EFFICIENT NUMERICAL MODELLING OF FUNCTIONALLY GRADED SHELL MECHANICAL BEHAVIOR

Sana KOUBAA

sana.kouba@enis.tn
University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax (Tunisia)

Jamel MARS


University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax (Tunisia)

Fakhreddine DAMMAK


University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax (Tunisia)

Abstract

Numerical analysis of the static bending and free vibration mechanical behavior of FGM are performed using the UMAT-USDFLD subroutines in ABAQUS software. Different combinations of geometries, mechanical loading and boundary conditions are adopted. The material properties according to the coordinates of the integration points are defined in the developed numerical model. The First Order Deformation Theory is used for thin and moderately thick FG shells analysis. The accuracy and the robustness of the numerical model are illustrated through the solution of several non trivial structure problems. The proposed numerical procedure is significantly efficient from the computational point of view.


Keywords:

FGM, UMAT-USDFLD, Static, Free vibration

Abrate, S. A. (2006). Free vibration, buckling, and static deflections of functionally graded plates. Journal of Composites Science and Technology, 66, 2383–2394. https://doi.org/10.1016/j.compscitech.2006.02.032
DOI: https://doi.org/10.1016/j.compscitech.2006.02.032   Google Scholar

Alipour, M. M., & Shariyat, M. (2012). An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a maclaurin-type series solution. Eur J Mech A/Solids, 34, 78–101. https://doi.org/10.1016/j.euromechsol.2011.12.004
DOI: https://doi.org/10.1016/j.euromechsol.2011.12.004   Google Scholar

Apetre, N. A., Sanka, B. V., & Ambur, D. R. (2006). Low-velocity impact response of sandwich beams with functionally graded core. International Journal of Solids and Structures, 43, 2479–2496. https://doi.org/10.1016/j.ijsolstr.2005.06.003
DOI: https://doi.org/10.1016/j.ijsolstr.2005.06.003   Google Scholar

Chung, Y. L. & Chen, W. T. (2007). The flexibility of functionally graded material plates subjected to uniform load. Journal of Mechanics of Materials and Structures, 2, 63–86. https://doi.org/10.2140/jomms.2007.2.63
DOI: https://doi.org/10.2140/jomms.2007.2.63   Google Scholar

Draiche, K., Derras, M., Kaci, A. & Tounsi, A. (2013). Non-linear analysis of functionally graded plates of cylindrical bending based on a new refined shear deformation theory. Journal of theoretical and applied mechanics, 51, 339– 348.
  Google Scholar

Frikha, A. & Dammak, F. (2017). Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element. Computer Methods in Applied Mechanics and Engineering, 315, 1– 24. https://doi.org/10.1016/j.cma.2016.10.017
DOI: https://doi.org/10.1016/j.cma.2016.10.017   Google Scholar

Frikha, A., Wali, M., Hajlaoui, A & Dammak, F. (2016a). Dynamic response of functionally graded material shells with a discrete double directors shell element. Composite Structures, 154, 385–395. https://doi.org/10.1016/j.compstruct.2016.07.021
DOI: https://doi.org/10.1016/j.compstruct.2016.07.021   Google Scholar

Frikha, A., Wali, M., Hajlaoui, A & Dammak, F. (2016b). A new higher order c0 mixed beam element for fgm beams analysis. Composites part B, 106, 181– 189. https://doi.org/10.1016/j.compositesb.2016.09.024
DOI: https://doi.org/10.1016/j.compositesb.2016.09.024   Google Scholar

GhannadPour, S. A. M. & Alinia, M. M. (2006). Large deflection behavior of functionally graded plates under pressure loads. Journal of composite structures, 75, 67–71. https://doi.org/10.1016/j.compstruct.2006.04.004
DOI: https://doi.org/10.1016/j.compstruct.2006.04.004   Google Scholar

Ghanned, M. & Nejad, M. Z. (2013). Elastic solution of pressurized clamped-clamped thick cylindrical shelles made of functionally graded materials. Journal of theoretical and applied mechanics, 51, 1067–1079.
DOI: https://doi.org/10.5755/j01.mech.18.6.3158   Google Scholar

Lin, F. & Xiang, Y. (2014). Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories. Applied Mathematical Modelling, 38, 3741–3754. https://doi.org/10.1016/j.apm.2014.02.008
DOI: https://doi.org/10.1016/j.apm.2014.02.008   Google Scholar

