on buckling behaviors of porous bi-directional functionally graded micro-/nanobeams using two-phase local/nonlocal strain gradient theory", Europ. J. Mech.-A/Solids, 104554. https://doi.org/10.1016/j.euromechsol.2022.104554.
  67. Xia, W., Wang, L. and Yin, L. (2010), "Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration", Int. J. Eng. Science, 48(12), 2044-2053. https://doi.org/10.1016/j.ijengsci.2010.04.010
  68. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress-based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  69. Zeytinci, B.M., Sahin, M., Guler, M.A. and Tsavdaridis, K.D. (2021), "A practical design formulation for perforated beams with openings strengthened with ring type stiffeners subject to Vierendeel actions", J. Build. Eng., 43, 102915. https://doi.org/10.1016/j.jobe.2021.102915.
  70. Zulkefli, M.A., Mohamed, M.A., Siow, K.S., Majlis, B.Y., Kulothungan, J., Muruganathan, M. and Mizuta, H. (2018), "Stress analysis of perforated graphene nano-electro-mechanical (NEM) contact switches by 3D finite element simulation", Microsyst. Technol., 24(2), 1179-1187. https://doi.org/10.1007/s00542-017-3483-9.