DOI QR코드

DOI QR Code

Nonlinear deflection responses of layered composite structure using uncertain fuzzified elastic properties

  • Patle, B.K. (Department of Mechanical Engineering, CVR College of Engineering) ;
  • Hirwani, Chetan K. (Department of Mechanical Engineering, National Institute of Technology Patna) ;
  • Panda, Subrata Kumar (Department of Mechanical Engineering, National Institute of Technology Rourkela) ;
  • Katariya, Pankaj V. (Department of Mechanical Engineering, National Institute of Technology Rourkela) ;
  • Dewangan, Hukum Chand (Department of Mechanical Engineering, National Institute of Technology Rourkela) ;
  • Sharma, Nitin (School of Mechanical Engineering, KIIT Bhubaneswar)
  • Received : 2019.09.26
  • Accepted : 2020.05.23
  • Published : 2020.06.25

Abstract

In this article, the influence of fuzzified uncertain composite elastic properties on non-linear deformation behaviour of the composite structure is investigated under external mechanical loadings (uniform and sinusoidal distributed loading) including the different end boundaries. In this regard, the composite model has been derived considering the fuzzified elastic properties (through a triangular fuzzy function, α cut) and the large geometrical distortion (Green-Lagrange strain) in the framework of the higher-order mid-plane kinematics. The results are obtained using the fuzzified nonlinear finite element model via in-house developed computer code (MATLAB). Initially, the model accuracy has been established and explored later to show the dominating elastic parameter affect the deflection due to the inclusion of fuzzified properties by solving a set of new numerical examples.

