Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory |
Hadi, Amin
(School of Mechanical Engineering, University of Tehran)
Nejad, Mohammad Zamani (Department of Mechanical Engineering, Yasouj University) Rastgoo, Abbas (School of Mechanical Engineering, University of Tehran) Hosseini, Mohammad (Department of Mechanical Engineering, Shahid Chamran University of Ahvaz) |
1 | Nejad, M.Z., Jabbari, M. and Ghannad, M. (2017a), "A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness", Acta Mechanica, 228(1), 215-231. DOI |
2 | Nejad, M.Z., Jabbari, M. and Hadi, A. (2017b), "A review of functionally graded piezoelectric thick shells", J. Computat. Appl. Mech. DOI: 10.22059/JCAMECH.2017.247963.220 DOI |
3 | Nejad, M.Z., Hadi, A. and Farajpour, A. (2017c), "Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., Int. J., 63(2), 161-169. |
4 | Nguyen, N.-T., Kim, N.-I. and Lee, J. (2014), "Analytical solutions for bending of transversely or axially FG nonlocal beams", Steel Compos. Struct., Int. J., 17(5), 641-665. DOI |
5 | Pradhan, S. and Phadikar, J. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 33(2), 193-213. DOI |
6 | Rahmani, O., Refaeinejad, V. and Hosseini, S. (2017), "Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams", Steel Compos. Struct., Int. J., 23(3), 339-350. DOI |
7 | Sahmani, S. and Aghdam, M.M. (2017), "Nonlinear instability of hydrostatic pressurized hybrid FGM exponential shear deformable nanoshells based on nonlocal continuum elasticity", Compos. Part B: Eng., 114, 404-417. DOI |
8 | Shafiei, N., Mirjavadi, S.S., Afshari, B.M., Rabby, S. and Hamouda, A. (2017), "Nonlinear thermal buckling of axially functionally graded micro and nanobeams", Compos. Struct., 168, 428-439. DOI |
9 | Shishesaz, M., Hosseini, M., Tahan, K.N. and Hadi, A. (2017), "Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory", Acta Mechanica, 228(12), 4141-4168. DOI |
10 | Shu, C. and Chew, Y. (1998), "On the equivalence of generalized differential quadrature and highest order finite difference scheme", Comput. Methods Appl. Mech. Eng,, 155(3), 249-260. DOI |
11 | Simsek, M. and Al-shujairi, M. (2017), "Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads", Compos. Part B: Eng., 108, 18-34. |
12 | 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. DOI |
13 | Steinberg, M.A. (1986), "Materials for aerospace", Sci. Am., (United States), 255(4), 66-73. DOI |
14 | Taczala, M., Buczkowski, R. and Kleiber, M. (2017), "Nonlinear buckling and post-buckling response of stiffened FGM plates in thermal environments", Compos. Part B: Eng., 109, 238-247. DOI |
15 | Thai, H.-T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. DOI |
16 | Thai, H.-T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. |
17 | Toupin, R.A. (1962), "Elastic materials with couple-stresses", Arch. Rational Mech. Anal., 11(1), 385-414. DOI |
18 | Wang, Y.Q. and Zu, J.W. (2017), "Nonlinear dynamic thermoelastic response of rectangular FGM plates with longitudinal velocity", Compos. Part B: Eng., 117, 74-88. DOI |
19 | Yang, F., Chong, A., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. DOI |
20 | Wang, C., Zhang, Y., Ramesh, S.S. and Kitipornchai, S. (2006), "Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 39(17), 3904. DOI |
21 | Yu, Y. J., Xue, Z.-N., Li, C.-L. and Tian, X.-G. (2016), "Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity", Compos. Struct., 146, 108-113. DOI |
22 | Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V. and Darabi, M.A. (2016), "Coupled longitudinal-transverserotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory", Appl. Math. Model., 40(23-24), 9872-9891. DOI |
23 | Adeli, M.M., Hadi, A., Hosseini, M. and Gorgani, H.H. (2017), "Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory", Eur. Phys. J. Plus, 132(9), 393. DOI |
24 | Afshin, A., Nejad, M.Z. and Dastani, K. (2017), "Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions", J. Computat. Appl. Mech., 48(1), 15-26. |
25 | 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. DOI |
26 | Sadrabadi, S.A., Rahimi, G.H., Citarella, R., Shahbazi Karami, J., Sepe, R. and Esposito, R. (2017), "Analytical solutions for yield onset achievement in FGM thick walled cylindrical tubes undergoing thermomechanical loads", Compos. Part B: Eng., 116, 211-223. DOI |
27 | Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E. and Mahmoud, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. DOI |
