Steel and Composite Structures

  • 제31권4호
  • /
  • Pages.397-408
  • /
  • 2019
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Geometrically nonlinear meshfree analysis of 3D-shell structures based on the double directors shell theory with finite rotations

  • Mellouli, Hana (Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax) ;
  • Jrad, Hanen (Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax) ;
  • Wali, Monther (Department of Mechanical Engineering, College of Engineering, King Khalid University) ;
  • Dammak, Fakhreddine (Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax)
  • 투고 : 2019.01.17
  • 심사 : 2019.03.29
  • 발행 : 2019.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a geometrically nonlinear meshfree analysis of 3D various forms of shell structures using the double director shell theory with finite rotations is proposed. This theory is introduced in the present method to remove the shear correction factor and to improve the accuracy of transverse shear stresses with the consideration of rotational degrees of freedom.The present meshfree method is based on the radial point interpolation method (RPIM) which is employed for the construction of shape functions for a set of nodes distributed in a problem domain. Discrete system of geometrically nonlinear equilibrium equations solved with the Newton-Raphson method is obtained by incorporating these interpolations into the weak form. The accuracy of the proposed method is examined by comparing the present results with the accurate ones available in the literature and good agreements are found.

키워드

과제정보

연구 과제 주관 기관 : King Khalid University

참고문헌

  1. Atri, H.R. and Shojaee, S. (2018), "Truncated hierarchical B-splines in isogeometric analysis of thin shell structures", Steel Compos. Struct., Int. J., 26(2), 171-182.
  2. Belinha, J. and Dinis, L.M.J.S. (2007), "Nonlinear analysis of plates and laminates using the element free Galerkin method", Compos. Struct., 78(3), 337-350. https://doi.org/10.1016/j.compstruct.2005.10.007
  3. Brendel, B. and Ramm, E. (1980), "Linear and nonlinear stability analysis of cylindrical shells", Comput. Struct., 12(4), 549-558. https://doi.org/10.1016/0045-7949(80)90130-3
  4. Dinis, L.M.J.S., Jorge, R.N. and Belinha, J. (2008), "Analysis of plates and laminates using the natural neighbour radial point interpolation method", Eng. Anal. Bound. Elem., 32(3), 267-279. https://doi.org/10.1016/j.enganabound.2007.08.006
  5. Ferreira, A.J.M., Roque, C.M.C. and Jorge, R.M.N. (2005), "Analysis of composite plates by trigonometric shear deformation theory and multiquadrics", Comput. Struct., 83(27), 2225-2237. https://doi.org/10.1016/j.compstruc.2005.04.002
  6. Ferreira, A.J.M., Roque, C.M.C. and Jorge, R.M.N. (2006), "Static and free vibration analysis of composite shells by radial basis functions", Eng. Anal. Bound. Elem., 30(9), 719-733. https://doi.org/10.1016/j.enganabound.2006.05.002
  7. Frikha, A. and Dammak, F. (2017), "Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element", Comput. Methods Appl. Mech. Eng., 315, 1-24. https://doi.org/10.1016/j.cma.2016.10.017
  8. Ivannikov, V., Tiago, C. and Pimenta, P.D.M. (2014), "Meshless implementation of the geometrically exact Kirchhoff-Love shell theory", Int. J. Numer. Methods Eng., 100(1), 1-39. https://doi.org/10.1002/nme.4687
  9. Jrad, H., Mallek, H., Wali, M. and Dammak, F. (2018a), "Finite element formulation for active functionally graded thin-walled structures", Comptes Rendus Mecanique, 346(12), 1159-1178. https://doi.org/10.1016/j.crme.2018.07.010
  10. Jrad, H., Mars, J., Wali, M. and Dammak, F. (2018b), "An extended finite element method for modeling elastoplastic FGM plate-shell type structures", Struct. Eng. Mech., Int. J., 68(3), 299-312.
  11. Jrad, H., Mars, J., Wali, M. and Dammak, F. (2018c), "Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells", Eng. Comput., 1-15. DOI: https://doi.org/10.1007/s00366-018-0633-3
  12. Kazemi, Z., Hematiyan, M.R. and Vaghefi, R. (2017), "Meshfree radial point interpolation method for analysis of viscoplastic problems", Eng. Anal. Bound. Elem., 82, 172-184. https://doi.org/10.1016/j.enganabound.2017.06.012
  13. Kim, K.D., Lomboy, G.R. and Han, S.C. (2008), "Geometrically non-linear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element", J. Compos. Mater., 42(5), 485-511. https://doi.org/10.1177/0021998307086211
  14. Krysl, P. and Belytschko, T. (1996), "Analysis of thin shells by the element-free Galerkin method", Int. J. Solids Struct., 33(20-22), 3057-3080. https://doi.org/10.1016/0020-7683(95)00265-0
  15. Lei, Z. and Zhang, Y. (2018), "Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers", Steel Compos. Struct., Int. J., 28(4), 495-508.