Keywords

References

  1. Adhikari, S. and Khodaparast, H.H. (2014), "A spectral approach for fuzzy uncertainty propagation in finite element analysis", Fuzzy Sets Syst., 243, 1-24. https://doi.org/10.1016/j.fss.2013.10.005.
  2. Akhras, G. and Li, W. (2005), "Static and free vibration analysis of composite plates using spline finite strips with higher-order shear deformation", Compos. Part B, 36(6-7), 496-503. https://doi.org/10.1016/j.compositesb.2005.03.001.
  3. Akpan, U.O., Koko, T.S., Orisamolu, I.R. and Gallant, B.K. (2001), "Fuzzy finite-element analysis of smart structures", Smart Mater. Struct., 10(2), 273. https://doi.org/10.1088/0964-1726/10/2/312.
  4. Akpan, U.O., Koko, T.S., Orisamolu, I.R. and Gallant, B.K. (2001), "Practical fuzzy finite element analysis of structures", Finite Elem. Anal. Des., 38(2), 93-111. https://doi.org/10.1016/S0168-874X(01)00052-X.
  5. Arefi, M., Mohammadi, M., Tabatabaeian, A., Dimitri, R. and Tornabene, F. (2018), "Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels", Steel Compos. Struct., 27(4), 525-536. https://doi.org/10.12989/scs.2018.27.4.525.
  6. Behera, D. and Chakraverty, S. (2013), "Fuzzy finite element based solution of uncertain static problems of structural mechanics", Int. J. Comput. Appl. Technol., 69(15), 6-11. https://doi.org/10.5120/11916-8040.
  7. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  8. Bouiadjra, R.B., Mahmoudi, A., Benyoucef, S., Tounsi, A. and Bernard, F. (2018), "Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models", Struct. Eng. Mech., 66(3), 317-328. https://doi.org/10.12989/sem.2018.66.3.317.
  9. Bui, T. Q., Tran, A.V. and Shah, A.A., (2014), Improved knowledge-based neural network (KBNN) model for predicting spring-back angles in metal sheet bending, Int. J. Modeling, Simul, Scientific Computing, 5, 1350026. https://doi.org/10.1142/S1793962313500268
  10. Bui, T.Q. and Nguyen, M.N. (2013), "Mesh-free galerkin kriging model for bending and buckling analysis of simply supported laminated composite plates", Int. J. Comp. Meth., 10(3), 1350011-26. https://doi.org/10.1142/S0219876213500114.
  11. Cherki, A., Plessis, G., Lallemand, B., Tison, T. and Level, P. (2000), "Fuzzy behavior of mechanical systems with uncertain boundary conditions", Comput Method Appl. M., 189(3), 863-873. https://doi.org/10.1016/S0045-7825(99)00401-6.
  12. Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2000), Concepts and Applications of Finite Element Analysis, 3rd Edition, John Willy and Sons (Asia) Pvt. Ltd., Singapore.
  13. Dash, P. and Singh B.N. (2010), "Geometrically nonlinear bending analysis of laminated composite plate", Commun. Nonlinear Sci. Numer. Simul., 15(10), 3170-3181. https://doi.org/10.1016/j.cnsns.2009.11.017.
  14. Dash, P. and Singh, B.N. (2012), "Geometrically nonlinear free vibration of laminated composite plate embedded with piezoelectric layers having uncertain material properties", J. Vib. Acoust., 134(6). https://doi.org/10.1115/1.4006757
  15. De Gersem, H., Moens, D., Desmet, W. and Vandepitte, D. (2007), "Interval and fuzzy dynamic analysis of finite element models with superelements", Comput. Struct., 85(5-6), 304-319. https://doi.org/10.1016/j.compstruc.2006.10.011.
  16. Ghannadpour, S.A.M., Ovesy, H.R. and Zia-Dehkordi E. (2014), "An exact finite strip for the calculation of initial post-buckling stiffness of shear-deformable composite laminated plates", Compos. Struct., 108, 504-513. https://doi.org/10.1016/j.compstruct.2013.09.049
  17. Ghannadpour, S.A.M. and Barekati, M. (2006), "Initial imperfection effects on post-buckling response of laminated plates under end-shortening strain using Chebyshev techniques", Compos. Struct., 75(1-4), 106-113. https://doi.org/10.1016/j.compstruct.2006.04.006
  18. Giannini, O. and Hanss, M. (2008), "The component mode transformation method: a fast implementation of fuzzy arithmetic for uncertainty management in structural dynamics", J. Sound Vib., 311(3-5), 1340-1357. https://doi.org/10.1016/j.jsv.2007.10.029.
  19. Heydari, M.M., Kolahchi, R., Heydari, M. and Abbasi, A. (2014), "Exact solution for transverse bending analysis of embedded laminated Mindlin plate". Struct. Eng. Mech., 49(5), 661-672. https://doi.org/10.12989/sem.2014.49.5.661.
  20. Houari, T., Bessaim, A., Houari, M.S.A., Benguedia, M. and Tounsi, A. (2018), "Bending analysis of advanced composite plates using a new quasi 3D plate theory", Steel Compos. Struct., 26(5), 557-572. https://doi.org/10.12989/scs.2018.26.5.557.
  21. Jones, R.M. (1975), Mechanics of Composite Materials, Taylor and Francis, Philadelphia.
  22. Keleshteri, M.M., Asadi, H. and Aghdam, M. (2019), "Nonlinear bending analysis of FG-CNTRC annular plates with variable thickness on elastic foundation", Thin Wall. Struct., 135, 453-462. https://doi.org/10.1016/j.tws.2018.11.020.
  23. Kolahchi, R., Mohammad, A., Bidgoli, M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55(5), 1001-1014. https://doi.org/10.12989/sem.2015.55.5.1001.
  24. Liu, Q. and Rao, S.S. (2005), "Fuzzy finite element approach for analysis of fiber-reinforced laminated composite beams", AIAA J., 43(3), 651-661. https://doi.org/10.2514/1.940.
  25. Liu, W.K., Belytschko, T. and Mani, A. (1986), "Random field finite elements", Int. J. Numer. Methods Eng., 23(10), 1831-1845. https://doi.org/10.1002/nme.1620231004
