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http://dx.doi.org/10.12989/sem.2019.71.1.089

Effects of porosity models on static behavior of size dependent functionally graded beam  

Hamed, Mostafa A. (Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University)
Sadoun, Ayman M. (Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University)
Eltaher, Mohamed A. (Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University)
Publication Information
Structural Engineering and Mechanics / v.71, no.1, 2019 , pp. 89-98 More about this Journal
Abstract
In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.
Keywords
porosity models; static bending; functionally graded beam; nonlocal elasticity; finite element method;
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1 Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014b), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.   DOI
2 Eltaher, M., Khater, M., and Emam, S. (2016a), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.   DOI
3 Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016b), "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.2016.4.1.051.   DOI
4 Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018a), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.   DOI
5 Eltaher, M.A., Kabeel, A.M., Almitani, K.H. and Abdraboh, A.M. (2018b), "Static bending and buckling of perforated nonlocal size-dependent nanobeams", Microsyst. Technol., 24(12), 4881-4893. https://doi.org/10.1007/s00542-018-3905-3.   DOI
6 Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), pp.1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.   DOI
7 Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. http://dx.doi.org/10.12989/sss.2018.21.1.015.   DOI
8 Yousfi, M., Atmane, H.A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66(3), 353-368. http://dx.doi.org/10.12989/sem.2018.66.3.353.   DOI
9 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. http://dx.doi.org/10.12989/sem.2015.54.4.693.   DOI
10 Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018c), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24, 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.   DOI
11 Eltaher M.A., Mohamed N., Mohamed S. and Seddek L.F. (2019), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, https://doi.org/10.4028/www.scientific.net/JNanoR.57.136.
12 Eltaher M.A., Almalki T.A., Ahmed K. I.E., and Almitani K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano. Res., 7(1), 39-49. https://doi.org/10.12989/anr.2019.7.1.039.   DOI
13 Hamza-Cherif, R., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, S. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1.   DOI
14 Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. http://dx.doi.org/10.12989/sem.2017.64.2.145.   DOI
15 Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999.   DOI
16 Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. http://dx.doi.org/10.12989/scs.2017.25.6.717.   DOI
17 Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.   DOI
18 Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006.   DOI
19 Akbas, S.D. (2017), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 579-589. http://dx.doi.org/10.12989/scs.2017.24.5.579.   DOI
20 Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. http://dx.doi.org/10.12989/scs.2016.20.5.963.   DOI
21 Heshmati, M. and Daneshmand, F. (2018), "A study on the vibrational properties of weight-efficient plates made of material with functionally graded porosity", Compos. Struct., 200, 229-238. https://doi.org/10.1016/j.compstruct.2018.05.099.   DOI
22 Houari, M.S.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.   DOI
23 Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., 65(5), 621-631. http://dx.doi.org/10.12989/sem.2018.65.5.621.   DOI
24 Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., 55, 42-56. https://doi.org/10.4028/www.scientific.net/JNanoR.55.42   DOI
25 Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. http://dx.doi.org/10.12989/eas.2018.14.2.103.   DOI
26 Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. http://dx.doi.org/10.12989/scs.2017.25.3.361.   DOI
27 Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070.   DOI
28 Al Rjoub, Y.S. and Hamad, A.G. (2017), "Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method", KSCE J. Civil Eng., 21(3), 792-806. https://doi.org/10.1007/s12205-016-0149-6.   DOI
29 Atmane, H.A., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", J. Mech. Mater. Design, 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x.   DOI
30 Bakhadda, B., Bouiadjra, M.B., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. http://dx.doi.org/10.12989/was.2018.27.5.311.   DOI
31 Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. http://dx.doi.org/10.12989/scs.2015.18.4.1063.   DOI
32 Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. http://dx.doi.org/10.12989/sem.2017.62.6.695.   DOI
33 Kim, H.S., Yang, Y., Koh, J. T., Lee, K.K., Lee, D.J., Lee, K.M. and Park, S.W. (2009), "Fabrication and characterization of functionally graded nano-micro porous titanium surface by anodizing", J. Biomed. Mater. Res. Part B, 88(2), 427-435. https://doi.org/10.1002/jbm.b.31124.
