Geometrically nonlinear analysis of FGM shells using solid-shell element with parabolic shear strain distribution
Source abstract
Abstract
This paper presents a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. Moreover, zero transverse shear stress on the top and bottom surfaces of the shell is satisfied exactly and the shear correction factors is no longer needed. Furthermore, the developed solid-shell element allows an efficient and accurate analysis of functionally graded material shells under geometric nonlinear static conditions. A simple power-law functionally graded distribution of the shells along the thickness direction is considered. The validity and accuracy of the developed solid-shell element are illustrated through the solution of several known problems taken from the literature. The influences of power-law index on the nonlinear static behavior of the FGM shells are discussed.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Structural Load-Bearing Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (76)
Show source-provided references
1. Alibeigloo, A.: Exact solution for thermo-elastic response of functionally graded rectangular plates. Compos. Struct. 92, 113–121 (2010). https://doi.org/10.1016/J.COMPSTRUCT.2009.07.00310.1016/J.COMPSTRUCT.2009.07.003 ↗
2. Alves de Sousa, R.J., Natal Jorge, R.M., Fontes Valente, R.A., César de Sá, J.M.A.: A new volumetric and shear locking-free 3D enhanced strain element. Eng. Comput. 20, 896–925 (2003). https://doi.org/10.1108/0264440031050203610.1108/02644400310502036 ↗
3. Arciniega, R.A., Reddy, J.N.: Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052 (2007). https://doi.org/10.1016/J.IJSOLSTR.2006.08.03510.1016/J.IJSOLSTR.2006.08.035 ↗
4. Başar, Y., Ding, Y.: Finite-rotation elements for the non-linear analysis of thin shell structures. Int. J. Solids Struct. 26, 83–97 (1990). https://doi.org/10.1016/0020-7683(90)90096-E10.1016/0020-7683(90)90096-E ↗
5. Behjat, B., Khoshravan, M.R.: Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates. Compos. Struct. 94, 874–882 (2012). https://doi.org/10.1016/J.COMPSTRUCT.2011.08.02410.1016/J.COMPSTRUCT.2011.08.024 ↗
6. Betsch, P., Stein, E.: An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element. Commun. Numer. Methods Eng. 11, 899–909 (1995). https://doi.org/10.1002/cnm.164011110410.1002/cnm.1640111104 ↗
7. Bettaieb, A.B., Velosa De Sena, J.L., Alves De Sousa, R.J., Valente, R.A.F., Habraken, A.M., Duchêne, L.: On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications. Finite Elem. Anal. Des. 107, 44–59 (2015). https://doi.org/10.1016/j.finel.2015.08.00510.1016/j.finel.2015.08.005 ↗
8. Buechter, N., Ramm, E.: Shell theory versus degeneration—a comparison in large rotation finite element analysis. Int. J. Numer. Methods Eng. 34, 39–59 (1992). https://doi.org/10.1002/nme.162034010510.1002/nme.1620340105 ↗
9. Cardoso, R.P.R., Yoon, J.W., Mahardika, M., Choudhry, S., Alves de Sousa, R.J., Fontes Valente, R.A.: Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements. Int. J. Numer. Methods Eng. 75, 156–187 (2008). https://doi.org/10.1002/nme.225010.1002/nme.2250 ↗
10. Carrera, E.: Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56, 287 (2003). https://doi.org/10.1115/1.155761410.1115/1.1557614 ↗
11. Caseiro, J.F., Alves de Sousa, R.J., Valente, R.A.F.: A systematic development of EAS three-dimensional finite elements for the alleviation of locking phenomena. Finite Elem. Anal. Des. 73, 30–41 (2013). https://doi.org/10.1016/J.FINEL.2013.05.00610.1016/J.FINEL.2013.05.006 ↗
12. Dvorkin, E.N., Bathe, K.: A continuum mechanics based four-node shell element for general non-linear analysis. Eng. Comput. 1, 77–88 (1984). https://doi.org/10.1108/eb02356210.1108/eb023562 ↗
