| [1] |
Autumn, K.; Liang, Y. A.; Hsieh, S. T.; Zesch, W.; Chan, W. P.; Kenny, T. W.; Fearing, R.; Full, R. J., Adhesive force of a single gecko foot-hair, Nature, 405, 681-685 (2000) |
| [2] |
Kopperger, E.; List, J.; Madhira, S.; Rothfischer, F.; Lamb, D. C.; Simmel, F. C., A self-assembled nanoscale robotic arm controlled by electric fields, Science, 359, 296-300 (2018) |
| [3] |
Wang, Z. L.; Song, J. H., Piezoelectric nanogenerators based on zinc oxide nanowire arrays, Science, 312, 242-246 (2006) |
| [4] |
Xiang, R.; Inoue, T.; Zheng, Y. J.; Kumamoto, A.; Qian, Y.; Sato, Y.; Liu, M.; Tang, D. M.; Gokhale, D.; Guo, J.; Hisama, K.; Yotsumoto, S.; Ogamoto, T.; Arai, H.; Kobayashi, Y.; Zhang, H.; Hou, B.; Anisimov, A.; Maruyama, M.; Miyata, Y.; Okada, S.; Chiashi, S.; Li, Y.; Kong, J.; Kauppinen, E. I.; Ikuhara, Y.; Suenaga, K.; Maruyama, S., One-dimensional van der Waals heterostructures, Science, 367, 537-542 (2020) |
| [5] |
Peisker, H.; Michels, J.; Gorb, S. N., Evidence for a material gradient in the adhesive tarsal setae of the ladybird beetle Coccinella septempunctata, Nature Communications, 4, 1661 (2013) |
| [6] |
Alibardi, L., Review: mapping proteins localized in adhesive setae of the tokay gecko and their possible influence on the mechanism of adhesion, Protoplasma, 255, 1785-1797 (2018) |
| [7] |
Nix, W. D.; Gao, H. J., Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46, 411-425 (1998) · Zbl 0977.74557 |
| [8] |
Huang, Y.; Zhang, F.; Hwang, K. C.; Nix, W. D.; Pharr, G. M.; Feng, G., A model of size effects in nano-indentation, Journal of the Mechanics and Physics of Solids, 54, 1668-1686 (2006) · Zbl 1120.74658 |
| [9] |
Zhu, X. W.; Li, L., Closed form solution for a nonlocal strain gradient rod in tension, International Journal of Engineering Science, 119, 16-28 (2017) · Zbl 1423.74334 |
| [10] |
Guo, S.; He, Y. M.; Lei, J.; Li, Z. K.; Liu, D. B., Individual strain gradient effect on torsional strength of electropolished microscale copper wires, Scripta Materialia, 130, 124-127 (2017) |
| [11] |
Greer, J. R.; Oliver, W. C.; Nix, W. D., Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta Materialia, 53, 1821-1830 (2005) |
| [12] |
Lu, L.; Guo, X. M.; Zhao, J. Z., Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, International Journal of Engineering Science, 116, 12-24 (2017) · Zbl 1423.74499 |
| [13] |
Eringen, A. C., Theory of nonlocal elasticity and some applications, Res Mechanica, 21, 313-342 (1987) |
| [14] |
Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703-4710 (1983) |
| [15] |
Eringen, A. C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1-16 (1972) · Zbl 0229.73006 |
| [16] |
Ghannadpour, S. A M.; Mohammadi, B.; Fazilati, J., Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method, Composite Structures, 96, 584-589 (2013) |
| [17] |
Khodabakhshi, P.; Reddy, J. N., A unified integro-differential nonlocal model, International Journal of Engineering Science, 95, 60-75 (2015) · Zbl 1423.74133 |
| [18] |
Sobhy, M.; Zenkour, A. M., Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate, Composites Part B: Engineering, 154, 492-506 (2018) |
| [19] |
Lu, L.; Guo, X. M.; Zhao, J. Z., A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms, International Journal of Engineering Science, 119, 265-277 (2017) |
| [20] |
Mirjavadi, S. S.; Rabby, S.; Shafiei, N.; Afshari, B. M.; Kazemi, M., On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment, Applied Physics A-Materials Science Processing, 123, 315 (2017) |
| [21] |
Barati, M. R.; Zenkour, A. M., Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions, Composite Structures, 182, 91-98 (2017) |
| [22] |
Al-Shujairi, M.; Mollamahmutoglu, C., Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect, Composites Part B: Engineering, 154, 292-312 (2018) |
| [23] |
Wang, Y. B.; Zhu, X. W.; Dai, H. H., Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model, AIP Advances, 6, 22 (2016) |
| [24] |
Zhang, P.; Qing, H.; Gao, C. F., Theoretical analysis for static bending of circular Euler-Bernoulli beam using local and Eringen’s nonlocal integral mixed model, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, 99, 8 (2019) · Zbl 07785951 |
| [25] |
Zhang, P.; Qing, H.; Gao, C. F., Analytical solutions of static bending of curved Timoshenko microbeams using Eringen’s two-phase local/nonlocal integral model, ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, 100, 7 (2020) · Zbl 07809732 |
