Advances in nano research

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Nonlocal orthotropic shell model for buckling of microtubules embedded within elastic medium

  • Muhammad Taj (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Manzoor Ahmad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Muzamal Hussain (Department of Mathematics, University of Sahiwal) ;
  • Lahcen Azrar (Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University of Rabat) ;
  • Muhammad Safeer (Department of Mathematics University of Poonch ) ;
  • Hamdi Ayed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Emad Ghandourah (Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Abir Mouldi (Department of Industrial Engineering, College of Engineering, King Khalid University)
  • Received : 2021.08.11
  • Accepted : 2024.09.10
  • Published : 2024.11.25
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Abstract

Nonlocal influences are taken into account when studying the buckling behavior of protein microtubules in the elastic medium. The protein microtubules are modeled using the Winkler model as an orthotropic shell. Combining the two models, a new nonlocal orthotropic Winkler model is created that accounts for nonlocal influences in order to study the buckling of protein microtubules within the elastic medium. The wave propagation approach, a well-known numerical technique, is used to solve the governing equations. The primary goal of the current work is to examine microtubule buckling against dimensionless axial wavelength. This findings and observations supported the conclusions of the earlier investigations.

Keywords

Acknowledgement

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/95/45.

References

  1. Akbas, S.D. (2017), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9(2), 147-155. https://doi.org/10.24107/ijeas.322375
  2. Akbas, S.D. (2018a), "Forced vibration analysis of cracked nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(8), 1-11. https://doi.org/10.1007/s40430-018-1315-1
  3. Akbas, S.D. (2018b), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 21. https://doi.org/10.12989/anr.2018.6.3.219
  4. Akbas, S.D. (2019), "Axially forced vibration analysis of cracked a nanorod", J. Comput. Appl. Mech., 50(1), 63-68. https://doi.org/10.22059/JCAMECH.2019.281285.392
  5. Albert, O.T. (1994), "Biology and ecology of Norway pout (Trisopterus esmarki Nilsson, 1855) in the Norwegian Deep", ICES J. Marine Sci., 51(1), 45-61. https://doi.org/10.1006/jmsc.1994.1005.
  6. AlSaleh, R.J. and Fuggini, C. (2020), "Combining GPS and accelerometers' records to capture torsional response of cylindrical tower", Smart Struct. Syst., 25(1), 111. https://doi.org/10.12989/sss.2020.25.1.111.
  7. Arani, A.G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct. Syst., 18(4), 787-800. http://doi.org/10.12989/sss.2016.18.4.787
  8. Arefi, M. and Zenkour, A.M. (2017), "Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor", Smart Struct Syst, 19(1), 33-38. https://doi.org/10.12989/sss.2017.19.1.033
  9. Arshad, R., Jalil, M., Hussain, M. and Tounsi, A. (2024), "A novel framework for the construction of cryptographically secure S-boxes", Comput. Concr., 34(1), 79-91. https://doi.org/10.12989/cac.2024.34.1.079.
  10. Asghar, S., Naeem, M.N. and Hussain, M. (2020), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E, 116, 113726. https://doi.org/10.1016/j.physe.2019.113726
  11. Banoqitah, E.M., Hussain, M., Khadimallah, M.A., Ghandourah, E., Yahya, A., Basha, M. and Alshoaibi, A. (2022), "A simplified directly determination of natural frequencies of CNT: Via aspect ratio", Adv. Nano Res., 13(3), 207. https://doi.org/10.12989/anr.2022.13.3.207
  12. Barany, M., Barron, J.T., Gu, L. and Barany, K. (2001), "Exchange of the actin-bound nucleotide in intact arterial smooth muscle", J. Biol. Chem., 276(51), 48398-48403. https://doi.org/10.1074/jbc.M106227200
  13. Bennett, V. and Baines, A.J. (2001). "Spectrin and ankyrin-based pathways: metazoan inventions forintegrating cells into tissues," Physiol. Rev., 81(3), 1353-1392. https://doi.org/10.1152/physrev.2001.81.3.1353
  14. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)," Comput. Concr., 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.6.1053
  15. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197
  16. Brangwynne, C.P., MacKintosh, F.C., Kumar, S., Geisse, N.A., Talbot, J., Mahadevan, L., Parker, K.K., Ingber, D.E. and Weitz, D.A. (2006), "Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement", J. Cell Biol., 173(5), 733-741. https://doi.org/10.1083/jcb.200601060
  17. Cammarata, R. (1997), "Surface and interface stress effects on interfacial and nanostructured materials," Mater. Sci. Eng. A, 237(2), 180-184. https://doi.org/10.1016/S0921-5093(97)00128-7
  18. Chang, L. and Goldman, R.D. (2004), "Intermediate filaments mediate cytoskeletal crosstalk", Nature Rev. Mole. Cell Biol., 5(8), 601-613. https://doi.org/10.1038/nrm1438.
