Steel and Composite Structures

  • 제36권3호
  • /
  • Pages.293-305
  • /
  • 2020
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models

  • Ghandourh, Emad E. (Mining Engineering Dept., Faculty of Engineering, King Abdulaziz University) ;
  • Abdraboh, Azza M. (Physics Department, Faculty of Science, Banha University)
  • 투고 : 2020.04.30
  • 심사 : 2020.07.07
  • 발행 : 2020.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

키워드

과제정보

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-296-135-1440). The authors, therefore, gratefully acknowledge DSR technical and financial support.

참고문헌

  1. Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963.
  2. Agwa, M.A. and Eltaher, M.A. (2016), "Vibration of a carbyne nanomechanical mass sensor with surface effect", Appl. Phys. A, 122(4), 335. https://doi.org/10.1007/s00339-016-9934-9.
  3. Akbas, S.D. (2015), "Free vibration and bending of functionally graded beams resting on elastic foundation", Research on Engineering Structures and Materials, 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107
  4. Akbas, S.D. (2017a), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009.
  5. Akbas, S.D. (2017b), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764.
  6. Akbas, S.D. (2017c), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.
  7. Akbas, S.D. (2017d), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
  8. Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39. https://doi.org/10.12989/anr.2018.6.1.039.
  9. Akbas, S.D. (2018b), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059.
  10. Akbas, S.D. (2018c), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  11. Akbas, S.D. (2019a), "Longitudinal forced vibration analysis of porous a nanorod", Muhendislik Bilimleri ve Tasarim Dergisi, 7(4), 736-743. https://doi.org/10.21923/jesd.553328
  12. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupled Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.
  13. Akbas, S.D. (2019c), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459
  14. Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load", Eng. with Comput., https://doi.org/10.1007/s00366-020-01070-3.
  15. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "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.
  16. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi:10.1016/j.apm.2010.07.006.
  17. Amar, L.H.H., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/sem.2017.64.5.527.
  18. Apuzzo, A., Barretta, R., Luciano, R., de Sciarra, F.M. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model", Compos. Part B: Eng., 123, 105-111. https://doi.org/10.1016/j.compositesb.2017.03.057.
  19. Aria, A.I. and Friswell, M.I. (2019), "A nonlocal finite element model for buckling and vibration of functionally graded nanobeams", Compos. Part B: Eng., 166, 233-246. https://doi.org/10.1016/j.compositesb.2018.11.071.
  20. Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Dynamic analysis of layered functionally graded viscoelastic deep beams with different boundary conditions due to a pulse load", Int. J. Appl. Mech., https://doi.org/10.1142/S1758825120500556.
  21. Bambaeechee, M. (2019), "Free vibration of AFG beams with elastic end restraints", Steel Compos. Struct., 33(3), 403-432. https://doi.org/10.12989/scs.2019.33.3.403.
  22. Barretta, R., Canadija, M., Feo, L., Luciano, R., de Sciarra, F.M., and Penna, R. (2018), "Exact solutions of inflected functionally graded nano-beams in integral elasticity", Compos. Part B: Eng., 142, 273-286. https://doi.org/10.1016/j.compositesb.2017.12.022.
  23. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.
  24. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  25. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205.
  26. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Mathematics Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090.
  27. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013a), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030. .
  28. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013b), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039.
  29. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013c), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016.
  30. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014a), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.
  31. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014b), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.
  32. Eltaher, M.A. and Agwa, M.A. (2016), "Analysis of size-dependent mechanical properties of CNTs mass sensor using energy equivalent model", Sensor. Actuat. A: Phys., 246, 9-17. https://doi.org/10.1016/j.sna.2016.05.009.
  33. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016a), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. ttps://doi.org/10.1016/j.apm.2015.11.026.
  34. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016b), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51. https://doi.org/10.12989/anr.2016.4.1.051.
  35. Eltaher, M.A., El-Borgi, S. and Reddy, J.N. (2016c). "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013.
  36. Eltaher, M.A., Attia, M.A., Soliman, A.E. and Alshorbagy, A.E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097.
  37. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.
  38. Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018c), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsystem Technologies, 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3.
  39. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018d), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsystem Technologies, 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.