Mao, Y., Fu, Y., & Fang, D. (2013). Interfacial damage analysis of shallow spherical shell with fgm coating under low velocity impact. International Journal of Mechanical Sciences, 71, 30–40. https://doi.org/10.1016/j.ijmecsci.2013.03.004
DOI: https://doi.org/10.1016/j.ijmecsci.2013.03.004   Google Scholar

Nie, G. & Zhong, Z. (2007). Axisymmetric bending of two-directional functionally graded circular and annular plates. Acta Mechanica Solida Sinica, 20, 289– 295. https://doi.org/10.1007/s10338-007-0734-9
DOI: https://doi.org/10.1007/s10338-007-0734-9   Google Scholar

Praveen, G. N. & Reddy, J. N. (1997). Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. International Journal of Solids and Structures, 35, 4457–4476. https://doi.org/10.1016/S0020-7683(97)00253-9
DOI: https://doi.org/10.1016/S0020-7683(97)00253-9   Google Scholar

Shariyat, M. & Alipour, M. M. (2014). A novel shear correction factor for stress and modal analyses of annular fgm plates with non-uniform inclined tractions and nonuniform elastic foundations. International Journal of Mechanical Sciences, 87, 60–71.
DOI: https://doi.org/10.1016/j.ijmecsci.2014.05.032   Google Scholar

Simo, J. C., Fox, D. D. & Rifai, M. S. (1989). On a stress resultant geometrically exact shell model. part II: The linear theory; Computational aspects. Computer Methods in Applied Mechanics and Engineering, 73, 53–92. https://doi.org/10.1016/0045-7825(89)90098-4
DOI: https://doi.org/10.1016/0045-7825(89)90098-4   Google Scholar

Thai, H. T., & Kim, S. E. (2015). A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures, 128, 70–86. https://doi.org/10.1016/j.compstruct.2015.03.010
DOI: https://doi.org/10.1016/j.compstruct.2015.03.010   Google Scholar

Tornabene, F. (2009). Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput. Methods Appl. Mech. Engrg, 198, 2911–2935. https://doi.org/10.1016/j.cma.2009.04.011
DOI: https://doi.org/10.1016/j.cma.2009.04.011   Google Scholar

Wali, M., Hajlaoui, A. & Dammak, F. (2014). Discrete double directors shell element for the functionally graded material shell structures analysis. Computer Methods in Applied Mechanics and Engineering, 278, 388–403. https://doi.org/10.1016/j.cma.2014.05.011
DOI: https://doi.org/10.1016/j.cma.2014.05.011   Google Scholar

Wali, M., Hentati, T., Jarraya, A., & Dammak, F. (2015). Free vibration analysis of fgm shell structures with a discrete double directors shell element. Composite Structures, 125, 295–303. https://doi.org/10.1016/j.compstruct.2015.02.032
DOI: https://doi.org/10.1016/j.compstruct.2015.02.032   Google Scholar

Yanga. J., & Shen, H. S. (2003). Non-linear analysis of functionally graded plates under transverse and in-plane loads. International Journal of Non- Linear Mechanics, 38(4), 467–482. https://doi.org/10.1016/S0020-7462(01)00070-1
DOI: https://doi.org/10.1016/S0020-7462(01)00070-1   Google Scholar

Zenkour, A. M. (2006). Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling, 30 (1), 67–84. https://doi.org/10.1016/j.apm.2005.03.009
DOI: https://doi.org/10.1016/j.apm.2005.03.009   Google Scholar

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Published
2019-03-30

Cited by

KOUBAA, S., MARS, J., & DAMMAK, F. (2019). EFFICIENT NUMERICAL MODELLING OF FUNCTIONALLY GRADED SHELL MECHANICAL BEHAVIOR. Applied Computer Science, 15(1), 84–94. https://doi.org/10.23743/acs-2019-07

Authors

Sana KOUBAA 
sana.kouba@enis.tn
University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax Tunisia

Authors

Jamel MARS 

University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax Tunisia

Authors

Fakhreddine DAMMAK 

University of Sfax, National Engineering School of Sfax, Electro-Mechanical System's Laboratory, B.P 1173-3038 Street Soukra Km 3.5, Sfax Tunisia

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