  19. Chang, T.,and Hou, J. (2006), "Molecular dynamics simulations on buckling of multiwalled carbon nanotubes under bending", J. Appl. Phys., 100(11), 114327. https://doi.org/10.1063/1.2400096
  20. Chen, C., Yin, L., Song, X., Yang, H., Ren, X., Gong, X., Wang, F. and Yang, L. (2016), "Effects of vimentin disruption on the mechanoresponses of articular chondrocyte", Biochem. Biophys. Res. Commun., 469(1), 132-137. https://doi.org/10.3390/cells7100147
  21. Chen, T., Chiu, M.S. and Weng, C.N. (2006), "Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids", J. Appl. Phys., 100(7), 074308. https://doi.org/10.1063/1.2356094
  22. Civalek, O ., Demir, C . and Akgoz, B. (2010), "Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model", Math. Comput. Appl., 15(2), 289-298. https://doi.org/10.3390/mca15020289.
  23. Ece, M. and Aydogdu, M. (2007), "Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes", Acta Mechanica, 190(1-4), 185-195. https://doi.org/10.1007/s00707-006-0417-5
  24. Elbaum, M., Fygenson, D.K. and Libchaber, A. (1996), "Buckling microtubules in vesicles", Phys. Rev. Lett., 76(21), 4078. https://doi.org/10.1103/PhysRevLett.76.4078.
  25. Elzinga, M., Collins, J.H., Kuehl, W.M. and Adelstein, R.S. (1973), "Complete amino-acid sequence of actin of rabbit skeletal muscle", Proceedings of the National Academy of Sciences, 70(9), 2687-2691. https://doi.org/10.1073/pnas.70.9
  26. 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.
  27. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. http://doi.org/10.1016/0020-7225(72)90039-0
  28. Fatahi-Vajari, A., Azimzadeh, Z. and Hussain, M. (2019), "Nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes using homotopy perturbation method", Micro Nano Lett., 14(14), 1366-1371. https://doi.org/10.1049/mnl.2019.0203
  29. Felgner, H., Frank, R. and Schliwa, M. (1996), "Flexural rigidity of microtubules measured with the use of optical tweezers", J. Cell Sci., 109(2), 509-516. https://doi.org/10.1529/biophysj.104.055483
  30. Fu, Y. and Zhang, J. (2010), "Modeling and analysis of micro-tubules based on a modified couple stress theory", Physica E, 42(5), 1741-1745. https://doi.org/10.1016/j.physe.2010.01.033.
  31. Gao, Y., Wang, J. and Gao, H. (2010), "Persistence length of microtubules based on a continuum anisotropic shell model", J. Comput. Theor. Nanosci., 7(7), 1227-1237. https://doi.org/10.1166/jctn.2010.1476.
  32. Gao, Y. and Lei, F.M. (2009), "Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory", Biochem. Biophys. Res. Commun., 387(3), 467-471. https://doi.org/10.1016/j.bbrc.2009.07.042
  33. Gardel, M.L., Shin, J.H., MacKintosh, F.C., Mahadevan, L., Matsudaira, P. and Weitz, D.A. (2004), "Elastic behavior of cross-linked and bundled actin networks", Science, 304(5675), 1301-1305. https://doi.org/10.1126/science.1095087
  34. Gasser, T.C. (2007), "Validation of 3D crack propagation in plain concrete. Part II: Computational modeling and predictions of the PCT3D test", Comput. Concr., 4(1), 67-82. https://doi.org/10.1007/s40430-018-1315-1
  35. Ghoshdastider, U., Jiang, S., Popp, D. and Robinson, R.C. (2015), "In search of the primordial actin filament", Proceedings of the National Academy of Sciences, 112(30), 9150-9151. https://doi.org/10.1073/pnas.1511568112
  36. Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concr., 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431
  37. Grishchuk, E.L., Molodtsov, M.I., Ataullakhanov, F.I. and McIntosh, J.R. (2005), "Force production by disassembling microtubules", Nature, 438(7066), 384-388. https://doi.org/10.1021/bi00480a014.
