Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Optimization of porosity distribution of FGP beams considering buckling strength

  • Farrokh, Mojtaba (Advanced Structures Research Lab., K. N. Toosi University of Technology) ;
  • Taheripur, Mohammad (Advanced Structures Research Lab., K. N. Toosi University of Technology)
  • Received : 2020.11.06
  • Accepted : 2021.07.20
  • Published : 2021.09.25
⟨ Previous Next ⟩

Abstract

In this paper, the porosity distribution of functionally graded porous (FGP) beams are optimized using the genetic algorithm to achieve the maximum ratio of the normalized buckling load to the beam's weight. The analytical forms for critical buckling loads of the FGP beams under different end conditions are determined analytically using principle virtual work based on the Euler and Timoshenko beam theories. The effects of Nano Graphene Platelets (NGPs) on the critical buckling load of the nanocomposite FGP beams are also taken into account. The sensitivity analyses show that porosity will reduce the buckling load-to-weight ratio of porous beams to conventional beams in some cases. Based on the optimization results, the optimum distribution of the porosity and NGPs' volume fraction are proposed for several porosity coefficients. The obtained results indicate that the optimum distribution for porosity has a symmetric sandwich-like shape while the optimum distribution for NGPs' volume fraction is uniform.

Keywords

References

  1. Ansari, R. and Torabi, J. (2016), "Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading", Compos. Part B: Eng., 95, 196-208. https://doi.org/10.1016/j.compositesb.2016.03.080.
  2. 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.
  3. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108-109, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025.
  4. Fritsch, F.N. and Carlson, R.E. (1980), "TMonotone piecewise cubic interpolation", SIAM J. Numer. Anal., 17(2), 238-246. https://doi.org/10.1137/071702.
  5. Grygorowicz, M., Magnucki, K. and Malinowski, M. (2015), "Elastic buckling of a sandwich beam with variable mechanical properties of the core", Thin Wall. Struct., 87, 127-132. https://doi.org/10.1016/j.tws.2014.11.014.
  6. Hadj, B., Rabia, B. and Daouadji, T.H. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 61-70. https://doi.org/10.12989/sem.2019.72.1.061.
  7. Halpin Affdl, J.C and Kardos, K.L (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  8. Hamed, M.A, Sadoun, A.M. and Eltaher, M.A (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.
  9. Jamshidi, M. and Arghavani, J. (2017), "Optimal design of two-dimensional porosity distribution in shear deformable functionally graded porous beams for stability analysis", Thin Wall. Struct., 120, 81-90. http://dx.doi.org/10.1016/j.tws.2017.08.027.
  10. Jasion, P., Magnucka-Blandzi, E., Szyc, W. and Magnucki, K. (2012), "Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core", Thin Wall. Struct., 61, 154-161. https://doi.org/10.1016/j.tws.2012.04.013.
  11. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  12. Lieu, Q.X. and Lee, J. (2019), "An isogeometric multimesh design approach for size and shape optimization of multidirectional functionally graded plates", Comput. Meth. Appl. Mech. Eng., 343, 407-437. https://doi.org/10.1016/j.cma.2018.08.017.
  13. Magnucki, K. and Stasiewicz, P. (2004), "Elastic buckling of a porous beam", J. Theo. Appl. Mech., 42(4), 859-868.
  14. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer International Publishing.
  15. Mirjavadi, S.S., Forsat, M., Yahya, Z., Barati, M., Jayasimha, A.N. and Hamouda, A. (2020), "Porosity effects on post-buckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners", Struct. Eng. Mech., 75(6), 701-711. http://doi.org/10.12989/sem.2020.75.6.701.
  16. Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin Wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008.
  17. Ochoa, O.O. and Reddy, J.N. (1992), "Finite element analysis of composite laminates", Finite Element Analysis of Composite Laminates, Springer, Dordrecht.
  18. Park, S., Yoo, H.H. and Chung, J. (2013), "Vibrations of an axially moving beam with deployment or retraction", AIAA J., 51(3), 686-696. https://doi.org/10.2514/1.J052059.
  19. Phung-van, P., Ferreira, A.J.M. and Thai, C.H. (2020), "Computational optimization for porosity-dependent isogeometric analysis of functionally graded sandwich nanoplates", Compos. Struct., 239, 112029. https://doi.org/10.1016/j.compstruct.2020.112029.
  20. Phung-van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019a), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B: Eng., 164, 215-225. https://doi.org/10.1016/j.compositesb.2018.11.036.
  21. Phung-van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019b), "An isogeometric approach of static and free vibration analyses for porous FG nanoplates", Eur. J. Mech.-A/Solid., 78, 103851. https://doi.org/10.1016/j.euromechsol.2019.103851.
  22. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, 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.
  23. Roberts, A.P. and Garboczi, E.J. (2002), "Computation of the linear elastic properties of random porous materials with a wide variety of microstructure", Proc. Roy. Soc. London. Ser. A: Math. Phys. Eng. Sci., 458, 1033-1054. https://doi.org/10.1098/rspa.2001.0900
  24. Shokrieh, M.M., Esmkhani, M., Shokrieh, Z. and Zhao, Z. (2014), "Stiffness prediction of graphene nanoplatelet/epoxy nanocomposites by a combined molecular dynamics-micromechanics method", Comput. Mater. Sci., 92, 444-450. https://doi.org/10.1016/j.commatsci.2014.06.002.
  25. Wu, H.L., Yang, J. and Kitipornchai, S. (2016), "Nonlinear vibration of functionally graded carbon nanotubereinforced composite beams with geometric imperfections", Compos. Part B: Eng., 90, 86-96. https://doi.org/10.1016/j.compositesb.2015.12.007.
  26. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048.