Steel and Composite Structures

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Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method

  • Received : 2018.07.22
  • Accepted : 2020.01.04
  • Published : 2020.02.25
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Abstract

This paper presents a free vibration analysis of shell panels made of functionally graded material (FGM) in the form of the ordinary and sandwich FGM and laminated shells using the isogeometric B3-spline finite strip method (IG-SFSM). B3-spline and Lagrangian interpolation are employed along the longitudinal and transverse directions respectively in this type of finite strip. The introduced finite strip formulation is based on the degenerated shell method, which provides variable thickness, arbitrary geometries, and analysis of thin or thick shells. Validity of the obtained natural frequencies by IG-SFSM is checked by comparison with results extracted from references for similar cases in different examples. These examples incorporate several geometries, materials, boundary conditions, and continuous thickness variation. A comparison of these two kinds of results and their proximity showed that the introduced IG-SFSM is a reliable tool which can be used in analysis of shells with the aforementioned properties.

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References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel. Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.
  2. Au, F.T.K. and Cheung, Y.K. (1996), "Free vibration and stability analysis of shells by the isoparametric spline finite strip method", Thin-Wall. Struct., 24(1), 53-82. https://doi.org/10.1016/0263-8231(95)00040-2.
  3. Bacciocchi, M., Eisenberger, M., Fantuzzi, N., Tornabene, F. and Viola, E. (2015), "Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method", Compos. Struct., 156, 218-237. https://doi.org/10.1016/j.compstruct.2015.12.004.
  4. 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. https://doi.org/10.12989/eas.2018.14.2.103.
  5. Benson, P.R. and Hinton, E. (1976), "A thick finite strip solution for static, free vibration and stability problems", Int. J. Numer. Method. Eng., 10(3), 665-678. https://doi.org/10.1002/nme.1620100314.
  6. 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. https://doi.org/10.12989/scs.2016.20.2.227.
  7. 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", Wind. Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  8. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel. Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409.
  9. Chieslar, J.D. and Ghali, A. (1987), "Solid to shell element geometric transformation", Comput. Struct., 25(3), 451-455. https://doi.org/10.1016/0045-7949(87)90136-2.
  10. Darilmaz, K. (2017), "Static and free vibration behaviour of orthotropic elliptic paraboloid shells", Steel Compos. Struct., 23(6), 737-746. https://doi.org/10.12989/scs.2017.23.6.737.
  11. Dawe, D.J. and Wang, S. (1992), "Vibration of shear-deformable beams using a spline function approach", Int. J. Numer. Method. Eng., 33(4), 819-844. https://doi.org/10.1002/nme.1620330410.
  12. Dvorkin, E.N. and Bathe, K. (1984), "A continuum mechanics based four‐node shell element for general non‐linear analysis", Eng. Comput., 1(1), 77-88. https://doi.org/10.1108/eb023562.
  13. Eccher, G., Rasmussen, K.J.R. and Zandonini, R. (2008), "Isoparametric spline finite strip method for the bending of perforated plates", Int. J. Numer., Method. Eng., 74(9), 1448-1472 https://doi.org/10.1002/nme.2220.
  14. El-Haina, F., Bakora, A., Bousahla, A. A., Tounsi, A., and Mahmoud, S. R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  15. Fan, S.C. and Cheung, Y.K. (1983), "Analysis of shallow shells by spline finite strip method", Eng. Struct., 5(4), 255-263. https://doi.org/10.1016/0141-0296(83)90004-4.
  16. Fan, S.C. and Luah, M.H. (1990), "New spline finite element for analysis of shells of revolution", J. Eng. Mech., 116(3), 709-726. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:3(709).
  17. Foroughi, H. and Azhari, M. (2014), "Mechanical buckling and free vibration of thick functionally graded plates resting on elastic foundation using the higher order B-spline finite strip method", Meccanica, 49(4), 981-993. http-://doi.org/10.1007/s11012-013-9844-2.
  18. Hu, X. (1997), "Free vibration analysis of symmetrical cylindrical honeycomb panels by using the finite strip method", J. Vib. Control, 3(1), 19-32. https://doi.org/10.1177%2F107754639700300103/. https://doi.org/10.1177/107754639700300103
  19. Jabareen, M. and Mtanes, E. (2018), "A solid-shell Cosserat point element for the analysis of geometrically linear and nonlinear laminated composite structures", Finite Elem. Anal. Des., 142, 61-80. https://doi.org/10.1016/j.finel.2017.12.006.