  38. Gu, B., Mai, Y.W. and Ru, C.Q. (2009), "Mechanics of micro-tubules modeled as orthotropic elastic shells with transverse shearing", Acta Mechanica, 207(3-4), 195-209. https://doi.org/10.1007/s00707-008-0121-8.
  39. Gunning, P.W., Ghoshdastider, U., Whitaker, S., Popp, D. and Robinson, R.C. (2015),"The evolution of compositionally and functionally distinct actin filaments", J. Cell Sci., 128(11), 2009-2019. https://doi.org/10.1242/jcs.165563
  40. Gurtin, M.E., Weissmuller, J. and Larche, F. (1998), "A general theory of curved deformable interfaces in solids at equilibrium", Philos. Mag. A, 78(5), 1093-1109. https://doi.org/10.1080/01418619808239977
  41. Halliburton, W. (1887), "On muscle-plasma", J. Phys., 8(3-4), 133. https://doi.org/10.1113/jphysiol.1887.sp000252
  42. Hess, H., Howard, J. and Vogel, V. (2002), "A piconewton forcemeter assembled from microtubules and kinesins", Nano Lett., 2(10), 1113-1115. https://doi.org/10.1021/nl025724i
  43. Holmes, K.C., Pop, D., Gebhard, W. and Kabsch, W. (1990), "The most detailed model of the actin filament available at present", Nature, 347, 44-49. https://doi.org/10.1038/347044a0.
  44. Huang, H., Xue, C., Zhang, W. and Guo, M. (2022), "Torsion design of CFRP-CFST columns using a data-driven optimization approach", Eng. Struct., 251, 113479. https://doi.org/10.1016/j.engstruct.2021.113479
  45. Hussain, M. (2022), "Controlling of ring based structure of rotating FG shell: Frequency distribution", Adv. Concr. Constr., 14(1), 35-43. https://doi.org/10.12989/acc.2022.14.1.035
  46. Hussain, M. (2024), Small-scale Computational Vibration of Carbon Nanotubes: Composite Structure, CRC Press.
  47. Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nano-tubes using Galerkin's method", Compos. Part B Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144
  48. Hussain, M., Naeem, M.N., Asghar, S. and Tounsi, A. (2020a), "Theoretical impact of Kelvin's theory for vibration of double walled carbon nanotubes", Adv. Nano Res., 8(4), 307-322. https://doi.org/10.12989/anr.2020.8.4.307
  49. Hussain, M., Naeem, M. N., Khan, M. S. and Tounsi, A. (2020b), "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concr., 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411
  50. Ishida, T., Thitamadee, S. and Hashimoto, T. (2007), "Twisted growth and organization of cortical microtubules," J. Plant Res., 120(1), 61-70. https://doi.org/10.1007/s10265-006-0039-y
  51. Janosi, L., Mori, H., Sekine, Y., Abragan, J., Janosi, R., Hirokawa, G. and Kaji, A. (2000), "Mutations influencing the frr gene coding for ribosome recycling factor (RRF)", J. Mol. Biol., 295(4), 815-829. https://doi.org/10.1006/jmbi.1999.3401.
  52. Jiang, H. and Zhang, J. (2008), "Mechanics of microtubule buckling supported by cytoplasm", J. Appl. Mech., 75(6), 061019. https://doi.org/10.1115/1.2966216
  53. Jiang, S., Narita, A., Popp, D., Ghoshdastider, U., Lee, L.J., Srinivasan, R., Balasubramanian, M.K., Oda, T., Koh, K. and Larsson, M. (2016), "Novel actin filaments from Bacillus thuringiensis form nanotubules for plasmid DNA segregation", Proceedings of the National Academy of Sciences, 113(9), E1200-E1205. https://doi.org/10.1073/pnas.1600129113.
