Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov's foundation

  • Bamdad, Mostafa (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Alambeigi, Kazem (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.05.05
  • Accepted : 2020.07.15
  • Published : 2020.09.25
⟨ Previous Next ⟩

Abstract

The aim of this research is to analyze buckling and bending behavior of a sandwich Reddy beam with porous core and composite face sheets reinforced by boron nitride nanotubes (BNNTs) and shape memory alloy (SMA) wires resting on Vlasov's foundation. To this end, first, displacement field's equations are written based on the higher-order shear deformation theory (HSDT). And also, to model the SMA wire properties, constitutive equation of Brinson is used. Then, by utilizing the principle of minimum potential energy, the governing equations are derived and also, Navier's analytical solution is applied to solve the governing equations of the sandwich beam. The effect of some important parameters such as SMA temperature, the volume fraction of SMA, the coefficient of porosity, different patterns of BNNTs and porous distributions on the behavior of buckling and bending of the sandwich beam are investigated. The obtained results show that when SMA wires are in martensite phase, the maximum deflection of the sandwich beam decreases and the critical buckling load increases significantly. Furthermore, the porosity coefficient plays an important role in the maximum deflection and the critical buckling load. It is concluded that increasing porosity coefficient, regardless of porous distribution, leads to an increase in the critical buckling load and a decrease in the maximum deflection of the sandwich beam.

Keywords

Acknowledgement

The authors would like to thank the referees for their valuable comments. Also, they are thankful to the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work (Grant Number: 891238/6).