  26. Luo, Z., Atamturktur, S., Juang, C.H., Huang, H. and Lin, P.S. (2011), "Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach", Comput. Geotech., 38(8), 1031-1040. https://doi.org/10.1016/j.compgeo.2011.07.009.
  27. Massa, F., Lallemand, B., Tison, T. and Level, P. (2004), "Fuzzy eigensolutions of mechanical structures", Eng. Computation, 21(1), 66-77. https://doi.org/10.1108/02644400410511846.
  28. Massa, F., Tison, T. and Lallemand, B. (2009), "Fuzzy modal analysis: Prediction of experimental behaviours", J. Sound Vib., 322(1-2), 135-154. https://doi.org/10.1016/j.jsv.2008.10.032.
  29. Mehrparvar, M. and Ghannadpour, S.A.M. (2018), "Plate assembly technique for nonlinear analysis of relatively thick functionally graded plates containing rectangular holes subjected to inplane compressive load", Compos. Struct., 202, 867-880. https://doi.org/10.1016/j.compstruct.2018.04.053
  30. Moens, D. and Vandepitte, D. (2005), "A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1-Procedure", J. Sound Vib., 288(3), 431-462. https://doi.org/10.1016/j.jsv.2005.07.001.
  31. Mukhopadhyay, M. (2009), Mechanics of Composite Materials and Structures, Universities Press, Hyderabad, India.
  32. Noor, A.K., Starnes Jr, J.H. and Peters, J.M. (2000), "Uncertainty analysis of composite structures", Comput Method Appl. M., 185(2-4), 413-432. https://doi.org/10.1016/S0045-7825(99)00269-8.
  33. Ovesy, H.R. and Ghannadpour, S.A.M. (2006), "Geometric non-linear analysis of imperfect composite laminated plates, under end shortening and pressure loading, using finite strip method", Compos. Struct., 75, 100-105. https://doi.org/10.1016/j.compstruct.2006.04.005.
  34. Ovesy, H.R. and Ghannadpour, S.A.M. (2007), "Large deflection finite strip analysis of functionally graded plates under pressure loads", Int. J. Struct. Stab. Dyn., 7(2), 193-211. https://doi.org/10.1142/S0219455407002241.
  35. Ovesy, H.R., Ghannadpour, S.A.M. and Morada, G. (2006), "Post-buckling behavior of composite laminated plates under end shortening and pressure loading, using two versions of finite strip method", Compos. Struct., 75, 106-113. https://doi.org/10.1016/j.compstruct.2006.04.006.
  36. Ovesy, H.R., Ghannadpour, S.A.M. and Nassirnia, M. (2015), "Post-buckling analysis of rectangular plates comprising Functionally Graded Strips in thermal environments", Comput. Struct., 147, 209-215. https://doi.org/10.1016/j.compstruc.2014.09.011.
  37. Patle, B.K., Hirwani, C.K., Singh, R.P. and Panda, S.K. (2018), "Eigenfrequency and frequency analysis of layered structure using uncertain elastic properties-a fuzzy finite element approach", Int. J. Approximate Reasoning, 98, 163-176. https://doi.org/10.1016/j.ijar.2018.04.013.
  38. Pawar, P.M., Nam Jung, S. and Ronge, B.P. (2012), "Fuzzy approach for uncertainty analysis of thin walled composite beams", Aircr. Eng. Aerosp. Tec., 84(1), 13-22. https://doi.org/10.1108/00022661211194942.
  39. Rao, S. and Sawyer, J.P. (1995), "Fuzzy finite element approach for analysis of imprecisely defined systems", AIAA J., 33(12), 2364-2370. https://doi.org/10.2514/3.12910.
  40. Razavi, S.V., Jumaat, M.Z., EI-Shafie, E.H. and Ronagh, H.R. (2015) "Load-deflection analysis prediction of CFRP strengthened RC slab using RNN", Adv. Concr. Constr., 3(2). https://doi.org/10.12989/acc.2015.3.2.091.
  41. Reddy, J.N. and Liu, C.F. (1985), "A higher-order shear deformation theory of laminated elastic shells", Int. J. Eng. Sci., 23(3), 319-330. https://doi.org/10.1016/0020-7225(85)90051-5.
  42. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Braz. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s4043.
  43. Singh, R.P. (2015), Vibration and bending behavior of laminated composite plate with uncertain material properties using fuzzy finite element method, (M.Tech. thesis).
  44. Singh, V.K. and Panda, S.K. (2014), "Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels", Thin Wall. Struct., 85, 341-349. https://doi.org/10.1016/j.tws.2014.09.003.
  45. Szekrenyes, A. and Jozsef, U.J. (2007), "Over-leg Bending Test for Mixed-mode I/II Inter laminar Fracture in Composite Laminates". Int. J. Damage Mech., 16(1), 5-33. https://doi.org/10.1177/1056789507060774.
  46. Taghizadeh, M., Ovesy, H.R. and Ghannadpour, S.A.M. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., 54(4), 755-769 https://doi.org/10.12989/sem.2015.54.4.755.
  47. Talha, M. and Singh, B.N. (2014), "Stochastic perturbation-based finite element for buckling statistics of FGM plates with uncertain material properties in thermal environments", Compos. Struct., 108(1), 823-833. https://doi.org/10.1016/j.compstruct.2013.10.013.
  48. Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O. A., Rabczuk, T., Bui, T.Q. and Bordas, S.P.A. (2013a), "NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter", Compos. Struct., 99, 309-326. https://doi.org/10.1016/j.compstruct.2012.11.008
  49. Xia, Y. and Friswell, M. (2014), "Efficient solution of the fuzzy eigenvalue problem in structural dynamics", Eng. Computation, 31(5), 864-878. https://doi.org/10.1108/EC-02-2013-0052.
  50. Zaghloul, S.A. and Kennedy, J.B. (1975), "Nonlinear behaviour of symmetrically laminated plates", J. Appl. Mech., 42, 234-236. https://doi.org/10.1115/1.3423532.