  54. Jordan, M.A. and Wilson, L. (2004), "Microtubules as a target for anticancer drugs", Nature Rev. Cancer, 4(4), 253. https://doi.org/10.1038/nrc1317
  55. Khadimallah, M.A., Hussain, M., Khedher, K.M., Naeem, M.N. and Tounsi, A. (2020a), "Backward and forward rotating of FG ring support cylindrical shells", Steel Compos. Struct., 37(2), 137-150. https://doi.org/10.12989/scs.2020.37.2.137
  56. Khadimallah, M.A., Hussain, M. and Harbaoui, I. (2020b), "Application of Kelvin's theory for structural assessment of FG rotating cylindrical shell: Vibration control", Adv. Concr. Constr., 10(6), 499-507. https://doi.org/10.12989/acc.2020.10.6.499
  57. Krommer, M., Vetyukova, Y. and Staudigl, E. (2016), "Nonlinear modelling and analysis of thin piezoelectric plates: buckling and post-buckling behavior", Smart Struct. Syst., 18(1), 155-181. https://doi.org/10.12989/sss.2016.18.1.155 
  58. Kurachi, M., Hoshi, M. and Tashiro, H. (1995), "Buckling of a single microtubule by optical trapping forces: Direct measurement of microtubule rigidity", Cell Motil. Cytoskel., 30(3), 221-228. https://doi.org/10.1002/cm.970300306
  59. Landau, L. and Lifshitz, E.M. (1986), "Theoretical Physics", Hydrodyn. Nauka Moscow, 6. https://doi.org/10.1134/S0021364009010044.
  60. Lee, S.Y., Huynh, T.C., Dang, N.L. and Kim, J.T. (2019), "Vibration characteristics of caisson breakwater for various waves, sea levels, and foundations", Smart Struct. Syst., 24(4), 525-539. https://doi.org/10.12989/sss.2019.24.4.525.
  61. Li, T. (2008), "A mechanics model of microtubule buckling in living cells", J. Biomech., 41(8), 1722-1729. https://doi.org/10.1016/j.jbiomech.2008.03.003
  62. Meftah, S.A., Tounsi, A. and Adda Bedia, E.A. (2006), "Dynamic behaviour of stiffened and damaged coupled shear walls", Comput. Concr., 3(5), 1-15. https://doi.org/10.12989/cac.2006.3.5.285
  63. Mirny, L. and Shakhnovich, E. (2001), "Protein folding theory: from lattice to all-atom models", Ann Rev. Biophys. Biomol. Struct., 30(1), 361-396. https://doi.org/10.1146/annurev.biophys.30.1.361
  64. Mofrad, M.R. and Kamm, R.D. (2006), Cytoskeletal Mechanics: Models and Measurements in Cell Mechanics, Cambridge University Press, Cambridge, U.K. https://doi.org/10.1017/CBO9780511607318
  65. Murmu, T. and Pradhan, S. (2009), "Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory", J. Appl. Phys., 105(6), 064319. https://doi.org/10.1063/1.3091292
  66. Muzamal, H. (2022), "Structural stability of laminated composite material for the effectiveness of half axial wave mode: frequency impact", Adv. Concr. Constr., 14(5), 309-315. https://doi.org/10.12989/acc.2022.14.5.309
  67. Narita, A., Takeda, S., Yamashita, A. and Maeda, Y. (2006), "Structural basis of actin filament capping at the barbed-end: A cryo-electron microscopy study", The EMBO J, 25(23), 5626-5633. https://doi.org/10.1038/sj.emboj.7601395
  68. Needleman, D.J., Ojeda-Lopez, M.A., Raviv, U., Ewert, K., Jones, J.B., Miller, H.P., Wilson, L. and Safinya, C.R. (2004), "Synchrotron X-ray diffraction study of microtubules buckling and bundling under osmotic stress: a probe of interprotofilament interactions", Phys. Rev. Lett., 93(19), 198104. https://doi.org/10.1103/PhysRevLett.93.198104
  69. Nitta, T. and Hess, H. (2005), "Dispersion in active transport by kinesin-powered molecular shuttles", Nano Lett., 5(7), 1337-1342. https://doi.org/10.1021/nl050586t
  70. Nogales, E. (2001), "Structural insights into microtubule function", Ann Rev. Biophys. Biomol. Struct., 30(1), 397-420. https://doi.org/10.1146/annurev.biophys.30.1.397.
  71. Nogales, E., Wolf, S.G. and Downing, K.H. (1998), "Correction: Structure of the αβ tubulin dimer by electron crystallography", Nature, 393(6681), 191. https://doi.org/10.1038/34465
  72. Oriol, C., Dubord, C. and Landon, F. (1977), "Crystallization of native striated-muscle actin", FEBS Lett., 73(1), 89-91. https://doi.org/10.1016/0014-5793(77)80022-7.
