Analytical Modeling of Buckling Behavior of Porous FGM Cylindrical Shell Embedded within an Elastic Foundation

Abstract

The aim of this paper is to investigate the buckling behavior of porous Functionally Graded Materiel (FGM) cylindrical shells based on Donnell shell theory. In this context, we develop an explicit analytical expression which takes into consideration the effect of porosities through the thickness of the structure and that of the elastic foundation using a modified power-law function and the models of Winkler and Pasternak, respectively. We use the modified rule of mixture to determinate the behavior of the porous FGM cylindrical shell. The effects of porosity volume fraction, power-law index, and Young’s modulus ratio are investigated. Moreover, we also discuss the influence of different parameters on the stability behavior of the porous FGM shell.

Keywords

• Stability analysis
• Elastic foundation
• Porous FGM shell
• Cylindrical shell theory

References

1. [1] Mahamood, R.M., Akinlabi, E.T., “Types of functionally graded materials and their areas of application”, Functionally Graded Materials, Springer, 5: 9-21, (2017).
2. [2] Bessaim, A. , Houari, M. S. A., Tounsi, A. , Mahmoud, S. R., Adda Bedia, E.A., “A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets”, J. Sandw. Struct. Mater., 15(6): 671-703, (2013).
3. [3] Tounsi, A., Houari, M.S.A., Benyoucef, S., Adda Bedia, E.A., “A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates”, Aerosp. Scı. technol., 24(1): 209-220, (2013).
4. [4] Boggarapu, V., Gujjala, R., Ojha, S., Acharya, S., Venkateswara babu, P., Chowdary, S., kumar Gara, D., “State of the art in functionally graded materials”, Compos. Struct., 262: 113596, (2021).
5. [5] Bakhti, K., Kaci, A. , Bousahla, A.A. , Houari, M.S.A., Tounsi, A. , Adda Bedia, E. A., “Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory”, Steel Compos. Struct., 14(4): 335-347, (2013).
6. [6] Banerjee, J.R., Ananthapuvirajah, A., “Free vibration of functionally graded beams and frameworks using the dynamic stiffness method”, J. Sound Vib., 422: 34-47, (2018).
7. [7] Ould Larbi, L., Kaci, A., Houari, M.S.A., Tounsi, A., “An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams”, Mech. Based Des. Struct. Mach., 41(4): 421-433, (2013).
8. [8] Kou, K., Yang, Y., “A meshfree boundary-domain integral equation method for free vibration analysis of the functionally graded beams with open edged cracks”, Compos. B. Eng., 156: 303-309, (2019).