  16. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014), "Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338. https://doi.org/10.1016/j.compstruct.2014.03.035
  17. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2015), "Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method", Compos. Struct., 127, 245-259. https://doi.org/10.1016/j.compstruct.2015.03.019
  18. Li, S.R., Fu, X.H. and Batra, R.C. (2010), "Free vibration of three-layer circular cylindrical shells with functionally graded middle layer", Mech. Res. Commun., 37(6), 577-580. https://doi.org/10.1016/j.mechrescom.2010.07.006
  19. Li, W., Nguyen-Thanh, N. and Zhou, K. (2018), "Geometrically nonlinear analysis of thin-shell structures based on an isogeometric-meshfree coupling approach", Comput. Methods Appl. Mech. Eng., 336, 111-134. https://doi.org/10.1016/j.cma.2018.02.018
  20. Liew, K.M., Wang, J., Tan, M.J. and Rajendran, S. (2004), "Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT", Comput. Methods Appl. Mech. Eng., 193(45-47), 4763-4779. https://doi.org/10.1016/j.cma.2004.03.013
  21. Liew, K.M., Peng, L.X. and Kitipornchai, S. (2007), "Nonlinear analysis of corrugated plates using a FSDT and a meshfree method", Comput. Methods Appl. Mech. Eng., 196(21-24), 2358-2376. https://doi.org/10.1016/j.cma.2006.11.018
  22. Liew, K.M., Zhao, X. and Ferreira, A.J. (2011), "A review of meshless methods for laminated and functionally graded plates and shells", Compos. Struct., 93(8), 2031-2041. https://doi.org/10.1016/j.compstruct.2011.02.018
  23. Liu, G.R. and Gu, Y.T. (2005), An Introduction to Meshfree Methods and their Programming, Springer Science & Business Media.
  24. Mallek, H., Jrad, H., Algahtani, A., Wali, M. and Dammak, F. (2019a), "Geometrically non-linear analysis of FG-CNTRC shell structures with surface-bonded piezoelectric layers", Comput. Methods Appl. Mech. Eng., 347, 679-699. https://doi.org/10.1016/j.cma.2019.01.001
  25. Mallek, H., Jrad, H., Wali, M. and Dammak, F. (2019b), "Geometrically nonlinear finite element simulation of smart laminated shells using a modified first-order shear deformation theory", J. Intel. Mater. Syst. Struct., 30(4), 517-535. https://doi.org/10.1177/1045389X18818386
  26. Mallek, H., Jrad, H., Wali, M. and Dammak, F. (2019c), "Piezoelastic response of smart functionally graded structure with integrated piezoelectric layers using discrete double directors shell element", Compos. Struct., 210, 354-366. https://doi.org/10.1016/j.compstruct.2018.11.062
  27. Marinkovic, D. and Rama, G. (2017), "Co-rotational shell element for numerical analysis of laminated piezoelectric composite structures", Compos. Part B: Eng., 125, 144-156. https://doi.org/10.1016/j.compositesb.2017.05.061
  28. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2019a), "Meshfree implementation of the double director shell model for FGM shell structures analysis", Eng. Anal. Bound. Elem., 99, 111-121. https://doi.org/10.1016/j.enganabound.2018.10.013
  29. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2019b), "Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory", Comput. Math. Appl., 77, 34-49. https://doi.org/10.1016/j.camwa.2018.09.010
  30. Nguyen, T.N., Thai, C.H., Nguyen-Xuan, H. and Lee, J. (2018), "Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory", Compos. Struct., 193, 268-280. https://doi.org/10.1016/j.compstruct.2018.03.036
  31. Noguchi, H., Kawashima, T. and Miyamura, T. (2000), "Element free analyses of shell and spatial structures", International J. Numer. Methods Eng., 47(6), 1215-1240. https://doi.org/10.1002/(SICI)1097-0207(20000228)47:6<1215::AID-NME834>3.0.CO;2-M
  32. Qian, L.F., Batra, R.C. and Chen, L.M. (2003), "Elastostatic deformations of a thick plate by using a higher-order shear and normal deformable plate theory and two meshless local Petrov-Galerkin (MLPG) methods", Comput. Model. Eng. Sci., 4(1), 161-176.
  33. Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov-Galerkin method", Computat. Mech., 33(4), 263-273. https://doi.org/10.1007/s00466-003-0527-z
  34. Rama, G. (2017), "A 3-node piezoelectric shell element for linear and geometrically nonlinear dynamic analysis of smart structures", Facta Universitatis, Series: Mechanical Engineering, 15(1), 31-44. https://doi.org/10.22190/FUME170225002R
  35. Rama, G., Marinkovic, D. and Zehn, M. (2018), "Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures", J. Intel. Mater. Syst. Struct., 29(3), 345-357. https://doi.org/10.1177/1045389X17705538