  73. Otterbein, L.R., Graceffa, P. and Dominguez, R. (2001), "The crystal structure of uncomplexed actin in the ADP state", Science, 293(5530), 708-711. https://doi.org/10.1126/science.1059700
  74. Park, H.S., Klein, P.A. and Wagner, G.J. (2006), "A surface Cauchy-Born model for nanoscale materials", Int. J. Numer. Meth. Eng., 68(10), 1072-1095. https://doi.org/10.1002/nme.1754
  75. Pokorny, J. (2003), "Viscous effects on polar vibrations in microtubules", Electromagn. Biol. Med., 22(1), 15-29. https://doi.org/10.1081/JBC-120020349
  76. Pokorny, J. (2004), "Excitation of vibrations in microtubules in living cells", Bioelectrochemistry, 63(1-2), 321-326. https://doi.org/10.1016/j.bioelechem.2003.09.028
  77. Pollard, T.D. and J.A. Cooper (2009), "Actin, a central player in cell shape and movement", Science, 326(5957), 1208-1212. https://doi.org/10.1126/science.1175862
  78. Poplawski, B., Mikulowski, G., Pisarski, D., Wiszowaty, R. and Jankowski, L. (2019), "Optimum actuator placement for damping of vibrations using the Prestress-Accumulation Release control approach", Smart Struct. Syst., 24(1), 27-35. https://doi.org/10.12989/sss.2019.24.1.027
  79. Qazaq, A., Hussain, M., Mujalli, M. and Tounsi, A. (2022), "Fundamental computer assessment of ring support with exponent of trigonometric function: Safety geometrical perfection", Adv. Concr. Constr., 14(6), 381. https://doi.org/10.12989/acc.2022.14.6.381
  80. Qian, X.S., Zhang, J.Q. and Ru, C.Q. (2007), "Wave propagation in orthotropic microtubules", J. Appl. Phys., 101(8), 084702. https://doi.org/10.1063/1.2717573
  81. Radi, Z.A. and Khan, N.K. (2006), "Comparative expression and distribution of c-fos, estrogen receptorα (ERα), and p38α in the uterus of rats, monkeys, and humans", Toxicol. Pathol., 34(4), 327-335. https://doi.org/10.3390/ani10020334
  82. Reddy, J. and Pang, S. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511. https://doi.org/10.1063/1.2833431
  83. Sedighi, H.M. and Daneshmand, F. (2014), "Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He's iteration perturbation method", J. Mech. Sci. Technol., 28, 3459-3469. https://doi.org/10.1007/s12206-014-0807-x
  84. Shen, H.S. (2010a), "Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model", J. Theor. Biol., 264(2), 386-394. https://doi.org/10.1016/j.jtbi.2010.02.014
  85. Shen, H.S. (2010b), "Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium", Biomech. Model. Mechanobiol., 9(3), 345-357. https://doi.org/10.1007/s10237-009-0180-3.
  86. Sirenko, Y.M., Stroscio, M.A. and Kim, K. (1996), "Elastic vibrations of microtubules in a fluid", Phys. Rev. E, 53(1), 1003. https://doi.org/10.1103/PhysRevE.53.1003
  87. Straub, F. and Feuer, G. (1950), "Adenosinetriphosphate the functional group of actin," Biochimica et Biophysica Acta, 4, 455-470. https://doi.org/10.1021/ja01188a515
  88. Su, Y., Iyela, P.M., Zhu, J., Chao, X., Kang, S. and Long, X. (2024), "A Voronoi-based gaussian smoothing algorithm for efficiently generating RVEs of multi-phase composites with graded aggregates and random pores", Mater. Des., 244, 113159. https://doi.org/10.1016/j.matdes.2024.113159
  89. Taj, M. and Zhang. J. (2012), "Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model", Biochem. Biophys. Res. Commun., 424(1), 89-93. https://doi.org/10.1016/j.bbrc.2012.06.072
  90. Taj, M. and Zhang, J.Q. (2011), "Buckling of embedded microtubules in elastic medium", Appl. Math. Mech., 32(3), 293-300. https://doi.org/10.1007/s10483-011-1415-x.