  40. Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  41. Eltaher, M.A., Omar, F.A., Abdalla, W.S. and Gad, E.H. (2019a), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Waves in Random and Complex Media, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693.
  42. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019b), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039.
  43. Eltaher, M.A. and Mohamed, N.A. (2020a), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart Struct. Syst., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501.
  44. Eltaher, M.A. and Mohamed, N. (2020b), "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
  45. Eltaher, M.A. and Mohamed, S.A. (2020c), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.
  46. 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.
  47. Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Nonlocal nonlinear dynamic behavior of composite piezo-magnetic beams using a refined higher-order beam theory", Steel Compos. Struct., 35(4), 545-554. https://doi.org/10.12989/scs.2020.35.4.545.
  48. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037.
  49. Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999.
  50. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115.
  51. Gul, U. and Aydogdu, M. (2018), Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics", Compos. Part B: Eng., 137, 60-73. https://doi.org/10.1016/j.compositesb.2017.11.005.
  52. Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.
  53. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.
  54. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020a), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  55. Hamed M.A., Abu-bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020b), "Influence of Axial Load Function and Optimization on Static Stability of Sandwich Functionally Graded Beams with Porous Core", Eng. with Comput.. https://doi.org/10.1007/s00366-020-01023-w.
  56. Heydari, A. (2018), "Exact vibration and buckling analyses of arbitrary gradation of nano-higher order rectangular beam", Steel Compos. Struct., 28(5), 589-606. https://doi.org/10.12989/scs.2018.28.5.589 .
  57. Jandaghian, A.A. and Rahmani, O. (2017), "Vibration analysis of FG nanobeams based on third-order shear deformation theory under various boundary conditions", Steel Compos. Struct., 25(1), 67-78. https://doi.org/10.12989/scs.2017.25.1.067.
  58. Karami, B., Janghorban, M. and Rabczuk, T. (2020), "Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory", Compos. Part B: Eng., 182, 107622. https://doi.org/10.1016/j.compositesb.2019.107622.
  59. Khater, M.E., Eltaher, M.A., Abdel-Rahman, E. and Yavuz, M. (2014), "Surface and thermal load effects on the buckling of curved nanowires", Eng. Sci. Technol. Int. J., 17(4), 279-283. https://doi.org/10.1016/j.jestch.2014.07.003.
  60. Khatir, S., Tiachacht, S., Thanh, C.L., Bui, T.Q. and Wahab, M.A. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  61. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. http://dx.doi.org/10.1016/j.matdes.2016.12.061.
  62. Lee, J.C. and Ahn, S.H. (2018), "Bulk density measurement of porous functionally graded materials", Int. J. Precision Eng. Manufact., 19(1), 31-37. DOI: 10.1007/s12541-018-0004-4.
  63. Liu, H., Lv, Z. and Wu, H. (2019), "Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory", Compos. Struct., 214, 47-61. https://doi.org/10.1016/j.compstruct.2019.01.090.
  64. Matula, I., Dercz, G. and Barczyk, J. (2019), "Titanium/Zirconium functionally graded materials with porosity gradients for potential biomedical applications", Mater. Sci. Technol., 1-6. https://doi.org/10.1080/02670836.2019.1593603.
  65. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Bourada, F. and Tounsi, A. (2019), "Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution", Struct. Eng. Mech., 72(4), 513-524. https://doi.org/10.12989/sem.2019.72.4.513.
  66. Melaibari, A., Khoshaim, A. B., Mohamed, S.A. and Eltaher, M. A. (2020), "Static stability and of symmetric and sigmoid functionally graded beam under variable axial load", Steel Compos. Struct., 35(5), 671-685. https://doi.org/10.12989/scs.2020.35.5.671.
  67. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  68. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (Eds.). (2013), "Functionally graded materials: design, processing and applications" (Vol. 5), Springer Science & Business Media.
  69. Mirzaei, M.M.H., Loghman, A. and Arefi, M. (2019), "Time-dependent creep analysis of a functionally graded beam with trapezoidal cross section using first-order shear deformation theory", Steel Compos. Struct., 30(6), 567-576. https://doi.org/10.12989/scs.2019.30.6.567.
  70. Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model", Eng. with Comput., 1-14. https://doi.org/10.1007/s00366-020-00976-2.
  71. Nguyen, D.K. and Tran, T.T. (2018), "Free vibration of tapered BFGM beams using an efficient shear deformable finite element model", Steel Compos. Struct., 29(3), 363-377. https://doi.org/10.12989/scs.2018.29.3.363.
  72. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Method. Appl. M., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002.
  73. Phung-Van, P., Ferreira, A.J.M., Nguyen-Xuan, H. and Wahab, M. A. (2017a), "An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates", Compos. Part B: Eng., 118, 125-134. https://doi.org/10.1016/j.compositesb.2017.03.012.
  74. Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H. and Abdel-Wahab, M. (2017b), "Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads", Nonlinear Dynam., 87(2), 879-894. https://doi.org/10.1007/s11071-016-3085-6.
