Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic analysis of nanotube-based nanodevices for drug delivery in sports-induced varied conditions applying the modified theories

  • Shaopeng Song (Sports Center, Xi'an Jiaotong University) ;
  • Tao Zhang (College of Physical Education, Shaanxi University of Technology) ;
  • Zhiewn Zhui (Center of excellence in design and manufacturing)
  • Received : 2022.02.24
  • Accepted : 2023.10.10
  • Published : 2023.12.10
⟨ Previous Next ⟩

Abstract

In the realm of nanotechnology, the nonlocal strain gradient theory takes center stage as it scrutinizes the behavior of spinning cantilever nanobeams and nanotubes, pivotal components supporting various mechanical movements in sport structures. The dynamics of these structures have sparked debates within the scientific community, with some contending that nonlocal cantilever models fail to predict dynamic softening, while others propose that they can indeed exhibit stiffness softening characteristics. To address these disparities, this paper investigates the dynamic response of a nonlocal cantilever cylindrical beam under the influence of external discontinuous dynamic loads. The study employs four distinct models: the Euler-Bernoulli beam model, Timoshenko beam model, higher-order beam model, and a novel higher-order tube model. These models account for the effects of functionally graded materials (FGMs) in the radial tube direction, giving rise to nanotubes with varying properties. The Hamilton principle is employed to formulate the governing differential equations and precise boundary conditions. These equations are subsequently solved using the generalized differential quadrature element technique (GDQEM). This research not only advances our understanding of the dynamic behavior of nanotubes but also reveals the intriguing phenomena of both hardening and softening in the nonlocal parameter within cantilever nanostructures. Moreover, the findings hold promise for practical applications, including drug delivery, where the controlled vibrations of nanotubes can enhance the precision and efficiency of medication transport within the human body. By exploring the multifaceted characteristics of nanotubes, this study not only contributes to the design and manufacturing of rotating nanostructures but also offers insights into their potential role in revolutionizing drug delivery systems.

Keywords

Acknowledgement

Research on the Design and Implementation of Taijiquan Exercise Prescription for Sub healthy College Students, Science and Technology Department of Shaanxi University of Technology SLGKY2017.

References

  1. Akbas, S.D. (2018), "Bending of a cracked functionally graded nanobeam", Advances Nano Res., 6(3), 219. http://dx.doi.org/10.12989/anr.2018.6.3.219.
  2. Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39. http://dx.doi.org/10.12989/anr.2018.6.1.039.
  3. Alimoradlu, K. and Zamani, A. (2022), "Hydrophobicity in nanocatalysis", Adv. Nano Res., 12(1), 49-63. http://dx.doi.org/10.12989/ANR.2022.12.1.049.
  4. Allahkarami, F., Nikkhah-Bahrami, M. and Saryazdi, M.G. (2017), "Damping and vibration analysis of viscoelastic curved microbeam reinforced with FG-CNTs resting on viscoelastic medium using strain gradient theory and DQM", Steel Compos. Struct., 25(2), 141-155. https://doi.org/10.12989/scs.2017.25.2.141.
  5. Alsultan Abdulmajeed, S. (2021), "Assessment of microstructure and surface effects on vibrational characteristics of public transportation", Adv. Nano Res., 11(1), 101-113. http://dx.doi.org/10.12989/ANR.2021.11.1.101.
  6. Arefi, M. and Zenkour, A.M. (2018), "Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory", Steel Compos. Struct., 26(4), 421-437. https://doi.org/10.12989/scs.2018.26.4.421.
  7. Atmane Hassen, A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. http://dx.doi.org/10.12989/SCS.2015.19.2.369.
  8. Attia, A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. http://dx.doi.org/10.12989/SCS.2015.18.1.187.
  9. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. http://dx.doi.org/10.12989/SCS.2019.30.6.603.
  10. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257. http://dx.doi.org/10.12989/anr.2018.6.3.257.
  11. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2016), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A. 123(1), 104. https://doi.org/10.1007/s00339-016-0712-5.
  12. Bamdad, M., Mohammadimehr, M. and Alambeigi, K. (2020), "Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov's foundation", Steel Compos. Struct., 36(6), 671-687. http://dx.doi.org/10.12989/SCS.2020.36.6.671.
  13. Behdinan, K. and Moradi-Dastjerdi, R. (2022), "Thermal buckling resistance of a lightweight lead-free piezoelectric nanocomposite sandwich plate", Adv. Nano Res., 12(6), 593-603. http://dx.doi.org/10.12989/ANR.2022.12.6.593.