28 | Apuzzo, A., Barretta, R., Luciano, R., Marotti de Sciarra, F. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nanobeams by the stress-driven nonlocal integral model", Compos. Part B: Eng., 123, 105-111. DOI |
29 | Aydogdu, M. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. DOI |
30 | Bahrami, A. and Teimourian, A. (2015), "Nonlocal scale effects on buckling, vibration and wave reflection in nanobeams via wave propagation approach", Compos. Struct., 134, 1061-1075. DOI |
31 | Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. DOI |
32 | Burlayenko, V.N., Altenbach, H., Sadowski, T., Dimitrova, S.D. and Bhaskar, A. (2017), "Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements", Appl. Math. Model., 45, 422-438. DOI |
33 | Chen, C., Li, S., Dai, L. and Qian, C. (2014), "Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces", Commun. Nonlinear Sci. Numer. Simul., 19(5), 1626-1637. DOI |
34 | Civalek, O . (2017), "Vibration of laminated composite panels and curved plates with different types of FGM composite constituent", Compos. Part B: Eng., 122, 89-108. DOI |
35 | Ebrahimi, F. and Barati, M.R. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. |
36 | Ebrahimi, F. and Barati, M.R. (2016a), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 39(3), 937-952. |
37 | Ebrahimi, F. and Barati, M.R. (2016b), "Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory", Acta Mechanica Solida Sinica, 29(5), 547-554. DOI |
38 | Ebrahimi, F. and Barati, M.R. (2016c), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. DOI |
39 | Ebrahimi, F. and Salari, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. DOI |
40 | Ebrahimi, F., Barati, M.R. and Zenkour, A.M. (2017), "A new nonlocal elasticity theory with graded nonlocality for thermomechanical vibration of FG nanobeams via a nonlocal thirdorder shear deformation theory", Mech. Adv. Mater. Struct., 25(6), 512-522. |
41 | Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.-A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Computat., 229, 283-295. DOI |
42 | Emam, S.A. (2013), "A general nonlocal nonlinear model for buckling of nanobeams", Appl. Math. Model., 37(10-11), 6929-6939. DOI |
43 | Eringen, A.C. (1972a), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. DOI |
44 | Fatehi, P. and Nejad, M.Z. (2014), "Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells", Int. J. Appl. Mech., 6(4), Article Number: 1450038. |
45 | Eringen, A.C. (1972b), "Theory of micromorphic materials with memory", Int. J. Eng. Sci, 10(7), 623-641. DOI |
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. DOI |
47 | Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science & Business Media. |
48 | Ghannad, M., Nejad, M.Z., Rahimi, G.H. and Sabouri, H. (2012), "Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials", Struct. Eng. Mech., Int. J., 43(1), 105-126. DOI |
49 | Ghannad, M., Rahimi, G.H. and Nejad, M.Z. (2013), "Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials", Compos. Part B-Eng., 45(1), 388-396. DOI |
50 | Ghannadpour, S., Mohammadi, B. and Fazilati, J. (2013), "Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method", Compos. Struct., 96, 584-589. DOI |
51 | Gharibi, M., Nejad, M.Z. and Hadi, A. (2017), "Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius", J. Computat. Appl. Mech., 48(1), 89-98. |
52 | Goodarzi, M., Nikkhah Bahrami, M. and Tavaf, V. (2017), "Refined plate theory for free vibration analysis of FG nanoplates using the nonlocal continuum plate model", J. Computat. Appl. Mech., 48(1), 123-136. |
53 | Hosseini, M., Shishesaz, M., Tahan, K.N. and Hadi, A. (2016), "Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials", Int. J. Eng. Sci., 109, 29-53. DOI |
54 | Gopalakrishnan, S. and Narendar, S. (2013), Wave Propagation in Nanostructures: Nonlocal Continuum Mechanics Formulations, Springer Science & Business Media. |
55 | Hadi, A., Rastgoo, A., Daneshmehr, A. and Ehsani, F. (2013), "Stress and strain analysis of functionally graded rectangular plate with exponentially varying properties", Indian J. Mater. Sci. |
56 | Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solids Struct., 48(18), 2496-2510. DOI |
57 | Hosseini, M., Gorgani, H.H., Shishesaz, M. and Hadi, A. (2017), "Size-Dependent Stress Analysis of Single-Wall Carbon Nanotube Based on Strain Gradient Theory", Int. J. Appl. Mech., 9(6), 1750087. DOI |
58 | Jabbari, M., Nejad, M.Z. and Ghannad, M. (2015), "Thermoelastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading", Int. J. Eng. Sci., 96, 1-18. DOI |