References

  1. Alambeigi K., Mohammadimehr M., Bamdad M. and Rabczuk, T. (2020), "Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov's foundation", Acta Mechanica, 231, 3199-3218. https://doi.org/10.1007/s00707-020-02697-5.
  2. Amiri, A., Mohammadimehr, M. and Anvari M. (2020), "Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets", Appl. Math. Mech., 41(7), 1027-1038. https://doi.org/10.1007/s10483-020-2627-7.
  3. Akbari, T. and Khalili, S.M.R. (2019), "Numerical simulation of buckling behavior of thin walled composite shells with embedded shape memory alloy wires", Thin-Wall. Struct., 143, 106193. https://doi.org/10.1016/j.tws.2019.106193.
  4. Akhavan-Alavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech.-A/Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  5. Akhavan-Rad, B. and Kheirikhah, M.M. (2019), "Static analysis of sandwich plates embedded with shape memory alloy wires using active strain energy tuning method", J. Brazilian Soc. Mech. Sci. Eng., 41(3), 160. https://doi.org/10.1007/s40430-019-1666-2.
  6. Arani, A.G., Arani, A.H.S. and Haghparast, E. (2018), "Bending analysis of magneto-electro-thermo-elastic functionally graded nano-beam based on first order shear deformation theory", Int. J. Bio-Inorg. Hybr. Nanomater, 7(2), 163-176.
  7. Arani, A.G., Pourjamshidian, M., Arefi, M. and Arani, M.R. (2019), "Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak's foundation based on higher order shear deformation theory", Struct. Eng. Mech., 69(4), 439-455. https://doi.org/10.12989/sem.2019.69.4.439.
  8. Arenal, R., Wang, M.S., Xu, Z., Loiseau, A. and Golberg, D. (2011), "Young modulus, mechanical and electrical properties of isolated individual and bundled single-walled boron nitride nanotubes", Nanotechnology, 22(26), 265704. https://doi.org/10.1088/0957-4484/22/26/265704.
  9. Babaeeian, M. and Mohammadimehr, M. (2020), "Investigation of the time elapsed effect on residual stress measurement in a composite plate by DIC method", Opt. Lasers Eng., 128. 106002. https://doi.org/10.1016/j.optlaseng.2020.106002
  10. Babaee, A., Sadighi, M., Nikbakht, A. and Alimirzaei, S. (2018), "Generalized differential quadrature nonlinear buckling analysis of smart SMA/FG laminated beam resting on nonlinear elastic medium under thermal loading", J. Therm. Stresses, 41(5), 583- 607. https://doi.org/10.1080/01495739.2017.1408048.
  11. Bamdad, M., Mohammadimehr, M. and Alambeigi, K. (2019), "Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: Magneto-electroelastic vibration and buckling solution", J. Vib. Control, 25(23-24), 2875-2893. https://doi.org/10.1177/1077546319860314.
  12. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.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.
  13. 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.
  14. De Sousa, V. C., Tan, D., De Marqui Jr, C. and Erturk, A. (2018), "Tunable metamaterial beam with shape memory alloy resonators: Theory and experiment", Appl. Phys. Lett., 113(14), 143502. https://doi.org/10.1063/1.5050213.
  15. Ebrahimi, F. and Barati, M.R. (2018), "Stability analysis of porous multi-phase nanocrystalline nonlocal beams based on a general higher-order couple-stress beam model", Struct. Eng. Mech., 65(4), 465-476. https://doi.org/10.12989/sem.2018.65.4.465.
  16. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.
  17. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., 7(2), 109. https://doi.org/10.12989 /anr.2019.7.2.109. https://doi.org/10.12989/ANR.2019.7.2.109
  18. Fang, W., Yu, T., Van Lich, L. and Bui, T.Q. (2019), "Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis", Compos. Struct., 221, 110890. https://doi.org/10.1016/j.compstruct.2019.04.062.
  19. Faraji-Oskouie, M., Norouzzadeh, A., Ansari, R. and Rouhi, H. (2019), "Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach", Appl. Math. Mech., 40(6), 767-782. https://doi.org/10.1007/s10483-019-2491-9.
  20. He, Y., Li, Y., Liu, Z. and Liew, K.M. (2017), "Buckling analysis and buckling control of thin films on shape memory polymer substrate", Eur. J. Mech.-A/Solids, 66, 356-369. https://doi.org/10.1016/j.euromechsol.2017.08.006.
  21. Heydari, A. and Shariati, M. (2018), "Buckling analysis of tapered BDFGM nano-beam under variable axial compression resting on elastic medium", Struct. Eng. Mech., 66(6), 737-748. https://doi.org/10.12989/sem.2018.66.6.737.
  22. Huang, Y., Lin, J., Tang, C., Bando, Y., Zhi, C., Zhai, T., Dierre, B., Sekiguchi, T. and Golberg, D. (2011), "Bulk synthesis, growth mechanism and properties of highly pure ultrafine boron nitride nanotubes with diameters of sub-10 nm", Nanotechnology, 22(14), 145602. https://doi.org/10.1088/0957-4484/22/14/145602.
