DOI QR코드

DOI QR Code

Strain recovery-based equilibrated transverse shear stresses in functionally graded shell-like structures

  • Jin-Rae Cho (Department of Naval Architecture and Ocean Engineering, Hongik University)
  • 투고 : 2024.05.27
  • 심사 : 2024.08.22
  • 발행 : 2024.09.10

초록

The standard numerical approximation of structural displacement field leads to the thickness-wise transverse shear stress distributions which are quite different from the exact ones. To overcome this inherent problem, an effective and reliable post-processing method is presented based on the strain recovery and the stress equilibrium, particularly for functionally graded cylindrical and conical elastic panels. The present method is developed in the framework of locking-free 2-D natural element method. Through the recovery of displacement component-wise derivatives, the element-wise discontinuous in-plane strain distributions are enhanced to be globally continuous and smoothened. And, using the continuous in-plane strains, the troublesome poor transverse shear stress distributions are enhanced through the thickness-wise integration of static equilibrium equations. The validity of present post-processing method is verified through the comparison with the reference solutions. In addition, the comparative experiments are also performed to investigate the difference between the present method and other available post-processing methods. The numerical results confirm that the present method provides the accurate transverse shear stress distributions which are consistent with the reference solutions and much better than other available methods.

키워드

과제정보

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2023-00240618). This work was supported by the 2024 Hongik University Research Fund.