| [26] |
Romano, G.; Barretta, R.; Diaco, M.; De Sciarra, F. M., Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, International Journal of Mechanical Sciences, 121, 151-156 (2017) |
| [27] |
Fernandez-Saez, J.; Zaera, R.; Loya, J. A.; Reddy, J. N., Bending of Euler-Bernoulli beams using Eringen’s integral formulation: a paradox resolved, International Journal of Engineering Science, 99, 107-116 (2016) · Zbl 1423.74477 |
| [28] |
Jiang, P.; Qing, H.; Gao, C. F., Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model, Applied Mathematics and Mechanics (English Edition), 41, 2, 207-232 (2020) · Zbl 1462.74100 |
| [29] |
Romano, G.; Barretta, R., Nonlocal elasticity in nanobeams: the stress-driven integral model, International Journal of Engineering Science, 115, 14-27 (2017) · Zbl 1423.74512 |
| [30] |
Barretta, R.; Fabbrocino, F.; Luciano, R.; De Sciarra, F. M.; Ruta, G., Buckling loads of nano-beams in stress-driven nonlocal elasticity, Mechanics of Advanced Materials and Structures, 27, 869-875 (2020) |
| [31] |
Barretta, R.; Faghidian, S. A.; Luciano, R., Longitudinal vibrations of nano-rods by stress-driven integral elasticity, Mechanics of Advanced Materials and Structures, 26, 1307-1315 (2019) |
| [32] |
Barretta, R.; Faghidian, S. A.; De Sciarra, F. M., Stress-driven nonlocal integral elasticity for axisymmetric nano-plates, International Journal of Engineering Science, 136, 38-52 (2019) · Zbl 1425.74055 |
| [33] |
Sedighi, H. M.; Malikan, M., Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment, Physica Scripta, 95, 055218 (2020) |
| [34] |
Zhang, P.; Qing, H.; Gao, C. F., Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model, Composite Structures, 245, 112362 (2020) |
| [35] |
Darban, H.; Fabbrocino, F.; Feo, L.; Luciano, R., Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model, Mechanics of Advanced Materials and Structures, 28, 2408-2416 (2020) |
| [36] |
Bian, P. L.; Qing, H., Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model, Applied Mathematics and Mechanics (English Edition), 42, 3, 425-440 (2021) · Zbl 1486.74058 |
| [37] |
Ma, Y. B., Size-dependent thermal conductivity in nanosystems based on non-Fourier heat transfer, Applied Physics Letters, 101, 211905 (2012) |
| [38] |
Dong, Y.; Cao, B. Y.; Guo, Z. Y., Size dependent thermal conductivity of Si nanosystems based on phonon gas dynamics, Physica E: Low-dimensional Systems and Nanostructures, 56, 256-262 (2014) |
| [39] |
Yu, Y. J.; Li, C. L.; Xue, Z. N.; Tian, X. G., The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale, Physics Letters A, 380, 255-261 (2016) |
| [40] |
Yu, Y. J.; Tian, X. G.; Liu, X. R., Size-dependent generalized thermoelasticity using Eringen’s nonlocal model, European Journal of Mechanics-A/Solids, 51, 96-106 (2015) · Zbl 1406.74186 |
| [41] |
Yu, Y. J.; Xue, Z. N.; Li, C. L.; Tian, X. G., Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity, Composite Structures, 146, 108-113 (2016) |
| [42] |
Lei, J.; He, Y. M.; Li, Z. K.; Guo, S.; Liu, D. B., Effect of nonlocal thermoelasticity on buckling of axially functionally graded nanobeams, Journal of Thermal Stresses, 42, 526-539 (2019) |
| [43] |
Barati, M. R.; Zenkour, A., Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments, Mechanics of Advanced Materials and Structures, 25, 669-680 (2018) |
| [44] |
Lei, J.; He, Y. M.; Guo, S.; Li, Z. K.; Liu, D. B., Thermal buckling and vibration of functionally graded sinusoidal microbeams incorporating nonlinear temperature distribution using DQM, Journal of Thermal Stresses, 40, 665-689 (2017) |
| [45] |
Sarkar, N., Thermoelastic responses of a finite rod due to nonlocal heat conduction, Acta Mechanica, 231, 947-955 (2020) · Zbl 1434.74043 |
| [46] |
Singh, P.; Yadava, R. D S., Effect of surface stress on resonance frequency of microcantilever sensors, IEEE Sensors Journal, 18, 7529-7536 (2018) |
| [47] |
Wu, J. Z.; Zhang, N. H., Clamped-end effect on static detection signals of DNA-microcantilever, Applied Mathematics and Mechanics (English Edition), 42, 10, 1423-1438 (2021) · Zbl 1492.74016 |
| [48] |
Wu, J. K., About beam, Mechanics in Engineering, 30, 106-109 (2008) |
| [49] |
Xi, Y. Y.; Lyu, Q.; Zhang, N. H.; Wu, J. Z., Thermal-induced snap-through buckling of simply-supported functionally graded beams, Applied Mathematics and Mechanics (English Edition), 41, 12, 1821-1832 (2020) · Zbl 1479.74039 |