  75. Phung-Van, P., Thanh, C.L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2018), "Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments", Compos. Struct., 201, 882-892. https://doi.org/10.1016/j.compstruct.2018.06.087.
  76. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2019), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B: Eng., 164, 215-225. https://doi.org/10.1016/j.compositesb.2018.11.036.
  77. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003.
  78. Rahmani, O., Hosseini, S.A.H., Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., 26(5), 607-20. https://doi.org/10.12989/scs.2018.26.5.607.
  79. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  80. Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59(11), 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008.
  81. Shaat, M., Eltaher, M.A., Gad, A.I. and Mahmoud, F.F. (2013), "Nonlinear size-dependent finite element analysis of functionally graded elastic tiny-bodies", Int. J. Mech. Sci., 77, 356-364. https://doi.org/10.1016/j.ijmecsci.2013.04.015.
  82. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038.
  83. Simsek, M. (2016), "Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach", Int. J. Eng. Sci., 105, 12-27. https://doi.org/10.1016/j.ijengsci.2016.04.013.
  84. 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. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.
  85. Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.
  86. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011.
  87. Thang, P.T., Nguyen-Thoi, T., Lee, D., Kang, J. and Lee, J. (2018), "Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions", Aerosp. Sci. Technol., 79, 278-287. https://doi.org/10.1016/j.ast.2018.06.010.
  88. Thanh, C.L., Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Wahab, M.A. (2018), "Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory", Compos. Struct., 184, 633-649. https://doi.org/10.1016/j.compstruct.2017.10.025.
  89. Thanh, C.L., Ferreira, A.J.M. and Wahab, M.A. (2019a), "A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis", Thin-Wall. Struct., 145, 106427. https://doi.org/10.1016/j.tws.2019.106427.
  90. Thanh, C.L., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019b), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Method. Appl. M., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  91. Thanh, C.L., Tran, L.V., Vu-Huu, T., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019c), "Size-dependent nonlinear analysis and damping responses of FG-CNTRC micro-plates", Comput. Method. Appl. M., 353, 253-276. https://doi.org/10.1016/j.cma.2019.05.002.
  92. Thanh, C.L., Tran, L.V., Bui, T.Q., Nguyen, H.X. and Abdel-Wahab, M. (2019d), "Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates", Compos. Struct., 221, 110838. https://doi.org/10.1016/j.compstruct.2019.04.010.
  93. Trabelssi, M., El-Borgi, S., Ke, L. L., & Reddy, J. N. (2017), "Nonlocal free vibration of graded nanobeams resting on a nonlinear elastic foundation using DQM and LaDQM", Compos. Struct., 176, 736-747. https://doi.org/10.1016/j.compstruct.2017.06.010.
  94. Wang, Y.Q., Wan, Y.H. and Zhang, Y.F. (2017), "Vibrations of longitudinally traveling functionally graded material plates with porosities", Eur. J. Mech.-A/Solids, 66, 55-68. http://dx.doi.org/10.1016/j.euromechsol.2017.06.006.
  95. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  96. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  97. Yousfi, M., Atmane, H.A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66(3), 353-368. https://doi.org/10.12989/sem.2018.66.3.353.
  98. Yuksel, Y.Z. and Akbas, S.D. (2019), "Buckling analysis of a fiber reinforced laminated composite plate with porosity", J. Comput. Appl. Mech., 50(2), 375-380. 10.22059/JCAMECH.2019.291967.448.
  99. Zhang, Y. and Wang, J. (2017), "Fabrication of functionally graded porous polymer structures using thermal bonding lamination techniques", Procedia Manufact., 10, 866-875. https://doi.org/10.1016/j.promfg.2017.07.073.
  100. Zhao, X., Zheng, S. and Li, Z. (2020), "Effects of porosity and flexoelectricity on static bending and free vibration of AFG piezoelectric nanobeams", Thin-Wall. Struct., 151, 106754. https://doi.org/10.1016/j.tws.2020.106754.

피인용 문헌

  1. Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory vol.37, pp.6, 2020, https://doi.org/10.12989/scs.2020.37.6.695
  2. Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation vol.38, pp.1, 2020, https://doi.org/10.12989/scs.2021.38.1.001
  3. Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method vol.27, pp.1, 2020, https://doi.org/10.12989/cac.2021.27.1.073
  4. Static analysis of cutout microstructures incorporating the microstructure and surface effects vol.38, pp.5, 2020, https://doi.org/10.12989/scs.2021.38.5.583
  5. Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.051
  6. Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory vol.39, pp.1, 2020, https://doi.org/10.12989/scs.2021.39.1.095
  7. On the free vibration response of laminated composite plates via FEM vol.39, pp.2, 2020, https://doi.org/10.12989/scs.2021.39.2.149
  8. An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells vol.40, pp.2, 2020, https://doi.org/10.12989/scs.2021.40.2.307
  9. A n-order refined theory for free vibration of sandwich beams with functionally graded porous layers vol.79, pp.3, 2020, https://doi.org/10.12989/sem.2021.79.3.279
  10. Mechanical and thermal buckling analysis of laminated composite plates vol.40, pp.5, 2020, https://doi.org/10.12989/scs.2021.40.5.697