Browse > Article
http://dx.doi.org/10.12989/sem.2020.76.3.413

Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method  

Ahmed, Ridha A. (Al-Mustansiriah University)
Mustafa, Nader M. (Al-Mustansiriah University)
Faleh, Nadhim M. (Al-Mustansiriah University)
Fenjan, Raad M. (Al-Mustansiriah University)
Publication Information
Structural Engineering and Mechanics / v.76, no.3, 2020 , pp. 413-420 More about this Journal
Abstract
Considering inverse cotangential shear strain function, the present paper studies nonlinear stability of nonlocal higher-order refined beams made of metal foams based on Chebyshev-Ritz method. Based on inverse cotangential beam model, it is feasible to incorporate shear deformations needless of shear correction factor. Metal foam is supposed to contain different distributions of pores across the beam thickness. Also, presented Chebyshev-Ritz method can provide a unified solution for considering various boundary conditions based on simply-supported and clamped edges. Nonlinear effects have been included based upon von-karman's assumption and nonlinear elastic foundation. The buckling curves are shown to be affected by pore distribution, geometric imperfection of the beam, nonlocal scale factor, foundation and geometrical factors.
Keywords
nonlinear stability; Chebyshev-Ritz method; metal foam; refined beam theory; nonlocal elasticity;
Citations & Related Records
Times Cited By KSCI : 65  (Citation Analysis)
연도 인용수 순위
1 Bourada, F., Amara, K., Bousahla, A. A., Tounsi, A. and Mahmoud, S. R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.   DOI
2 Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A. A., Tounsi, A. and Mahmoud, S. R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.   DOI
3 Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A. and Mahmoud, S. R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.   DOI
4 Tounsi, A., Al-Dulaijan, S. U., Al-Osta, M. A., Chikh, A., Al-Zahrani, M. M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511. https://doi.org/10.12989/scs.2020.34.4.511.   DOI
5 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.   DOI
6 Xiao, W., Li, L. and Wang, M. (2017), "Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory", Appl. Physics A, 123(6), 388. https://doi.org/10.1007/s00339-017-1007-1.   DOI
7 Younsi, A., Tounsi, A., Zaoui, F. Z., Bousahla, A.A. and Mahmoud, S. R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519.   DOI
8 Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.   DOI
9 Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A. A., Bourada, M., Tounsi, A. and Al-Osta, M. A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.   DOI
10 Chaabane, L. A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F. Z., Tounsi, A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.   DOI
11 Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025.   DOI
12 Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617   DOI
13 Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909.   DOI
14 Zhu, X and Li, L. (2017), "Closed form solution for a nonlocal strain gradient rod in tension", J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019.   DOI
15 Eringen, A. C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Physics, 54(9), 4703-4710. https://doi.org/10.1063/1.332803.   DOI
16 Daouadji, T. H., Benferhat, R. and Adim, B. (2016), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Materials Res., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107.   DOI
17 Draiche et al. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11, 671-690. https://doi.org/10.12989/gae.2016.11.5.671.   DOI
18 El-Hassar, S. M., Benyoucef, S., Heireche, H. and Tounsi, A. (2016), "Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory", Geomech. Eng., 10(3), 357-386. https://doi.org/10.12989/gae.2016.10.3.357.   DOI
19 Eltaher, M. A., Khater, M. E., Park, S., Abdel-Rahman, E and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51-64. http://dx.doi.org/10.12989/anr.2016.4.1.000.   DOI
20 Elmerabet, A. H., Heireche, H., Tounsi, A and Semmah, A. (2017), "Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model," Adv. Nano Res., 5(1), 1-12. https://doi.org/10.12989/anr.2017.5.1.001.   DOI
21 Fallah, A. and Aghdam, M. M. (2011), "Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation.", European J. Mech. A/Solids, 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005.   DOI
22 Fenjan, R. M., Ahmed, R. A., Alasadi, A. A. and Faleh, N. M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupled Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.   DOI
23 Kheroubi, B., Benzair, A., Tounsi, A and Semmah, A. (2016), "A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams," Adv. Nano Res., 4(4), 251-264. https://doi.org/10.12989/anr.2016.4.4.251.   DOI
24 Fourn, H., Atmane, H. A., Bourada, M., Bousahla, A. A., Tounsi, A. and Mahmoud, S. R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.   DOI
25 Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A. A. and Mahmoud, S. R. (2019). Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., https://doi.org/10.1177%2F1099636219845841.