  14. Bellifa, H., Bakora, A., Tounsi, A., Bousahla Abdelmoumen, A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. http://dx.doi.org/10.12989/SCS.2017.25.3.257.
  15. Belmin, J. and Valensi, P. (2003), "Novel Drug Delivery Systems for Insulin", Drugs Aging. 20(4), 303-312. https://doi.org/10.2165/00002512-200320040-00006.
  16. Bennai, R., Atmane Hassen, A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. http://dx.doi.org/10.12989/SCS.2015.19.3.521.
  17. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279. http://dx.doi.org/10.12989/anr.2018.6.3.279.
  18. Cao, C., Wang, J., Kwok, D., Cui, F., Zhang, Z., Zhao, D., Li, M.J. and Zou, Q. (2022), "webTWAS: a resource for disease candidate susceptibility genes identified by transcriptome-wide association study", Nucleic Acids Res., 50(D1), D1123-D1130. https://doi.org/10.1093/nar/gkab957.
  19. Cao, Y., Xu, N., Wang, H., Zhao, X. and Ahmad, A.M. (2023), "Neural networks-based adaptive tracking control for full-state constrained switched nonlinear systems with periodic disturbances and actuator saturation", Int. J. Syst. Sci., 54(14), 2689-2704. https://doi.org/10.1080/00207721.2023.2241959.
  20. Chaht Fouzia, L., Kaci, A., Houari Mohammed Sid, A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. http://dx.doi.org/10.12989/SCS.2015.18.2.425.
  21. Dai, W., Zand, Y., Sadighi, A.A., Selmi, A., Roco-Videla, A., Wakil, K. and Issakhov, A. (2021), "The economic and management use of rhododendron petals in potas-sium-ion nano batteries anode via efficient computer simulation", Adv. Nano Res., 10(6), 517-529. http://dx.doi.org/10.12989/ANR.2021.10.6.517.
  22. Dehghanbanadaki, A., Rashid, A.S.A., Ahmad, K., Yunus, N.Z.M. and Said, K.N.M. (2022), "A computational estimation model for the subgrade reaction modulus of soil improved with DCM columns", Geomech. Eng., 28(4), 385. https://doi.org/10.12989/gae.2022.28.4.385.
  23. Du, S., Xie, H., Yin, J., Sun, Y., Wang, Q., Liu, H., Qi, W., Cai, C., Bi, G., Xiao, D., Chen, W., Shen, X., Yin, W.-Y. and Zheng, R. (2023), "Giant hot electron thermalization via stacking of graphene layers", Carbon. 203, 835-841. https://doi.org/10.1016/j.carbon.2022.12.017.
  24. Ebrahimi, F., Kokaba, M., Shaghaghi, G. and Selvamani, R. (2020), "Dynamic characteristics of hygro-magneto-thermo-electrical nanobeam with non-ideal boundary conditions", Adv. Nano Res., 8(2), 169-182. https://doi.org/10.12989/anr.2020.8.2.169.
  25. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., 5(2), 141. http://dx.doi.org/10.12989/anr.2017.5.2.141.
  26. Eringen, A.C.A. and Wegner, J.L.R. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56(2), B20-B22. https://doi.org/10.1115/1.1553434.
  27. Esen, I. (2019), "Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass", Int. J. Mech. Sci., 153-154 21-35. https://doi.org/10.1016/j.ijmecsci.2019.01.033.
  28. 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.
  29. 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.
  30. Ghadiri, M., Shafiei, N., Salekdeh, S.H., Mottaghi, P. and Mirzaie, T. (2016), "Investigation of the dental implant geometry effect on stress distribution at dental implant-bone interface", J. Brazil. Soc. Mech. Sci. Eng., 38(2), 335-343. https://doi.org/10.1007/s40430-015-0472-8.
  31. Hamidi, A., Houari, M.S.A., Mahmoud, S. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235.
  32. Houari Mohammed Sid, A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. http://dx.doi.org/10.12989/SCS.2016.22.2.257.
  33. Huang, Y., Karami, B., Shahsavari, D. and Tounsi, A. (2021), "Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels", Archiv. Civil Mech. Eng., 21(4), 139. https://doi.org/10.1007/s43452-021-00291-7.