34 Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Walled Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.   DOI
35 Karami, B., Janghorban, M. and Tounsi, A. (2018b), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. http://dx.doi.org/10.12989/scs.2018.27.2.201.   DOI
36 Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. http://dx.doi.org/10.12989/sem.2017.64.4.391.   DOI
37 Kim, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.   DOI
38 Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.   DOI
39 Li, J.F., Takagi, K., Ono, M., Pan, W., Watanabe, R., Almajid, A. and Taya, M. (2003), "Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators", J. American Ceramic Soc., 86(7), 1094-1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x.   DOI
40 Komijani, M., Esfahani, S.E., Reddy, J.N., Liu, Y.P. and Eslami, M.R. (2014), "Nonlinear thermal stability and vibration of pre/post-buckled temperature-and microstructure-dependent functionally graded beams resting on elastic foundation", Compos. Struct., 112, 292-307. https://doi.org/10.1016/j.compstruct.2014.01.041.   DOI
41 Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin Wall. Struct., 46(3), 333-337. https://doi.org/10.1016/j.tws.2007.06.006.   DOI
42 Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theoretical Appl. Mech., 47, 421-433.
43 Magnucka-Blandzi, E. (2010), "Non-linear analysis of dynamic stability of metal foam circular plate", J. Theoretical Appl. Mech., 48(1), 207-217.
44 Magnucki, K. and Stasiewicz, P. (2004), "Elastic buckling of a porous beam", J. Theoretical Appl. Mech., 42(4), 859-868.
45 Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126. http://dx.doi.org/10.12989/sss.2017.19.2.115.   DOI
46 Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory', Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601.   DOI
47 Biot, M.A. (1964), "Theory of buckling of a porous slab and its thermoelastic analogy", J. Appl. Mech., 31(2), 194-198.   DOI
48 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. andTounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. http://dx.doi.org/10.12989/anr.2018.6.2.147.   DOI
49 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., 20(2), 227-249. http://dx.doi.org/10.12989/scs.2016.20.2.227.   DOI
50 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30.   DOI
51 Chaht, F.L., Kaci, A., Houari, M.S.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.   DOI
52 Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008.   DOI
53 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. Brazil Soc. Mech. Sci. Eng., 38(8), 2193-2211. https://doi.org/10.1007/s40430-015-0482-6.   DOI
54 Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.   DOI
55 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
56 Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. http://dx.doi.org/10.12989/sss.2018.21.4.397.   DOI
57 Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. http://dx.doi.org/10.12989/sss.2017.20.3.369.   DOI
58 Shafiei, N. and Kazemi, M. (2017a), "Buckling analysis on the bidimensional functionally graded porous tapered nano-/microscale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.   DOI
59 Shafiei, N. and Kazemi, M. (2017b), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045.   DOI
60 Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", J. Mech. Sci., 108, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025.
61 Detournay, E. and Cheng, A.H.D. (1995), "Fundamentals of poroelasticity", Analysis Design Methods, 113-171. https://doi.org/10.1016/B978-0-08-040615-2.50011-3.
62 Detsi, E., Selles, M.S., Onck, P.R. and De Hosson, J.T.M. (2013), "Nanoporous silver as electrochemical actuator", Scripta Materialia, 69(2), 195-198. https://doi.org/10.1016/j.scriptamat.2013.04.003.   DOI
63 Ebrahimi, F. and Daman, M. (2017), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., 64(1), 121-133. http://dx.doi.org/10.12989/sem.2017.64.1.121.   DOI
64 Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016. http://dx.doi.org/10.1155/2016/9561504.
65 Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014a), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.   DOI
66 She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018a), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Europe. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5.   DOI
67 She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018b), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.   DOI
68 She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", J. Eng. Science, 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.   DOI
69 Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronautica, 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014.   DOI
70 Eltaher, M., Emam, S. and Mahmoud, F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030.   DOI
71 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
72 Shojaeefard, M.H., Googarchin, H.S., Ghadiri, M. and Mahinzare, M. (2017), "Micro temperature-dependent FG porous plate: free vibration and thermal buckling analysis using modified couple stress theory with CPT and FSDT", Appl. Math. Model., 50, 633-655. https://doi.org/10.1016/j.apm.2017.06.022.   DOI
73 Thang, P.T., Nguyen-Thoi, T., Lee, D., Kang, J. and Lee, J. (2018), "Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions", Aerosp. Sci. Technol.. https://doi.org/10.1016/j.ast.2018.06.010.