Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An extended finite element method for modeling elastoplastic FGM plate-shell type structures

  • Jrad, Hanen (Engineering Production Mechanics and Materials Unit (UGPMM), National Engineering School of Sfax, University of Sfax) ;
  • Mars, Jamel (Engineering Production Mechanics and Materials Unit (UGPMM), National Engineering School of Sfax, University of Sfax) ;
  • Wali, Mondher (Department of Mechanical Engineering, College of Engineering, King Khalid University) ;
  • Dammak, Fakhreddine (Engineering Production Mechanics and Materials Unit (UGPMM), National Engineering School of Sfax, University of Sfax)
  • Received : 2018.05.25
  • Accepted : 2018.08.08
  • Published : 2018.11.10
⟨ Previous Next ⟩

Abstract

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.

Keywords

Acknowledgement

Supported by : Tunisian Ministry of Higher Education and Scientific Research

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. Arciniega, R.A. and Reddy, J.N. (2007), "Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures", Comput. Meth. Appl. Mech. Eng., 196(4-6), 1048-1073. https://doi.org/10.1016/j.cma.2006.08.014
  3. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/SEM.2018.65.4.453
  4. Autay, R., Koubaa, S., Wali, M. and Dammak, F. (2017), "Numerical implementation of coupled anisotropic plasticityductile damage in sheet metal forming process", J. Mech., 34(4), 417-430.
  5. Baltacioglu, A.K., Civalek, O., Akgoz, B. and Demir, F. (2011), "Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution", Int. J. Press. Vess. Pip., 88(8-9), 290-300. https://doi.org/10.1016/j.ijpvp.2011.06.004
  6. Bao, G. and Wang, L. (1995), "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Sol. Struct., 32(19), 2853-2871. https://doi.org/10.1016/0020-7683(94)00267-Z
  7. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  8. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  9. Belhassen, L., Koubaa, S., Wali, M. and Dammak, F. (2016), "Numerical prediction of springback and ductile damage in rubber-pad forming process of aluminum sheet metal", Int. J. Mech. Sci., 117, 218-226. https://doi.org/10.1016/j.ijmecsci.2016.08.015
  10. Belhassen, L., Koubaa, S., Wali, M. and Dammak, F. (2017), "Anisotropic effects in the compression beading of aluminum thin-walled tubes with rubber", Thin-Wall. Struct., 119, 902-910. https://doi.org/10.1016/j.tws.2017.08.010
  11. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  12. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  13. Ben Said, L., Mars, J., Wali, M. and Dammak, F. (2017), "Numerical prediction of the ductile damage in single point incremental forming process", Int. J. Mech. Sci., 131, 546-558.
  14. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  15. Bocciarelli, M., Bolzon, G. and Maier, G. (2008), "A constitutive model of metal-ceramic functionally graded material behavior), pp. formulation and parameter identification", Comput. Mater. Sci., 43(1), 16-26. https://doi.org/10.1016/j.commatsci.2007.07.047
  16. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/SEM.2016.58.3.397
  17. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/SEM.2018.66.1.061
  18. 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
  19. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  20. Civalek, O. (2008), "Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory", J. Compos. Mater., 42(26), 2853-2867. https://doi.org/10.1177/0021998308096952
  21. Civalek, O. (2013), "Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches", Compos.: Part B, 50, 171-179.
  22. Demir, C., Mercan, K. and Civalek, O. (2016), "Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel", Compos. Part B, 94, 1-10.
  23. 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
  24. Elmossouess, B., Kebdani, S., Bouiadjra, M.B. and Tounsi, A. (2017), "A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates", Struct. Eng. Mech., 62(4), 401-415. https://doi.org/10.12989/sem.2017.62.4.401
  25. Fontes Valente, R.A., Natal Jorge, R.M., Cardoso, R.P.R., Cesar de Sa, J.M.A. and Gracio, J.J.A. (2003), "On the use of an enhanced transverse shear strain shell element for problems involving large rotations", Comput. Mech., 30(4), 286-296. https://doi.org/10.1007/s00466-002-0388-x
  26. Frikha, A. and Dammak, F. (2017), "Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element", Comput. Meth. Appl. Mech. Eng., 315, 1-24. https://doi.org/10.1016/j.cma.2016.10.017
  27. Frikha, A., Zghal, S. and Dammak, F. (2018), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Technol., 78, 438-451. https://doi.org/10.1016/j.ast.2018.04.048