  34. Jaber, N., Ramini, A. and Younis, M.I. (2016), "Multifrequency excitation of a clamped-clamped microbeam: Analytical and experimental investigation", Microsyst. Nanoeng., 2(1), 16002. https://doi.org/10.1038/micronano.2016.2.
  35. Jia, A., Liu, H., Ren, L., Yun, Y. and Tahouneh, V. (2020), "Influence of porosity distribution on vibration analysis of GPLs-reinforcement sectorial plate", Steel Compos. Struct., 35(1), 111-127. http://dx.doi.org/10.12989/SCS.2020.35.1.111.
  36. Jindal, A.B., Bhide, A.R., Salave, S., Rana, D. and Benival, D. (2023), "Long-acting parenteral drug delivery systems for the treatment of chronic diseases", Adv. Drug Delivery Rev., 198, 114862. https://doi.org/10.1016/j.addr.2023.114862.
  37. Kar Vishesh, R. and Panda Subrata, K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. http://dx.doi.org/10.12989/SCS.2015.18.3.693.
  38. Kar, V.R. and Panda, S.K. (2017), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Thermal Stresses. 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118.
  39. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2009), "Static and dynamic analysis of micro beams based on strain gradient elasticity theory", Int. J. Eng. Sci., 47(4), 487-498. https://doi.org/10.1016/j.ijengsci.2008.08.008.
  40. Lei, X., Li, Z., Zhong, Y., Li, S., Chen, J., Ke, Y., Lv, S., Huang, L., Pan, Q., Zhao, L., Yang, X., Chen, Z., Deng, Q. and Yu, X. (2022), "Gli1 promotes epithelial-mesenchymal transition and metastasis of non-small cell lung carcinoma by regulating snail transcriptional activity and stability", Acta Pharmaceutica Sinica B. 12(10), 3877-3890. https://doi.org/10.1016/j.apsb.2022.05.024.
  41. Liu, B., Zhou, H., Jin, H., Zhu, J., Wang, Z., Hu, C., Liang, L., Mu, S. and He, D. (2021), "A new strategy to access Co/N co-doped carbon nanotubes as oxygen reduction reaction catalysts", Chinese Chemical Lett., 32(1), 535-538. https://doi.org/10.1016/j.cclet.2020.04.002.
  42. Liu, Y., Lv, R., Sun, S., Tan, D., Dong, F., Golubev, Y.A., Nie, X., Kotova, O.B., Liu, J. and Wang, K. (2022), "High-performance cascade nanoreactor based on halloysite nanotubes-integrated enzyme-nanozyme microsystem", Chinese Chemical Lett., 33(2), 807-811. https://doi.org/10.1016/j.cclet.2021.06.087.
  43. Lu, S., Yang, B., Xiao, Y., Liu, S., Liu, M., Yin, L. and Zheng, W. (2023), "Iterative reconstruction of low-dose CT based on differential sparse", Biomedical Signal Processing Control. 79, 104204. https://doi.org/10.1016/j.bspc.2022.104204.
  44. Luan, D., Liu, A., Wang, X., Xie, Y. and Wu, Z. (2022), "Robust Two-Stage Location Allocation for Emergency Temporary Blood Supply in Postdisaster", Discrete Dyn. Nature Soc., 2022, 6184170. https://doi.org/10.1155/2022/6184170.
  45. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E., Tounsi, A., Mahmoud, S., Tounsi, A. and Benrahou, K. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Advances Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  46. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla Abdelmoumen, A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compo. Struct., 32(5), 595-610. http://dx.doi.org/10.12989/SCS.2019.32.5.595.
  47. Miao, Y., Wang, X., Wang, S. and Li, R. (2023), "Adaptive Switching Control Based on Dynamic Zero-Moment Point for Versatile Hip Exoskeleton Under Hybrid Locomotion", IEEE Transact. Ind. Electron., 70(11), 11443-11452. https://doi.org/10.1109/TIE.2022.3229343.
  48. Mirjavadi Seyed, S., Forsat, M., Barati Mohammad, R. and Hamouda, A.M.S. (2020), "Post-buckling of higher-order stiffened metal foam curved shells with porosity distributions and geometrical imperfection", Steel Compos. Struct., 35(4), 567-578. http://dx.doi.org/10.12989/SCS.2020.35.4.567.
  49. Mohammadi, A., Ebadi, T. and Boroomand, M.R. (2020), "Interface shear between different oil-contaminated sand and construction materials", Geomech. Eng., 20(4), 299. https://doi.org/10.12989/gae.2020.20.4.299.