26 Hussain, M., Naeem, M. N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431. https://doi.org/10.12989/anr.2019.7.6.431.   DOI
27 Issad, M. N., Fekrar, A., Bakora, A., Bessaim, A. and Tounsi, A. (2018), "Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory", Geomech. Eng., 15(1), 711-719. https://doi.org/10.12989/gae.2018.15.1.711.   DOI
28 Khiloun, M., Bousahla, A. A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S. R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Computers, 1-15. https://doi.org/10.1007/s00366-019-00732-1.
29 Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.   DOI
30 Li, L., Hu, Y and Ling, L. (2016b), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Systems and Nanostructures, 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028.   DOI
31 Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.   DOI
32 Li, L and Hu, Y. (2016), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Comput. Materials Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044.   DOI
33 Lim, C. W., Zhang, G and Reddy, J. N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Physics Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.   DOI
34 Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E. A. and Mahmoud, S. R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577.   DOI
35 Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E. A. and Mahmoud, S. R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandwich Struct. Materials, 21(2), 727-757. https://doi.org/10.1177/1099636217698443.   DOI
36 Mechab, I., Mechab, B., Benaissa, S., Serier, B and Bouiadjra, B. B. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Brazilian Society Mech. Sci. Eng., 38(8), 2193-2211. https://doi.org/10.1007/s40430-015-0482-6.   DOI
37 Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.   DOI
38 Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A. A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory. Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.   DOI
39 Ahmed, R. A., Fenjan, R. M. and Faleh, N. M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections," Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.   DOI
40 Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743.   DOI
41 Al-Maliki, A. F., Faleh, N. M. and Alasadi, A. A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities," Struct. Monitoring Maintenance, 6(2), 147-159. https:// doi.org/10.12989/smm.2019.6.2.147.   DOI
42 Sahla, M., Saidi, H., Draiche, K., Bousahla, A. A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663. https://doi.org/10.12989/scs.2019.33.5.663.   DOI
43 Merazi, M., Hadji, L., Daouadji, T. H., Tounsi, A. and Adda Bedia, E. A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305.   DOI
44 Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.   DOI
45 Sadoun, M., Houari, M. S. A., Bakora, A., Tounsi, A., Mahmoud, S. R. and Alwabli, A. S. (2018), "Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory", Geomech. Eng., 16(2), 141-150. https://doi.org/10.12989/gae.2018.16.2.141.   DOI
46 Semmah, A., Heireche, H., Bousahla, A. A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89. https://doi.org/10.12989/anr.2019.7.2.089.   DOI
47 Soltani, K., Bessaim, A., Houari, M. S. A., Kaci, A., Benguediab, M., Tounsi, A. and Alhodaly, M. S. (2019), "A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations", Steel Composite Struct., 30(1), 13-29. https://doi.org/10.12989/scs.2019.30.1.013.   DOI
48 Barati, M. R., Zenkour, A. M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory," Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056.   DOI
49 Attia, A., Bousahla, A. A., Tounsi, A., Mahmoud, S. R. and Alwabli, A. S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.   DOI
50 Atmane, H.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. https://doi.org/10.12989/scs.2015.19.2.369.   DOI
51 Berrabah, H. M., Tounsi, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351.   DOI
52 Besseghier, A., Heireche, H., Bousahla, A. A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029.   DOI
53 Shokravi, M. (2017), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM," Geomech. Eng., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327.   DOI
54 Sayyad, A. S. and Ghugal, Y. M. (2018), "An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation", Adv. Aircraft Spacecraft Sci., 5(6), 671-689. https://doi.org/10.12989/aas.2018.5.6.671.   DOI