  28. Frikha, A., Hajlaoui, A., Wali, M. and Dammak, F. (2016), "A new higher order C0 mixed beam element for FGM beams analysis", Compos. Part B, 106, 181-189. https://doi.org/10.1016/j.compositesb.2016.09.024
  29. Ghannad, M., Nejad, M.Z., Rahimi, G.H. and Sabouri, H. (2012), "Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials", Struct. Eng. Mech., 43(1), 105-126. https://doi.org/10.12989/sem.2012.43.1.105
  30. GhannadPour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75, 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004
  31. Gunes, R., Aydin, M., Apalak, M.K. and Reddy, J.N. (2014), "Experimental and numerical investigations of low velocity impact on functionally graded circular plates", Compos. Part B: Eng., 59, 21-32. https://doi.org/10.1016/j.compositesb.2013.11.022
  32. Gurses, M., Civalek, O., Korkmaz, A. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory", Int. J. Numer. Meth. Eng., 79(3), 290-313. https://doi.org/10.1002/nme.2553
  33. Hajlaoui, A., Triki, E., Frikha, A., Wali M. and Dammak, F. (2017), "Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element", Lat. Am. J. Sol. Struct., 14(1), 72-91. https://doi.org/10.1590/1679-78253323
  34. Hajlaoui, A., Jarraya, A., El Bikri, K. and Dammak, F. (2015), "Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction", Compos. Struct., 132, 87-97. https://doi.org/10.1016/j.compstruct.2015.04.059
  35. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  36. Hosseini Tehrani, P. and Talebi, M. (2012), "Stress and temperature distribution study in a functionally graded brake disk", Int. J. Automot. Eng., 2(3), 172-179.
  37. Jin, G., Te, Y., Me, X., Chen, Y., Su, X. and Xie, X. (2013), "A unified approach for the vibration analysis of moderately thick composite laminated cylindrical shells with arbitrary boundary conditions", Int. J. Mech. Sci., 75, 357-376.
  38. Kar, V.R. and Panda, S.K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661
  39. Lee, M., Park, I. and Lee, U. (2017), "An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration", Struct. Eng. Mech., 61(4), 551-561. https://doi.org/10.12989/SEM.2017.61.4.551
  40. Liew, K.M., He, X.Q., Tan, M.J. and Lim, H.K. (2004), "Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT meshfree method", Int. J. Mech. Sci., 46(3), 411-431. https://doi.org/10.1016/j.ijmecsci.2004.03.011
  41. Mahi, A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  42. Mars, J., Koubaa, S., Wali, M. and Dammak, F. (2017), "Numerical analysis of geometrically non-linear behavior of functionally graded shells", Lat. Am. J. Sol. Struct., 14(11), 1952-1978. https://doi.org/10.1590/1679-78253914
  43. Mars, J., Wali, M., Jarraya, A., Dammak, F. and Dhiab. (2015), "A Finite element implementation of an orthotropic plasticity model for sheet metal in low velocity impact simulations", Thin-Wall. Struct., 89, 93-100. https://doi.org/10.1016/j.tws.2014.12.019
  44. 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
  45. Mindiin, R.D. (1951), "Influence of rotary inertia and shear on flexural motion of isotropic elastic plates", J. Appl. Mech., 18, 31-38.
  46. Moita, J.S., Araujo, A.L., Mota Soares, C.M., Mota Soares, C.A. and Herskovits, J. (2016), "Material and geometric nonlinear analysis of functionally graded plate-shell type structures", Appl. Compos. Mater., 23(4), 537-554. https://doi.org/10.1007/s10443-016-9473-8
  47. Orlik, J. (2010), "Asymptotic homogenization algorithm for reinforced metal-matrix elastoplastic composites", Compos. Struct., 92(7), 1581-1590. https://doi.org/10.1016/j.compstruct.2009.11.021
  48. Pettermann, H.E., Huber, C.O., Luxner, M.H., Nogales, S. and Bohm, H.J. (2010), "An incremental Mori-Tanaka homogenization scheme for finite strain thermoelastoplasticity of mmcs", Mater., 3(1), 434-451. https://doi.org/10.3390/ma3010434
  49. Phung-Van, P., Nguyen-Thoi, T., Luong-Van, H. and Lieu-Xuan, Q. (2014), "Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT", Comput. Meth. Appl. Mech. Eng., 270, 15-36. https://doi.org/10.1016/j.cma.2013.11.019
  50. Rahman, S. and Chakraborty, A. (2007), "A stochastic micromechanical model for elastic properties of functionally graded materials", Mech. Mater., 39(6), 548-563. https://doi.org/10.1016/j.mechmat.2006.08.006
  51. Reddy, J.N. (1984), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Sol. Struct., 20(9-10), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  52. Shankara, C.A. and Iyengar, N.G.R. (1996), "A C0element for the free vibration analysis of laminated composite plates", J. Sound Vibr., 191(5), 721-738. https://doi.org/10.1006/jsvi.1996.0152
  53. Shaterzadeh, A. and Foroutan, K. (2016), "Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation", Struct. Eng. Mech., 60(4), 615-631. https://doi.org/10.12989/sem.2016.60.4.615