  50. Mousavi, S.M., Shafiei, N. and Dadvand, A. (2017), "Numerical simulation of subsonic turbulent flow over NACA0012 airfoil: evaluation of turbulence models", Sigma J. Eng. Nat. Sci., 35(1), 133-155. https://dergipark.org.tr/en/pub/sigma/issue/65585/1016455. 1016455
  51. Navi, B.R., Mohammadimehr, M. and Arani, A.G. (2019), "Active control of three-phase CNT/resin/fiber piezoelectric polymeric nanocomposite porous sandwich microbeam based on sinusoidal shear deformation theory", Steel Compos. Struct., 32(6), 753-767. https://doi.org/10.12989/scs.2019.32.6.753.
  52. Omidi, S., Oskooee, M.B. and Shafiei, N. (2013), "Finite element analysis of an ultra-fine grained Titanium dental implant covered by different thicknesses of hydroxyapatite layer", Indian J. Dentistry. 4(1), 1-4. https://doi.org/10.1016/j.ijd.2012.10.002.
  53. Parveen, N., Sheikh, A., Abourehab, M.A.S., Karwasra, R., Singh, S. and Kesharwani, P. (2023), "Self-nanoemulsifying drug delivery system for pancreatic cancer", Europ. Polymer J., 190 111993. https://doi.org/10.1016/j.eurpolymj.2023.111993.
  54. Perrie, Y., Badhan, R.K.S., Kirby, D.J., Lowry, D., Mohammed, A.R. and Ouyang, D. (2012), "The impact of ageing on the barriers to drug delivery", J. Controlled Release. 161(2), 389-398. https://doi.org/10.1016/j.jconrel.2012.01.020.
  55. Ramteke Prashik, M., Panda Subrata, K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. http://dx.doi.org/10.12989/SCS.2019.33.6.865.
  56. Singh, B., Kapil, R., Nandi, M. and Ahuja, N. (2011), "Developing oral drug delivery systems using formulation by design: vital precepts, retrospect and prospects", Expert Opinion Drug Delivery. 8(10), 1341-1360. https://doi.org/10.1517/17425247.2011.605120.
  57. Song, J., Karami, B., Shahsavari, D. and Civalek, O . (2021), "Wave dispersion characteristics of graphene reinforced nanocomposite curved viscoelastic panels", Compos. Struct., 277 114648. https://doi.org/10.1016/j.compstruct.2021.114648.
  58. Tashkin, D.P. (2016), "A review of nebulized drug delivery in COPD", Int. J. Chronic Obstructive Pulmonary Disease. 11, 2585-2596. https://doi.org/10.2147/COPD.S114034.
  59. Thakur, P., Chahar, D. and Thakur, A. (2022), "Visible light assisted photocatalytic degradation of methylene blue dye using Ni doped Co-Zn nanoferrites", Adv. Nano Res., 12(4), 415-426. http://dx.doi.org/10.12989/ANR.2022.12.4.415.
  60. Ugurlu, O.F. and Ozturk, C.A. (2021), "Experimental investigation for the use of tailings as paste-fill material through design of experiment", Geomech. Eng., 26(5), 465. https://doi.org/10.12989/gae.2021.26.5.465.
  61. Wang, J., Jiang, X., Zhao, L., Zuo, S., Chen, X., Zhang, L., Lin, Z., Zhao, X., Qin, Y., Zhou, X. and Yu, X.-Y. (2020a), "Lineage reprogramming of fibroblasts into induced cardiac progenitor cells by CRISPR/Cas9-based transcriptional activators", Acta Pharmaceutica Sinica B. 10(2), 313-326. https://doi.org/10.1016/j.apsb.2019.09.003.
  62. Wang, J., Zhang, Y., Liu, G., Zhang, T., Zhang, C., Zhang, Y., Feng, Y. and Chi, Q. (2023a), "Improvements in the magnesium ion transport properties of graphene/CNT-wrapped TiO2-B nanoflowers by nickel Doping", Small. n/a(n/a), 2304969. https://doi.org/10.1002/smll.202304969.
  63. Wang, T., Zhang, L., Xu, N. and Alharbi, K.H. "Adaptive critic learning for approximate optimal event-triggered tracking control of nonlinear systems with prescribed performances", Int. J. Control. 1-15. https://doi.org/10.1080/00207179.2023.2250880.