  23. Kabir, M.Z. and Tehrani, B.T. (2017), "Closed-form solution for thermal, mechanical, and thermo-mechanical buckling and post-buckling of SMA composite plates", Compos. Struct., 168, 535-548. https://doi.org/10.1016/j.compstruct.2017.02.046.
  24. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621.
  25. Kheirikhah, M.M. and Khosravi, P. (2018), "Buckling and free vibration analyses of composite sandwich plates reinforced by shape-memory alloy wires", J. Brazilian Soc. Mech. Sci. Eng., 40(11), 515. https://doi.org/10.1007/s40430-018-1438-4.
  26. Kozikowska, A. (2019), "Multi-objective topology and geometry optimization of statically determinate beams", Struct. Eng. Mech., 70(3), 367-380. https://doi.org/10.12989/sem.2019.70.3.367.
  27. Lee, J.W. and Lee, J.Y. (2018), "A transfer matrix method for in-plane bending vibrations of tapered beams with axial force and multiple edge cracks", Struct. Eng. Mech., 66(1), 125-138. https://doi.org/10.12989/sem.2018.66.1.125.
  28. Liu, Y., Su, S., Huang, H. and Liang, Y. (2019), "Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane", Compos. Part B: Eng., 168, 236-242. https://doi.org/10.1016/j.compositesb.2018.12.063.
  29. Mohammadimehr, M., Atifeh, S.J. and Rousta Navi, B. (2018a), "Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings", J. Vib. Control, 24(15), 3471-3486. https://doi.org/10.1177/1077546317706887.
  30. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Akhavan Alavi, S.M., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018b), "Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., 29(3), 405-422. https://doi.org/10.12989/scs.2018.29.3.405.
  31. Mohammadimehr, M. and Rostami, R. (2018), "Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields", Appl. Math. Mech., 39(2). 219-240, https://doi.org/10.1007/s10483-018-2301-6.
  32. Nguyen, N.D., Nguyen, T.K., Vo, T.P., Nguyen, T.N. and Lee, S. (2019), "Vibration and buckling behaviours of thin-walled composite and functionally graded sandwich I-beams", Compos. Part B: Eng., 166, 414-427. https://doi.org/10.1016/j.compositesb.2019.02.033.
  33. Polit, O., Anant, C., Anirudh, B. and Ganapathi, M. (2019), "Functionally graded graphene reinforced porous nanocomposite curved beams: Bending and elastic stability using a higher-order model with thickness stretch effect", Compos. Part B: Eng., 166, 310-327. https://doi.org/10.1016/j.compositesb.2018.11.074.
  34. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano, 3(12), 3884-3890. https://doi.org/10.1021/nn9010472.
  35. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  36. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082.
  37. Soltanieh, G., Kabir, M.Z. and Shariyat, M. (2019), "Improvement of the dynamic instability of shallow hybrid composite cylindrical shells under impulse loads using shape memory alloy wires", Compos.Part B: Eng., 167, 167-179. https://doi.org/10.1016/j.compositesb.2018.12.040.
  38. Tang, H., Li, L. and Hu, Y. (2018), "Buckling analysis of two-directionally porous beam", Aerosp. Sci. Technol., 78, 471-479. https://doi.org/10.1016/j.ast.2018.04.045.
  39. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
  40. Thanh, C.L., Tran, L.V., Bui, T.Q., Nguyen, H.X. and Abdel-Wahab, M. (2019), "Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates", Compos. Struct., 221, 110838. https://doi.org/10.1016/j.compstruct.2019.04.010.
  41. Wang, C.M., Reddy, J.N. and Lee, K.H. (Eds.) (2000), "Shear deformable beams and plates: Relationships with classical solutions", Elsevier.
  42. Wattanasakulpong, N. and Bui, T.Q. (2018), "Vibration analysis of third-order shear deformable FGM beams with elastic support by Chebyshev collocation method", Int. J. Struct. Stab. Dynam., 18(5), 1850071. https://doi.org/10.1142/S0219455418500712.
  43. Wu, H., Kitipornchai, S. and Yang, J. (2015), "Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets", Int. J. Struct. Stab. Dynam., 15(7), 1540011. https://doi.org/10.1142/S0219455415400118.
  44. Yazdani, R., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of Cooper-Naghdi micro saturated porous sandwich cylindrical shells with reinforced CNT face sheets under magneto-hydro-thermo-mechanical loadings", Struct. Eng. Mech., 70(3), 351-365. https://doi.org/10.12989/sem.2019.70.3.351.
  45. Yu, C., Kang, G. and Kan, Q. (2018), "A micromechanical constitutive model for grain size dependent thermo-mechanically coupled inelastic deformation of super-elastic NiTi shape memory alloy", Int. J.Plasticity, 105, 99-127. https://doi.org/10.1016/j.ijplas.2018.02.005.

Cited by

  1. Mechanical and thermal buckling analysis of laminated composite plates vol.40, pp.5, 2020, https://doi.org/10.12989/scs.2021.40.5.697