참고문헌

  1. Akbari, M., Kiani, Y., Aghdam, M.M. and Eslami, M.R. (2014), "Free vibration of FGM Levy conical panels", Compos. Struct., 116, 732-746. http://doi.org/10.1016/j.compstruct.2014.05.052.
  2. Ba, Z., Wu, M. and Liang, J. (2020), "3D dynamic responses of a multi-layered trenasversely isotropic saturated half-space under concentrated forced and pore pressure", Appl. Math. Model., 80, 859-878. https://doi.org/10.1016/j.apm.2019.11.014.
  3. Bagheri, H., Kiani, Y. and Eslami, M.R. (2021), "Free vibration of FGM conical-spherical shells", Thin Wall. Struct., 160, 107387. https://doi.org/10.1016/j.tws.2020.107387.
  4. Bathe, K.J., Bucalem, M.L. and Brezzi, F. (1990), "Displacement and stress convergence of our MITC plate bending elements", Eng. Comput., 7, 291-302. https://doi.org/10.1108/eb023816.
  5. Bisegna, P. and Sacco, E. (1997), "A rational deduction of plate theories from the three dimensional linear elasticity", ZAMM J. Appl. Math. Mech., 77, 349-366. https://doi.org/10.1002/zamm.19970770509.
  6. Chau-Dinh, T. (2023), "Analysis of shell structures by an improved 3-node triangular flat shell element with a bubble function and cell-based smoothing", Thin Wall. Struct., 182, 110222. https://doi.org/10.1016/j.tws.2022.110222.
  7. Cho, J.R. (2020), "Natural element approximation of hierarchical models of plate-like elastic structures", Finite. Elem. Anal. Des., 180, 103439. https://doi.org/10.1016/j.finel.2020.103439.
  8. Cho, J.R. (2021), "Level-wise strain recovery and error estimation for natural element hierarchical plate models", Int. J. Numer. Meth. Eng., 122, 3120-3136. https://doi.org/10.1002/nme.6659.
  9. Cho, J.R. (2023), "Free vibration analysis of functionally graded porous cylindrical panels reinforced with grapheme platelets", Nanomater., 13(9), 1441. https://doi.org/10.3390/nano13091441.
  10. Cho, J.R. and Oden, J.T. (1997), "Locking and boundary layer in hierarchical models for thin elastic structures", Comput. Meth. Appl. Mech. Eng., 149, 33-48. https://doi.org/10.1016/S0045-7825(97)00057-1.
  11. Cho, J.R., Lee, H.W. and Yoo, W.S. (2013), "Natural element approximation of Reissnre-Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures", Comput. Meth. Appl. Mech. Eng., 256, 17-28. https://doi.org/10.1016/j.cma.2012.12.015.
  12. Daniel, P.M., Framby, J., Fagerstrom, M. and Maimi, P. (2020), "Complete transverse stress recovery model for linear shell elements in arbitrarily curved laminates", Compos. Struct., 252, 112675. https://doi.org/10.1016/j.compstruct.2020.112675.
  13. Di Sciuva, M. (1987), "An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates", J. Appl. Mech., 54, 589-596. https://doi.org/10.1115/1.3173074.
  14. Gao, Q., Ding, Z. and Liao, W. (2022), "Effective elastic properties of irregular auxetic structures", Compos. Struct., 287, 115269. https://doi.org/10.1016/j.compstruct.2022.115269.
  15. Hou, P.F. and Zhang, W.H. (2020), "3D axisymmetric exact solutions of the piezo-coating sensors for coating/substrate system under charged conical contact", Int. J. Solid. Struct., 185-186, 342-364. https://doi.org/10.1016/j.ijsolstr.2019.08.031.
  16. Jun, H.M., Yoon, K.H., Lee, P.S. and Bathe, K.J. (2018), "The MITC3+ shell element enriched in membrane displacements by interpolation covers", Comput. Meth. Appl. Mech. Eng., 337, 458-480. https://doi.org/10.1016/j.cma.2018.04.007.
  17. Kiani, Y. (2017), "Analysis of FG-CNT reinforced composite conical panel subjected to moving load using Ritz method", Thin Wall. Struct., 119, 47-57. http://doi.org/10.1016/j.tws.2017.05.031.
  18. Kiani, Y., Dimitri, R. and Tornabene, F. (2018), "Free vibration study of composite conical panels reinforced with FG-CNTs", Eng. Struct., 172, 472-482. https://doi.org/10.1016/j.engstruct.2018.06.006.
  19. Leonetti, L., Nguyen-Xuan, H. and Liu, G.R. (2023), "A new mixed node-based solid-like finite element method (MNS-FEM) for laminated shell structures", Thin Wall. Struct., 192, 111126. https://doi.org/10.1016/j.tws.2023.111126.
  20. Liu, K., Zong, S., Li, Y., Wang, Z., Hu, Z. and Wang, Z. (2022), "Structural response of the U-type corrugated core sandwich panel used in ship structures under the lateral quasi-static compression load", Maine Struct., 84, 103198. https://doi.org/10.1016/j.marstruc.2022.103198.
  21. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), "A higher order theory of plate deformation-Part 1: Homogeneous plates", ASME J. Appl. Mech., 44, 663-668. https://doi.org/10.1115/1.3424154.
  22. Mangalgiri, P.D. (1999), "Comosite materials for aerospace applications", Buii. Mater. Sci., 22. 657-664. https://doi.org/10.1007/BF02749982.
  23. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motion of isotropic elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217.
  24. Noor, A.K. and Burton, W.S. (1998), "Assessment of shear deformation theories for multi-layered composite plates", Appl. Mech. Rev., 42(1), 1-13. https://doi.org/10.1115/1.3152418.
  25. Okstad, K.M., Kvamsdal, T. and Mathisen, K.M. (1999), "Superconvergent patch recovery for plate problems using statically admissible stress resultant fields", Int. J. Numer. Meth. Engng., 44(5), 697-727. https://doi.org/10.1002/(SICI)1097-0207(19990220)44:5<697::AID-NME 526>3.0.CO;2-L.
  26. Papadopoulos, P. and Taylor, R.L. (1990), "A triangular element based on Reissner-Mindlin plate theory", Int. J. Numer. Meth. Eng., 30(5), 1029-1049. https://doi.org/10.1002/nme.1620300506.
  27. Pitkaranta, J. (1992), "The problem of membrane locking in finite element analysis of cylindrical shells", Numner. Math., 61, 523-542. https://doi.org/10.1007/BF01385524.
  28. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  29. Reese, S., Wriggers, P. and Reddy, B.D. (2000), "A new locking-free element technique for large deformation problems in elasticity", Comput. Struct., 75(3), 291-304. https://doi.org/10.1016/S0045-7949(99)00137-6.
  30. Reissner, E.A. (1972), "Consistent treatment of transverse shear deformations in laminated anisotropic plates", AIAA J., 10, 716-718. https://doi.org/10.2514/3.50194.
  31. Salmanizadeh, A., Kiani, Y. and Eslami, M.R. (2022), "Vibrations of functionally graded conical panel subjected to instantaneous thermal shock using Chebyshev-Ritz route", Eng. Anal. Bound. Elem., 144, 422-432. https://doi.org/10.1016/j.enganabound.2022.08.040.
  32. Shen, Y.L., Finot, M., Needleman, A. and Suresh, S. (1994), "Effective elastic response of two-phase composites", Acta Metall. Mater., 42(1), 77-97. https://doi.org/10.1016/0956-7151(94)90050-7.
  33. Simo, J.C. and Rifai, M.S (1990), "A class of mixed assumed strain methods and the method of incompatible modes", Int. J. Numer. Meth. Eng., 29(8), 1595-1638. https://doi.org/10.1002/nme.1620290802.
  34. Sukumar, N., Moran, B. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Meth. Eng., 43(5), 839-887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R.
  35. Tessler, A., Riggs, H.R., Freese, C.E. and Cook, G.M. (1998), "An improved variational method for finite element stress recovery and a posteriori error estimation", Comput. Meth. Appl. Mech. Eng., 155(1-2), 15-30. https://doi.org/10.1016/S0045-7825(97)00135-7.
  36. Tornabene, F. and Viola, E. (2009), "Free vibrations of four-parameter functionally graded parabolic panels and shells of revolutions", Eur. J. Mech. A/Solid., 28, 991-1013. https://doi.org/10.1016/j.euromechsol.2009.04.005.
  37. Viola, E., Rossetti, L. and Fantuzzi, N. (2012), "Numerical investigation of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery", Compos. Struct., 94, 3736-3758. https://doi.org/10.1016/j.compstruct.2012.05.034.
  38. Viola, E., Rossetti, L.., Fantuzzi, N. and Tornabene, F. (2014), "Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order coupled with the stress recovery", Compos. Struct., 112, 44-65. https://doi.org/10.1016/j.compstruct.2014.01.039.
  39. Wang, Y. and Sigmund, O. (2023), "Multi-material topology optimization for maximizing structural stability under thermomechanical loading", Comout. Meth. Appl. Mech. Eng., 407, 115938. https://doi.org/10.1016/j.cma.2023.115938.
  40. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", ASME J. Appl. Mech., 37, 1031-1036. https://doi.org/10.1115/1.3408654.
  41. Xu, S., Jing, X., Zhu, P., Jin, H., Paik, K.W., He, P. and Zhang, S. (2023), "Equilibrium phase diagram design and structural optimization of SAC/Sn-Pb composite structure solder joint for prefereable stress distribution", Mater. Charact., 206, 113389. https://doi.org/10.1016/j.matchar.2023.113389.
  42. Zienkiewicz, O.C. and Taylor, R.L. (1991), The Finite Element Method, Vol. 2, McGraw-Hill, New York.