59 | Jabbari, M., Nejad, M.Z. and Ghannad, M. (2016), "Thermoelastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness", Compos. Part B-Eng., 96, 20-34. DOI |
60 | Jeyakarthikeyan, P.V., Subramanian, G. and Yogeshwaran, R. (2017), "An alternate stable midpoint quadrature to improve the element stiffness matrix of quadrilaterals for application of functionally graded materials (FGM)", Comput. Struct., 178, 71-87. DOI |
61 | 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. DOI |
62 | Kashkoli, M.D., Tahan, K.N. and Nejad, M.Z. (2017), "Time-Dependent Thermomechanical Creep Behavior of FGM Thick Hollow Cylindrical Shells Under Non-Uniform Internal Pressure", Int. J. Appl. Mech., 9(6), Article Number: 1750086. |
63 | Keivani, M., Koochi, A. and Abadyan, M. (2016), "Coupled effects of surface energy and size dependency on the stability of nanotweezers using GDQ method", Microsyst. Technol., 23(5), 1295-1308. |
64 | Lam, D., Yang, F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. DOI |
65 | Li, L. and Hu, Y. (2017a), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170. DOI |
66 | Li, L. and Hu, Y. (2017b), "Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory", Compos. Struct., 172, 242-250. DOI |
67 | Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. DOI |
68 | Li, X., Li, L., Hu, Y., Ding, Z. and Deng, W. (2017), "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory", Compos. Struct., 165, 250-265. DOI |
69 | Lu, C., Chen, W., Xu, R. and Lim, C.W. (2008), "Semi-analytical elasticity solutions for bi-directional functionally graded beams", Int. J. Solids Struct., 45(1), 258-275. DOI |
70 | Mazarei, Z., Nejad, M.Z. and Hadi, A. (2016), "Thermo-elastoplastic analysis of thick-walled spherical pressure vessels made of functionally graded materials", Int. J. Appl. Mech., 8(4), Article Number: 1650054. |
71 | Mindlin, R. and Tiersten, H. (1962), "Effects of couple-stresses in linear elasticity", Arch. Rational Mech. Anal, 11(1), 415-448. DOI |
72 | Najibi, A. and Talebitooti, R. (2017), "Nonlinear transient thermoelastic analysis of a 2D-FGM thick hollow finite length cylinder", Compos. Part B: Eng., 111, 211-227. DOI |
73 | Nejad, M.Z. and Fatehi, P. (2015), "Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials", Int. J. Eng. Sci., 86, 26-43. DOI |
74 | Nejad, M.Z. and Hadi, A. (2016a), "Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams", Int. J. Eng. Sci., 106, 1-9. |
75 | Nejad, M.Z. and Hadi, A. (2016b), "Non-local analysis of free vibration of bi-directional functionally graded Euler-Bernoulli nano-beams", Int. J. Eng. Sci., 105, 1-11. |
76 | Nejad, M.Z. and Rahimi, G.H. (2009), "Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load", Sci. Res. Essays, 4(3), 131-140. |
77 | Nejad, M.Z. and Rahimi, G.H. (2010), "Elastic analysis of FGM rotating cylindrical pressure vessels", J. Chinese Inst. Engr., 33(4), 525-530. DOI |
78 | Li, L., Li, X. and Hu, Y. (2018), "Nonlinear bending of a twodimensionally functionally graded beam", Compos. Struct., 184, 1049-1061. DOI |
79 | Nejad, M., Rastgoo, A. and Hadi, A. (2014a), "Effect of Exponentially-Varying Properties on Displacements and Stresses in Pressurized Functionally Graded Thick Spherical Shells with Using Iterative Technique", J. Solid Mech., 6(4), 366-377. |
80 | Nejad, M.Z., Rahimi, G.H. and Ghannad, M. (2009), "Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system", Mechanika, 77(3), 18-26. |
81 | Nejad, M.Z., Rastgoo, A. and Hadi, A. (2014b), "Exact elastoplastic analysis of rotating disks made of functionally graded materials", Int. J. Eng. Sci., 85, 47-57. DOI |
82 | Nejad, M.Z., Jabbari, M. and Ghannad M. (2015a), "Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading", Compos. Struct., 122, 561-569. DOI |
83 | Nejad, M.Z., Jabbari, M. and Ghannad, M. (2015b), "Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading", Int. J. Eng. Sci., 89, 86-99. DOI |
84 | Nejad, M.Z., Hadi, A. and Rastgoo, A. (2016a), "Buckling analysis of arbitrary two-directional functionally graded Euler-Bernoulli nano-beams based on nonlocal elasticity theory", Int. J. Eng. Sci., 103, 1-10. DOI |
85 | Nejad, M.Z., Abedi, M., Lotfian, M.H. and Ghannad, M. (2016b), "Exact and numerical elastic analysis for the FGM thick-walled cylindrical pressure vessels with exponentially-varying properties", Arch. Metal. Mater., 61(3), 1303-1308. DOI |