9. [9] Mercan, K., Demir, C., Civalek, Ӧ., “Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique”, Curved Layer. Struct., 3(1): 82-90, (2016).
10. [10] Dastjerdi, S., Akgöz, B., Civalek, Ӧ., “On the effect of viscoelasticity on behavior of gyroscopes”, Int. J. Eng. Sci., 149: 103236, (2020) .
11. [11] Naebe, M., Shirvanimoghaddam, K., “Functionally graded materials: A review of fabrication and properties“, Appl. Mater. Today, 5: 223-245, (2016).
12. [12] Gong, J., Xuan, L., Ying, B., Wang, H., “Thermoelastic analysis of functionally graded porous materials with temperature-dependent properties by a staggered finite volume method”, Compos. Struct., 224: 111071, (2019).
13. [13] Keleshteri, M., Jelovica, J., “Nonlinear vibration behavior of functionally graded porous cylindrical panels”, Compos. Struct., 239: 112028, (2020).
14. [14] Kim, J., Zur, K.K., Reddy, J., “Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates”, Compos. Struct., 209: 879-888, (2019).
15. [15] Chen, D., Yang, J., Kitipornchai, S., “Elastic buckling and static bending of shear deformable functionally graded porous beam”, Compos. Struct., 133: 54-61, (2015).
16. [16] Wang, Y., Wu, D., “Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory”, Aerosp. Sci. Technol., 66: 83-91, (2017).
17. [17] Zhou, C., Wang, P., Li, W., “Fabrication of functionally graded porous polymer via supercritical co2 foaming”, Compos. B Eng., 42: 318-325, (2011).
18. [18] Fiorenzo A.F., “Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations”, Compos. B Eng., 156: 303-309, (2019).
19. [19] Jalaei, M.H., Civalek, Ӧ., “dynamic instability of magnetically embedded viscoelastic porous FG nanobeam”, Int. J. Eng. Sci., 143: 14-32, (2019).
20. [20] Ebrahimi, F., Zia, M., “Large amplitude nonlinear vibration analysis of functionally graded timoshenko beams with porosities”, Acta Astronaut., 116: 117-125, (2015).
21. [21] Chen, D., Kitipornchai, S., Yang, J., “Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core”, Thin Walled Struct., 107: 39-48, (2016).
22. [22] Atmane, H.A., Tounsi, A., Bernard, F., “Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations”, Int. J. Mech. Mater. Des., 13:71-84, (2017).
23. [23] Berghouti, H., Adda Bedia, E.A., Benkhedda, A., Tounsi, A., “Vibration analysis of nonlocal porous nanobeams made of functionally graded material”, Adv. Nano Res., 7(5): 351-364, (2019).
24. [24] Medani, M., Benahmed, A., Zidour, A., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., “Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle”, Steel Compos. Struct., 32: 595-610, (2019).
25. [25] Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A., Al- Osta, M.A., “A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis”, Comput. Concr., 25(1): 37-57, (2020).
26. [26] Jena, S.K., Chakraverty, S., Malikan, M., “Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation”, Engineering with Computers, (2020). https://doi.org/10.1007/s00366-020-01018-7
27. [27] Tran, T.T., Pham, Q.H., Nguyen-Thoi, T., “An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)”, Math. Probl. Eng., 2020: 1-17, (2020).
28. [28] Ebrahimi, F., Dabbagh, A., Rastgoo, A., “Vibration analysis of porous metal foam shells rested on an elastic substrate”, J. Strain Anal. Eng. Des., 54(3):199-208, (2019).
29. [29] Jouneghani, F.Z., Dimitri, R., Bacciocchi, M., Tornabene, F., “Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory”, Appl. Sci., 7(12): 1252, (2017).
30. [30] Wang, Y., Ye, C., Zu, J.W., “Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities”, Appl. Math. Mech., 39: 1587-1604,(2018).
31. [31] Keddouri, A., Hadji, L., Tounsi, A., “Static analysis of functionally graded sandwich plates with porosities”, Adv. Mater. Res., 8(3): 155-177, (2019).
32. [32] Donnell, L.H., “Stability of Thin-Walled Tubes Under Torsion”, N.A.C.A. Technical Report No. 479, (1934).
33. [33] Timesli, A., “An efficient approach for prediction of the nonlocal critical buckling load of doublewalled carbon nanotubes using the nonlocal Donnell shell theory”, SN Appl. Sci., 2: 407, (2020).
34. [34] Timesli, A., “Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation”, Comput. Concr., 26(1): 53-62, (2020).
35. [35] Timesli, A., Braikat, B., Jamal, M., Damil, N. “Prediction of the critical buckling load of multi walled carbon nanotubes under axial compression”. C. R. Mecanique., 345(2): 158-168, (2017).
36. [36] Asghar, S., Naeem, M.N., Hussain, M., Taj, M., Tounsi, A., “Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis”, Comput. Concr., 25(2): 133-144, (2020).
37. [37] Erklig, A., Guzelbey, I.H. and Cevik, A., “Finite element analysis of finite strain elastoplastic contact-impact problems”, Gazi Univ. J. Sci., 23(3): 327 -338, (2010).
38. [38] Çelik, K., Kurt, E. and Uzun, Y., “Experimental and theoretical explorations on the buckling piezoelectric layer under magnetic excitation”. J. Electron. Mater., 46, 4003-4016, (2017).
39. [39] She, G.L., Yuan, F.G., Ren,Y.R., Liu, H.B., Xiao, W.S., “Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory”, Compos. Struct., 203 :614-623, (2018).
40. [40] Kerr, A.D., “Elastic and viscoelastic foundation models”, ASME. J. Appl. Mech., 31(3): 491-498, (1964).
41. [41] Kerr, A.D., “A study of a new foundation model”, Acta Mech., 1: 135-147, (1965).
42. [42] Winkler, E., “Die Lehre von Elastizitat und Festigkeit (on Elasticity and Fixity)”, Dominicus, Prague, (1867).
43. [43] Pasternak, P.L., “On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants”, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow, (1954).
44. [44] Çevik, M., “In-plane Vibration Analysis of Symmetric Angle-ply Laminated Composite Arches”, Gazi Univ. J. Sci., 23(2): 187-199, (2010).