  91. Timoshenko, S.P. and Gere, J.M. (2009), Theory of Elastic Stability, Courier Corporation, MA, U.S.A.
  92. Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527
  93. Tsiatas, G.C., Tsiptsis, I.N. and Siokas, A.G. (2020), "Nonlinear buckling and post-buckling of shape memory alloy shallow arches", J. Appl. Comput. Mech., 6(3), 665-683. https://doi.org/10.22055/JACM.2019.31795.1918
  94. Tsuda, Y., Yasutake, H., Ishijima, A. and Yanagida, T. (1996), "Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation", Proceedings of the National Academy of Sciences, 93(23), 12937-12942. https://doi.org/10.1073/pnas.93.23
  95. Vale, R.D. (2003), "The molecular motor toolbox for intracellular transport", Cell, 112(4), 467-480. https://doi.org/10.1016/S0092-8674(03)00111-9.
  96. Vaziri, A., Lee, H. and Mofrad, M.K. (2006), "Deformation of the cell nucleus under indentation: mechanics and mechanisms," J. Mater. Res., 21(8), 2126-2135. https://doi.org/10.1557/JMR.2006.0262.
  97. Vindin, H. and P. Gunning (2013), "Cytoskeletal tropomyosins: choreographers of actin filament functional diversity", J. Muscle Res. Cell Motil., 34(3-4), 261-274. http://doi.org/10.1007/ 978-0-387-84847-1_10
  98. Wang, C.Y., Ru, C.Q. and Mioduchowski, A. (2006), "Orthotropic elastic shell model for buckling of microtubules", Phys. Rev. E, 74(5), 052901. https://doi.org/10.1103/PhysRevE.74.052901
  99. Wang, C., Li, C. and Adhikari, S. (2009), "Dynamic behaviors of microtubules in cytosol", J. Biomech., 42(9), 1270-1274. https://doi.org/10.1016/j.jbiomech.2009.03.027.
  100. Wang, C., Ru, C. and Mioduchowski, A. (2006), "Orthotropic elastic shell model for buckling of microtubules", Phys. Rev. E, 74(5), 052901. https://doi.org/10.1103/PhysRevE.74.052901.
  101. Wang, G.F. and Feng, X.Q. (2007), "Effects of surface elasticity and residual surface tension on the natural frequency of microbeams", Appl. Phys. Lett., 90(23), 231904. https://doi.org/10.1063/1.2746950
  102. Wang, G.F. and Feng, X.Q. (2009), "Surface effects on buckling of nanowires under uniaxial compression", Appl. Phys. Lett., 94(14), 141913. https://doi.org/10.1063/1.3117505
  103. Wang, H., Hou, Y., He, Y., Wen, C., Giron-Palomares, B., Duan, Y., Gao, B., Vavilov, V.P. and Wang, Y. (2024), "A physical-constrained decomposition method of infrared thermography: Pseudo restored heat flux approach based on ensemble bayesian variance tensor fraction", IEEE T. Ind. Inform., 20(3), 3413-3424. https://doi.org/10.1109/TII.2023.3293863
  104. Wang, J., Fu, A., Liu, B., Chen, Y., Cao, Y., Zhou, H., Wang, B., Li, X., Li, J., Fang, Q. and Liu, Y. (2024), "Weakening the mechanical property anisotropy of additively manufactured medium entropy alloy by controlling the cellular structure", Add. Manuf., 89, 104303. https://doi.org/10.1016/j.addma.2024.10430
  105. Wang, Q. and Liew, K. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures", Phys. Lett. A, 363(3), 236-242. https://doi.org/10.1016/j.physleta.2006.10.093
  106. Wang, Y. and J. Qian (2019), "Buckling of filamentous actin bundles in filopodial protrusions", Acta Mechanica Sinica, 35(2), 365-375. https://doi.org/10.1007/s10409-019-00838-1
  107. Wang, Z., Yuan, Y., Zhang, S., Lin, Y. and Tan, J. (2024), "A multi-state fusion informer integrating transfer learning for metal tube bending early wrinkling prediction", Appl. Soft Comput., 151, 110991. https://doi.org/10.1016/j.asoc.2023.110991
  108. Woody, R., Roberts, G., Clark, D. and Bayley, P. (1982), "1H NMR evidence for flexibility in microtubule-associated proteins and microtubule protein oligomers", FEBS Lett., 141(2), 181-184. https://doi.org/10.1111/j.1432-1033.1977.tb11726.x
