Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element

  • Rezaiee-Pajand, M. (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Masoodi, Amir R. (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Arabi, E. (Department of Civil Engineering, Ferdowsi University of Mashhad)
  • Received : 2018.04.13
  • Accepted : 2018.06.02
  • Published : 2018.08.10
⟨ Previous Next ⟩

Abstract

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

Keywords

References

  1. Ahmad, S., Irons, B. and Zienkiewicz, O.C. (1970), "Analysis of thick and thin shell structures by curved finite elements", Int. J. Numer. Method. Eng., 2(3), 419-451. https://doi.org/10.1002/nme.1620020310
  2. Alankaya, V. and Oktem, A.S. (2016), "Static analysis of laminated and sandwich composite doubly-curved shallow shells", Steel Compos. Struct., Int. J., 20(5), 1043-1066. https://doi.org/10.12989/scs.2016.20.5.1043
  3. Arciniega, R.A. and Reddy, J.N. (2007a), "Large deformation analysis of functionally graded shells", Int. J. Solids Struct., 44(6), 2036-2052. https://doi.org/10.1016/j.ijsolstr.2006.08.035
  4. Arciniega, R.A. and Reddy, J.N. (2007b), "Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures", Comput. Method. Appl. Mech. Eng., 196(4-6), 1048-1073. https://doi.org/10.1016/j.cma.2006.08.014
  5. Barbosa, J.A.T. and Ferreira, A.J.M. (2009), "Geometrically nonlinear analysis of functionally gaded plates and shells", Mech. Adv. Mater. Struct., 17(1), 40-48. https://doi.org/10.1080/15376490903082870
  6. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Engiewood Cliffs.
  7. Beheshti, A. and Ramezani, S. (2015), "Nonlinear finite element analysis of functionally graded structures by enhanced assumed strain shell elements", Appl. Math. Model., 39(13), 3690-3703. https://doi.org/10.1016/j.apm.2014.11.064
  8. Caliri Jr., M.F., Ferreira, A.J.M. and Tita, V. (2016), "A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method", Compos. Struct., 156, 63-77. https://doi.org/10.1016/j.compstruct.2016.02.036
  9. Carrera, E., Cinefra, M., Li, G. and Kulikov, G.M. (2016), "MITC9 shell finite elements with miscellaneous through-thethickness functions for the analysis of laminated structures", Compos. Struct., 154, 360-373. https://doi.org/10.1016/j.compstruct.2016.07.032
  10. Chaudhuri, R.A. and Oktem, A.S. (2015), "Analysis of simply-supported saddle-shaped symmetric cross-ply panels with no surface-parallel boundary constraints", AIAA J., 54(2), 782-788.
  11. Chaudhuri, R.A., Oktem, A.S. and Guedes Soares, C. (2014), "Levy-type boundary Fourier analysis of thick clamped hyperbolic-paraboloidal cross-ply panels", AIAA J., 53(1), 140-149. https://doi.org/10.2514/1.J052986
  12. Chaudhuri, R.A., Oktem, A.S. and Guedes Soares, C. (2015), "Levy-type boundary Fourier analysis of thick cross-ply panels with negative Gaussian curvature", AIAA J., 53(9), 2492-2503. https://doi.org/10.2514/1.J053440
  13. Coda, H.B., Paccola, R.R. and Carrazedo, R. (2017), "Zig-Zag effect without degrees of freedom in linear and non linear analysis of laminated plates and shells", Compos. Struct., 161, 32-50. https://doi.org/10.1016/j.compstruct.2016.10.129
  14. Dvorkin, E.N. and Bathe, K.J. (1984), "A continuum mechanics based four-node shell element for general nonlinear analysis", Eng. Comput., 1(1), 77-88. https://doi.org/10.1108/eb023562
  15. Hughes, T.J.R. and Liu, W.K. (1981a), "Nonlinear finite element analysis of shells-part II. two-dimensional shells", Comput. Method. Appl. Mech. Eng., 27(2), 167-181. https://doi.org/10.1016/0045-7825(81)90148-1
  16. Hughes, T.J.R. and Liu, W.K. (1981b), "Nonlinear finite element analysis of shells: Part I. three-dimensional shells", Comput. Method. Appl. Mech. Eng., 26(3), 331-362. https://doi.org/10.1016/0045-7825(81)90121-3
  17. Jung, W.-Y., Han, S.-C., Lee, W.-H. and Park, W.-T. (2016), "Postbuckling analysis of laminated composite shells under shear loads", Steel Compos. Struct., Int. J., 21(2), 373-394. https://doi.org/10.12989/scs.2016.21.2.373
  18. Kaci, A., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2014), "Nonlinear cylindrical bending analysis of E-FGM plates with variable thickness", Steel Compos. Struct., Int. J., 16(4), 339-356. https://doi.org/10.12989/scs.2014.16.4.339
  19. Kapania, R.K. (1989), "A Review on the Analysis of Laminated Shells", J. Press. Vessel Tech., 111(2), 88-96. https://doi.org/10.1115/1.3265662
  20. Khabbaz, R.S., Manshadi, B.D. and Abedian, A. (2009), "Nonlinear analysis of FGM plates under pressure loads using the higher-order shear deformation theories", Compos. Struct., 89(3), 333-344. https://doi.org/10.1016/j.compstruct.2008.06.009