  36. Ray, M.C. and Batra, R.C. (2008), "Smart constrained layer damping of functionally graded shells using vertically/obliquely reinforced 1-3 piezocomposite under a thermal environment", Smart Mater. Struct., 17(5), 055007. https://doi.org/10.1088/0964-1726/17/5/055007
  37. Rezaiee Pajand, M., Masoodi, A. and Arabi, E. (2018), "Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element", Steel Compos. Struct., Int. J., 28(3), 389-401.
  38. Sladek, J., Sladek, V., Krivacek, J., Wen, P.H. and Zhang, C. (2007), "Meshless local Petrov-Galerkin (MLPG) method for Reissner-Mindlin plates under dynamic load", Comput. Methods Appl. Mech. Eng., 196(25-28), 2681-2691. https://doi.org/10.1016/j.cma.2007.01.014
  39. Tiago, C. and Pimenta, P.M. (2008), "An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations", Eng. Anal. Bound. Elem., 32(6), 494-511. https://doi.org/10.1016/j.enganabound.2007.10.014
  40. Timoshenko, S.P. and Gere, J.M. (1972), Mechanics of Materials. van Nordstrand Reinhold Company, New York, NY, USA.
  41. Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2019), "A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells", Eng. Struct., 178, 444-459. https://doi.org/10.1016/j.engstruct.2018.10.047
  42. Uysal, M.U. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells", Steel Compos. Struct., Int. J., 21(4), 849-862. https://doi.org/10.12989/scs.2016.21.4.849
  43. Vu, T.V., Khosravifard, A., Hematiyan, M.R. and Bui, T.Q. (2018), "A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates", Appl. Math. Model., 57, 514-534. https://doi.org/10.1016/j.apm.2018.01.004
  44. Wali, M., Hajlaoui, A. and Dammak, F. (2014), "Discrete double directors shell element for the functionally graded material shell structures analysis", Comput. Methods Appl. Mech. Eng., 278, 388-403. https://doi.org/10.1016/j.cma.2014.05.011
  45. Wang, J.G. and Liu, G.R. (2002), "On the optimal shape parameters of radial basis functions used for 2-D meshless methods", Comput. Methods Appl. Mech. Eng., 191(23-24), 2611-2630. https://doi.org/10.1016/S0045-7825(01)00419-4
  46. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., Int. J., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161
  47. 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. https://doi.org/10.1016/j.compstruct.2017.06.015
  48. Zhang, L.W. (2017), "An element-free based IMLS-Ritz method for buckling analysis of nanocomposite plates of polygonal planform", Eng. Anal. Bound. Elem., 77, 10-25. https://doi.org/10.1016/j.enganabound.2017.01.004
  49. Zhang, L.W. and Liew, K.M. (2016a), "Element-free geometrically nonlinear analysis of quadrilateral functionally graded material plates with internal column supports", Compos. Struct., 147, 99-110. https://doi.org/10.1016/j.compstruct.2016.03.034
  50. Zhang, L.W. and Liew, K.M. (2016b), "Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach", Compos. Struct., 138, 40-51. https://doi.org/10.1016/j.compstruct.2015.11.031
  51. Zhang, L.W. and Xiao, L.N. (2017), "Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading", Compos. Part B: Eng., 122, 219-230. https://doi.org/10.1016/j.compositesb.2017.03.041
  52. Zhang, L.W., Cui, W.C. and Liew, K.M. (2015a), "Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges", Int. J. Mech. Sci., 103, 9-21. https://doi.org/10.1016/j.ijmecsci.2015.08.021
  53. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015b), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach", Compos. Part B: Eng., 75, 36-46. https://doi.org/10.1016/j.compositesb.2015.01.033
  54. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015c), "Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLSRitz method", Compos. Struct., 128, 165-175. https://doi.org/10.1016/j.compstruct.2015.03.011
  55. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016a), "Postbuckling behavior of bi-axially compressed arbitrarily straight-sided quadrilateral functionally graded material plates", Comput. Methods Appl. Mech. Eng., 300, 593-610. https://doi.org/10.1016/j.cma.2015.11.030
  56. Zhang, L.W., Zhang, Y., Zou, G.L. and Liew, K.M. (2016b), "Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method", Compos. Struct., 149, 247-260. https://doi.org/10.1016/j.compstruct.2016.04.019
  57. Zhao, X., Liu, G.R., Dai, K.Y., Zhong, Z.H., Li, G.Y. and Han, X. (2008), "Geometric nonlinear analysis of plates and cylindrical shells via a linearly conforming radial point interpolation method", Computat. Mech., 42(1), 133-144. https://doi.org/10.1007/s00466-008-0242-x
  58. Zhu, P., Zhang, L.W. and Liew, K.M. (2014), "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001

피인용 문헌

  1. Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain vol.37, pp.3, 2019, https://doi.org/10.1108/ec-02-2019-0075
  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