  64. Wang, T., Zhou, G., Wang, J. and Wang, D. (2020b), "Impact of spatial variability of geotechnical properties on uncertain settlement of frozen soil foundation around an oil pipeline", Geomech. Eng., 20(1), 19. https://doi.org/10.12989/gae.2020.20.1.019.
  65. Wang, Y., Jia, Q. and Deng, T. (2023b), "The role of nanotechnology in reducing the impact on the ball and increasing the speed of its movement", Geomech. Eng., 32(5), 463-474. https://doi.org/10.12989/gae.2023.32.5.463.
  66. Wang, Y., Li, C., Shen, B., Zhu, L., Zhang, Y. and Jiang, L. (2023c), "Ultra-small Au/Pt NCs@GOX clusterzyme for enhancing cascade catalytic antibiofilm effect against F. nucleatum-induced periodontitis", Chemical Eng. J., 466 143292. https://doi.org/10.1016/j.cej.2023.143292.
  67. Wang, Y., Zhai, W., Li, J., Liu, H., Li, C. and Li, J. (2023d), "Friction behavior of biodegradable electrospun polyester nanofibrous membranes", Tribology Int. 188 108891. https://doi.org/10.1016/j.triboint.2023.108891.
  68. Wokovich, A.M., Prodduturi, S., Doub, W.H., Hussain, A.S. and Buhse, L.F. (2006), "Transdermal drug delivery system (TDDS) adhesion as a critical safety, efficacy and quality attribute", Europ. J. Pharmaceutics Biopharmaceutics. 64(1), 1-8. https://doi.org/10.1016/j.ejpb.2006.03.009.
  69. Xiang, J. and Xu, M. (2023), "The dynamic response of FG cylindrical beam subjected to bending and the centrifugal force of rotation on the basis of modified size-dependent high-order theories", Adv. Concrete Construct., 15(1), 47. https://doi.org/10.12989/acc.2023.15.1.047.
  70. Yan, P., Ren, Q., Zhong, F., Li, J., Wei, F., Li, J., Shi, X. and Dong, F. (2022), "Self-doped Br in Bi5O7Br ultrathin nanotubes: Efficient photocatalytic NO purification and mechanism investigation", Chinese Chemical Lett., 33(6), 3161-3166. https://doi.org/10.1016/j.cclet.2021.10.082.
  71. Zarga, D., Tounsi, A., Bousahla Abdelmoumen, A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. http://dx.doi.org/10.12989/SCS.2019.32.3.389.
  72. Zhang, H., Zou, Q., Ju, Y., Song, C. and Chen, D. (2022), "Distance-based Support Vector Machine to Predict DNA N6-methyladenine Modification", Current Bioinformatics. 17(5), 473-482. https://doi.org/10.2174/1574893617666220404145517.
  73. Zhang, L., Deng, S., Zhang, Y., Peng, Q., Li, H., Wang, P., Fu, X., Lei, X., Qin, A. and Yu, X. (2020), "Homotypic targeting delivery of siRNA with artificial cancer cells", Adv. Healthcare Mater., 9(9), 1900772. https://doi.org/10.1002/adhm.201900772.
  74. Zhang, P. and Fu, Y. (2013), "A higher-order beam model for tubes", Europ. J. Mech. - A/Solids. 38 12-19. https://doi.org/10.1016/j.euromechsol.2012.09.009.
  75. Zhao, K., Chen, Y., Yu, F., Jian, W., Zheng, M. and Zeng, H. (2022a), "A biodegradable magnesium alloy sample induced rat osteochondral defect repair through Wnt/β-catenin signaling pathway", Adv. Nano Res., 12(3), 301-317. http://dx.doi.org/10.12989/ANR.2022.12.3.301.
  76. Zhao, W., Suo, H., Wang, S., Ma, L., Wang, L., Wang, Q. and Zhang, Z. (2022b), "Mg gas infiltration for the fabrication of MgB2 pellets using nanosized and microsized B powders", J. Europ. Ceramic Society. 42(15), 7036-7048. https://doi.org/10.1016/j.jeurceramsoc.2022.08.029.
  77. Zhou, C., Zhang, Z., Zhang, J., Fang, Y. and Tahouneh, V. (2020), "Vibration analysis of FG porous rectangular plates reinforced by graphene platelets", Steel Compos. Struct., 34(2), 215-226. http://dx.doi.org/10.12989/SCS.2020.34.2.215.