  109. Wu, Q., Chen, N., Yao, M., Niu, Y. and Wang, C. (2024), "Nonlinear dynamic analysis of FG fluid conveying micropipes with initial imperfections", Int. J. Struct. Stabil. Dyn., 2550017. https://doi.org/10.1142/S0219455425500178
  110. Xu, S., Jing, X., Zhu, P., Jin, H., Paik, K., He, P. and Zhang, S. (2023), "Equilibrium phase diagram design and structural optimization of SAC/Sn-Pb composite structure solder joint for preferable stress distribution", Mater. Character., 206, 113389. https://doi.org/10.1016/j.matchar.2023.113389
  111. Yaman, I.O., Akbay, Z. and Aktan, H. (2006), "Numerical modelling and finite element analysis of stress wave propagation for ultrasonic pulse velocity testing of concrete", Comput. Concr., 3(6), 423-437. https://doi.org/10.12989/cac.2006.3.6.423
  112. Yang, C., Li, Z., Xu, P. and Huang, H. (2024), "Recognition and optimisation method of impact deformation patterns based on point cloud and deep clustering: Applied to thin-walled tubes", J. Ind. Inform. Integr., 40, 100607. https://doi.org/10.1016/j.jii.2024.100607
  113. Yao, R., Ge, Z., Wang, D., Shang, N. and Shi, J. (2024), "Self-sensing joints for in-situ structural health monitoring of composite pipes: A piezoresistive behavior-based method", Eng. Struct., 308, 118049. https://doi.org/10.1016/j.engstruct.2024.118049
  114. Yeh, J.Y. (2016), "Vibration characteristic analysis of sandwich cylindrical shells with MR elastomer", Smart Struct. Syst., 18(2), 233-247. https://doi.org/10.12989/sss.2016.18.2.233
  115. Yi, L., Chang, T. and Ru, C. (2008), "Buckling of microtubules under bending and torsion", Journal of Applied Physics, 103(10), 103516. https://doi.org/10.1063/1.2930882.
  116. Zahrai, S.M. and Kakouei, S. (2019), "Shaking table tests on a SDOF structure with cylindrical and rectangular TLDs having rotatable baffles", Smart Struct. Syst., 24(3), 391-401. https://doi.org/10.12989/sss.2019.24.3.391
  117. Zamani, A., Kolahchi, R.,and Bidgoli, M.R. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concr., 20(6), 671-68. https://doi.org/10.12989/cac.2017.20.6.671
  118. Zhang, C., Khorshidi, H., Najafi, E. and Ghasemi, M. (2023), "Fresh, mechanical and microstructural properties of alkali-activated composites incorporating nanomaterials: A comprehensive review", J. Clean. Prod., 384, 135390. https://doi.org/10.1016/j.jclepro.2022.135390
  119. Zhang, H., Liu, H. and Kuai, H. (2024a), "Stress intensity factor analysis for multiple cracks in orthotropic steel decks rib-to-floorbeam weld details under vehicles loading", Eng. Fail. Anal., 164, 108705. https://doi.org/10.1016/j.engfailanal.2024.108705
  120. Zhang, W., Kang, S., Liu, X., Lin, B. and Huang, Y. (2023), "Experimental study of a composite beam externally bonded with a carbon fiber-reinforced plastic plate", J. Build. Eng., 71, 106522. https://doi.org/10.1016/j.jobe.2023.106522
  121. Zhang, W., Lin, J., Huang, Y., Lin, B. and Kang, S. (2024b), "Temperature-dependent debonding behavior of adhesively bonded CFRP-UHPC interface", Compos. Struct., 340, 118200. https://doi.org/10.1016/j.compstruct.2024.118200
  122. Zhang, Y., Huang, Z., Wang, H. and Li, J. (2023), "Regulation of the interface compatibility of the 3D-printing interpenetration networks toward reduced structure anisotropy and enhanced performances", ACS Appl. Mater. Interf., 15(27), 32984-32992. https://doi.org/10.1021/acsami.3c06514
  123. Zhao, Y., Liu, K., Hou, H. and Chen, L. (2022), "Role of interfacial energy anisotropy in dendrite orientation in Al-Zn alloys: A phase field study", Mater. Des., 216, 110555. https://doi.org/10.1016/j.matdes.2022.110555