  54. Suquet, P. (1997), "Effective properties of nonlinear composites", Contin. Micromech., 377, 197-264.
  55. Sze, K.Y., Liua, X.H. and Lob, S.H. (2004), "Popular benchmark problems for geometric nonlinear analysis of shells", Fin. Elem. Analy. Des., 40(11), 1551-1569. https://doi.org/10.1016/j.finel.2003.11.001
  56. Talebitooti, M. (2013), "Three-dimensional free vibration analysis of rotating laminated conical shells: Layerwise differential quadrature (LW-DQ) method", Arch. Appl. Mech., 83(5), 765-781. https://doi.org/10.1007/s00419-012-0716-3
  57. Tamura, I., Tomota, Y. and Ozawa, H. (1973), "Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength", Proceedings of the 3rd International Conference on Strength of Metals and Alloys, Cambridge: Institute of Metals.
  58. Tjong, S.C. and Ma, Z.Y. (2000), "Microstructural and mechanical characteristics of in situ metal matrix composites ", Mater. Sci. Eng., 29(3-4), 49-113. https://doi.org/10.1016/S0927-796X(00)00024-3
  59. Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2018), "Thermal post-buckling analysis of functionally graded material structures using a modified FSDT", Int. J. Mech. Sci., 144, 74-89.
  60. Tu, T.M., Quoc, T.H. and Van Long, N. (2017), "Bending analysis of functionally graded plates using new eightunknown higher order shear deformation theory", Struct. Eng. Mech., 62(3), 311-324. https://doi.org/10.12989/sem.2017.62.3.311
  61. Vaghefi, R., Hematiyan, M.R. and Nayebi, A. (2016), "Threedimensional thermo-elastoplastic analysis of thick functionally graded plates using the meshless local Petrov-Galerkin method",Eng. Analy. Bound. Elem., 71, 34-49. https://doi.org/10.1016/j.enganabound.2016.07.001
  62. Wali, M., Autay, R., Mars, J. and Dammak, F. (2016), "A simple integration algorithm for a non-associated anisotropic plasticity model for sheet metal forming", Int. J. Numer. Meth. Eng., 107(3), 183-204. https://doi.org/10.1002/nme.5158
  63. Wali, M., Chouchene, H., Ben Said, L. and Dammak, F. (2015), "One-equation integration algorithm of a generalized quadratic yield functions with Chaboche non-linear isotropic/kinematic hardening", Int. J. Mech. Sci., 92, 223-232.
  64. Williamson, R.L., Rabin, B.H. and Drake, J.T. (1993), "Finite element analysis of thermal residual stresses at graded ceramic/metal interfaces), part I), pp. model description and geometrical effects", J. Appl. Phys., 74(2), 1310-1320. https://doi.org/10.1063/1.354910
  65. Woo, J. and Merguid, S.A. (2001), "Non-linear analysis of functionally graded plates and shallow shells", Int. J. Sol. Struct., 38(42-43), 7409-7421. https://doi.org/10.1016/S0020-7683(01)00048-8
  66. Xu, G., Huang, H. and Han, Q. (2018), "Study on postbuckling of axial compressed elastoplastic functionally graded cylindrical shells", Mech. Adv. Mater. Struct., 25(10), 820-828. https://doi.org/10.1080/15376494.2017.1308589
  67. Yang, J. and Shena, H.S. (2003), "Non-linear analysis of functionally graded plates under transverse and in-plane loads", Int. J. Non-Lin. Mech., 38(4), 467-482. https://doi.org/10.1016/S0020-7462(01)00070-1
  68. 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
  69. Yu, J. and Kidane, A. (2014), "Modeling functionally graded materials containing multiple heterogeneities", Acta Mech., 225(7), 1931-1943. https://doi.org/10.1007/s00707-013-1033-9
  70. Zghal, S., Frikha, A. and Dammak, F. (2018a), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures", Appl. Math. Modell., 53, 132-155. https://doi.org/10.1016/j.apm.2017.08.021
  71. Zghal, S., Frikha, A. and Dammak, F. (2017), "Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures", Compos. Struct., 176, 1107-1123 .
  72. Zghal, S., Frikha, A. and Dammak, F. (2018b), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B, 150(1), 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037
  73. Zghal, S., Frikha, A. and Dammak, F. (2018c), "Non-linear bending analysis of nanocomposites reinforced by graphenenanotubes with finite shell element and membrane enhancement", Eng. Struct., 158, 95-109.
  74. Zhao, X. and Liew, KM. (2009), "Geometrically nonlinear analysis of functionally graded shells", Int. J. Mech. Sci., 51, 131-144. https://doi.org/10.1016/j.ijmecsci.2008.12.004
  75. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermomechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34.

Cited by

  1. Analyzing FG shells with large deformations and finite rotations vol.16, pp.5, 2018, https://doi.org/10.1108/wje-10-2018-0357
  2. Dynamic analysis of functionally graded carbon nanotube-reinforced shell structures with piezoelectric layers under dynamic loads vol.26, pp.13, 2020, https://doi.org/10.1177/1077546319892753