  20. Javed, S., Viswanathan, K.K. and Aziz, Z.A. (2016), "Free vibration analysis of composite cylindrical shells with non-uniform thickness walls", Steel Compos. Struct., 20(5), 1087-1102. http://dx.doi.org/10.12989/scs.2016.20.5.1087.
  21. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel. Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  22. Kim, H.J., Seo, Y.D., and Youn, S.K. (2010), "Isogeometric analysis with trimming technique for problems of arbitrary complex topology", Comput. Method. Appl. M., 199(45-48), 2796-2812. https://doi.org/10.1016/j.cma.2010.04.015.
  23. Kwon, Y.B. and Hancock, G.J. (1991), "A nonlinear elastic spline finite strip analysis for thin-walled sections", Thin-Wall. Struct., 12(4), 295-319. https://doi.org/10.1016/0263-8231(91)90031-D.
  24. Li, W.Y., Tham, L.G., Cheung, Y.K. and Fan, S.C. (1990), "Free vibration analysis of doubly curved shells by spline finite strip method", J. Sound Vib., 140(1), 39-53. https://doi.org/10.1016/0022-460X(90)90905-F.
  25. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel. Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  26. Naghsh, A., Saadatpour, M.M. and Azhari, M. (2015), "Free vibration analysis of stringer stiffened general shells of revolution using a meridional finite strip method", Thin-Wall. Struct., 94, 651-662. https://doi.org/10.1016/j.tws.2015.05.015.
  27. Nguyen, V.P., Anitescu, C., Bordas, S.P., and Rabczuk, T. (2015), "Isogeometric analysis: an overview and computer implementation aspects", Math. Comput. Simulat., 117, 89-116. https://doi.org/10.1016/j.matcom.2015.05.008.
  28. Pang, F., Li, H., Wang, X., Miao, X. and Li, S. (2018), "A semi analytical method for the free vibration of doubly-curved shells of revolution", Comput. Math. with Appl., 75(9), 3249-3268. https://doi.org/10.1016/j.camwa.2018.01.045.
  29. Piegl, L. and Tiller, W. (1997), "The NURBS Book", Springer-Verlag Berlin, Heidelberg, Baden-Wurttemberg, Germany.
  30. Rezaiee-Pajand, M. and Arabi, E. (2016), "A curved triangular element for nonlinear analysis of laminated shells", Compos. Struct., 153, 538-548. https://doi.org/10.1016/j.compstruct.2016.06.052.
  31. Rypl, D., and Patzak, B. (2012), "From the finite element analysis to the isogeometric analysis in an object oriented computing environment", Adv. Eng. Softw., 44(1), 116-125. https://doi.org/10.1016/j.advengsoft.2011.05.032.
  32. Shahmohamadi, M.A. and Kabir, M.Z. (2017), "Effects of shear deformation on mechanical and thermo-mechanical nonlinear stability of FGM shallow spherical shells subjected to uniform external pressure", Sci. Iran., 24(2), 584-596. https://dx.doi.org/10.24200/sci.2017.2420.
  33. Sheikh, A.H. (2004), "An efficient technique to include shear deformation in spline finite strip analysis of composite plates", Int. J. Comput. Methods, 1(3), 491-505. https://doi.org/10.1142/S0219876204000241.
  34. Tornabene, F., Fantuzzi, N., Bacciocchi, M., Viola, E. and Reddy, J. (2017), "A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method", Appl. Sci., 7(2), 131. https://doi.org/10.3390/app7020131.
  35. Tornabene, F. and Viola, E. (2009), "Free vibration analysis of functionally graded panels and shells of revolution", Meccanica, 44(3), 255-281. https://doi.org/10.1007/s11012-008-9167-x.
  36. Uhm, T.-K. and Youn, S.-K. (2009), "T-spline finite element method for the analysis of shell structures", Int. J. Numer. Method. Eng., 80(4), 507-536. https://doi.org/10.1002/nme.2648.
  37. Van Erp, G.M. and Menken, C.M. (1990), "Spline finite-strip method in the buckling analyses of thin-walled structures", Commun. Appl. Numer. Methods, 6(6), 477-484. https://doi.org/10.1002/cnm.1630060608.
  38. Van Erp, G.M., Yuen, S.W. and Swannell, P. (1994), "A new type of B3-spline interpolation", Commun. Appl. Numer. Methods., 10(12), 1013-1020. https://doi.org/10.1002/cnm.1640101207.
  39. Ventsel, E. and Krauthammer, T. (2001), "Thin Plates and Shells: Theory: Analysis, and Applications", Marcel Dekker, New York City, New York, USA.
  40. Vu-Bac, N., Duong, T.X., Lahmer, T., Zhuang, X., Sauer, R.A., Park, H.S. and Rabczuk, T. (2018), "A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures", Comput. Method. Appl. M., 331, 427-455. https://doi.org/10.1016/j.cma.2017.09.034.
  41. Wang, S. and Dawe, D.J. (1999), "Buckling of composite shell structures using the spline finite strip method", Compos. Part B Eng., 30(4), 351-364. https://doi.org/10.1016/S1359-8368(99)00005-0.
  42. 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.
  43. 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. https://doi.org/10.12989/sem.2015.54.4.693.
  44. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125.

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