  21. Khayat, M., Poorveis, D. and Moradi, S. (2016), "Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method", Steel Compos. Struct., Int. J., 22(2), 301-321. https://doi.org/10.12989/scs.2016.22.2.301
  22. Khayat, M., Poorveis, D. and Moradi, S. (2017), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Compos. Struct., Int. J., 23(1), 1-16. https://doi.org/10.12989/scs.2017.23.1.001
  23. 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
  24. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82(11-12), 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004
  25. Levyakov, S.V. and Kuznetsov, V.V. (2011), "Application of triangular element invariants for geometrically nonlinear analysis of functionally graded shells", Comput. Mech., 48(4), 499-513. https://doi.org/10.1007/s00466-011-0603-8
  26. Liang, K. (2017), "Koiter-Newton analysis of thick and thin laminated composite plates using a robust shell element", Compos. Struct., 161, 530-539. https://doi.org/10.1016/j.compstruct.2016.10.071
  27. Liu, Q. and Paavola, J. (2016), "General analytical sensitivity analysis of composite laminated plates and shells for classical and first-order shear deformation theories", Compos. Struct., 183, 21-34.
  28. Liu, W.K., Law, E.S., Lam, D. and Belytschko, T. (1986), "Resultant-stress degenerated-shell element", Comput. Methods Appl. Mech. Eng., 55(3), 259-300. https://doi.org/10.1016/0045-7825(86)90056-3
  29. Crisfield, M. (1986), Finite Elements on Solution Procedures for Structural Analysis, (I) Linear Analysis, Pineridge Press, Swansea, UK.
  30. Masoodi, A.R. and Arabi, E. (2018), "Geometrically nonlinear thermomechanical analysis of shell-like structures", J. Thermal Stress., 41(1), 37-53. https://doi.org/10.1080/01495739.2017.1360166
  31. Park, K.C. and Stanley, G.M. (1986), "A curved C0 shell element based on assumed natural-coordinate strains", J. Appl. Mech., 53(2), 278-290. https://doi.org/10.1115/1.3171752
  32. Pascon, J.P. and Coda, H.B. (2013), "High-order tetrahedral finite elements applied to large deformation analysis of functionally graded rubber-like materials", Appl. Math. Model., 37(20), 8757-8775. https://doi.org/10.1016/j.apm.2013.03.062
  33. Reddy, J.N. and Arciniega, R.A. (2004), "Shear Deformation Plate and Shell Theories: From Stavsky to Present", Mech. Adv. Mater. Struct., 11(6), 535-582. https://doi.org/10.1080/15376490490452777
  34. 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
  35. Rezaiee-Pajand, M. and Masoodi, A.R. (2018), "Exact natural frequencies and buckling load of functionally graded material tapered beam-columns considering semi-rigid connections", J. Vib. Control, 24(9), 1787-1808. https://doi.org/10.1177/1077546316668932
  36. Rezaiee-Pajand, M., Arabi, E. and Masoodi, A.R. (2018a), "A triangular shell element for geometrically nonlinear analysis", Acta Mechanica, 229(1), 323-342. https://doi.org/10.1007/s00707-017-1971-8
  37. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018b), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Comput. Des., 3(2), 165-190. https://doi.org/10.12989/ACD.2018.3.2.165
  38. Sze, K.Y., Liu, X.H. and Lo, S.H. (2004), "Popular benchmark problems for geometric nonlinear analysis of shells", Finite Elem. Anal. Des., 40(11), 1551-1569. https://doi.org/10.1016/j.finel.2003.11.001
  39. Thai, H.-T. and Kim, S.-E. (2015), "A review of theories for the modeling and analysis of functionally graded plates and shells", Compos. Struct., 128(15), 70-86. https://doi.org/10.1016/j.compstruct.2015.03.010
  40. Tiar, A., Zouari, W., Kebir, H. and Ayad, R. (2016), "A nonlinear finite element formulation for large deflection analysis of 2D composite structures", Compos. Struct., 153, 262-270. https://doi.org/10.1016/j.compstruct.2016.05.102
  41. 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
  42. Wetherhold, R.C., Seelman, S. and Wang, J. (1996), "The use of functionally graded materials to eliminate or control thermal deformation", Compos. Sci. Technol., 56(9), 1099-1104. https://doi.org/10.1016/0266-3538(96)00075-9
  43. Woo, J. and Meguid, S.A. (2001), "Nonlinear analysis of functionally graded plates and shallow shells", Int. J. Solids Struct., 38(42), 7409-7421. https://doi.org/10.1016/S0020-7683(01)00048-8
  44. Zhao, X. and Liew, K.M. (2009), "Geometrically nonlinear analysis of functionally graded shells", Int. J. Mech. Sci., 51(2), 131-144. https://doi.org/10.1016/j.ijmecsci.2008.12.004