13. Fafard, M., Dhatt, G., Batoz, J.L.: A new discrete Kirchhoff plate/shell element with updated procedures. Comput. Struct. 31, 591–606 (1989). https://doi.org/10.1016/0045-7949(89)90336-210.1016/0045-7949(89)90336-2 ↗
14. Fahsi, B., Kaci, A., Tounsi, A., Bedia, E.A.A.: A four variable refined plate theory for nonlinear cylindrical bending analysis of functionally graded plates under thermomechanical loadings. J. Mech. Sci. Technol. 26, 4073–4079 (2012). https://doi.org/10.1007/s12206-012-0907-410.1007/s12206-012-0907-4 ↗
15. Ferreira, A.J.M.: Analysis of composite plates using a layerwise theory and multiquadrics discretization. Mech. Adv. Mater. Struct. 12, 99–112 (2005). https://doi.org/10.1080/1537649049049395210.1080/15376490490493952 ↗
16. Frikha, A., Dammak, F.: 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 (2017). https://doi.org/10.1016/j.cma.2016.10.01710.1016/j.cma.2016.10.017 ↗
17. Frikha, A., Wali, M., Hajlaoui, A., Dammak, F.: Dynamic response of functionally graded material shells with a discrete double directors shell element. Compos. Struct. 154, 385–395 (2016). https://doi.org/10.1016/J.COMPSTRUCT.2016.07.02110.1016/J.COMPSTRUCT.2016.07.021 ↗
18. Ghorbani Shenas, A., Ziaee, S., Malekzadeh, P.: Nonlinear vibration analysis of pre-twisted functionally graded microbeams in thermal environment. Thin-Walled Struct. 118, 87–104 (2017). https://doi.org/10.1016/J.TWS.2017.05.00310.1016/J.TWS.2017.05.003 ↗
19. Hajlaoui, A., Jarraya, A., Kallel-Kamoun, I., Dammak, F.: Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element. J. Mech. Sci. Technol. 26, 3213–3221 (2012). https://doi.org/10.1007/s12206-012-0829-110.1007/s12206-012-0829-1 ↗
20. Hajlaoui, A., Jarraya, A., El Bikri, K., Dammak, F.: Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction. Compos. Struct. 132, 87–97 (2015). https://doi.org/10.1016/j.compstruct.2015.04.05910.1016/j.compstruct.2015.04.059 ↗
21. Hajlaoui, A., Wali, M., Ben Jdidia, M., Dammak, F.: An improved enhanced solid shell element for static and buckling analysis of shell structures. Mech. Ind. (2016). https://doi.org/10.1051/meca/201510610.1051/meca/2015106 ↗
22. Hajlaoui, A., Triki, E., Frikha, A., Wali, M., Dammak, F.: Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element. Lat. Am. J. Solids Struct. 14, 72–91 (2017). https://doi.org/10.1590/1679-7825332310.1590/1679-78253323 ↗
23. Hosseini-Hashemi, S., Salehipour, H., Atashipour, S.R., Sburlati, R.: On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: explicit 3-D elasticity solutions. Compos. Part B Eng. 46, 108–115 (2013). https://doi.org/10.1016/J.COMPOSITESB.2012.10.00810.1016/J.COMPOSITESB.2012.10.008 ↗
24. Jrad, H., Mars, J., Wali, M., Dammak, F.: Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells. Eng. Comput. (2018). https://doi.org/10.1007/s00366-018-0633-310.1007/s00366-018-0633-3 ↗
25. Kim, K.-D., Gilson Rescober Lomboy, G.R., Han, S.-C.: Geometrically non-linear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element. J. Compos. Mater. 42, 485–511 (2008). https://doi.org/10.1177/002199830708621110.1177/0021998307086211 ↗
26. Klinkel, S., Gruttmann, F., Wagner, W.: A robust non-linear solid shell element based on a mixed variational formulation. Comput. Methods Appl. Mech. Eng. 195, 179–201 (2006). https://doi.org/10.1016/J.CMA.2005.01.01310.1016/J.CMA.2005.01.013 ↗
27. Levinson, M.: An accurate, simple theory of the statics and dynamics of elastic plates. Mech. Res. Commun. 7, 343–350 (1980). https://doi.org/10.1016/0093-6413(80)90049-X10.1016/0093-6413(80)90049-X ↗
28. Liu, N., Jeffers, A.E.: Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory. Compos. Struct. 176, 143–153 (2017). https://doi.org/10.1016/J.COMPSTRUCT.2017.05.03710.1016/J.COMPSTRUCT.2017.05.037 ↗
29. Liu, B., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A.: Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Compos. Struct. 136, 546–553 (2016). https://doi.org/10.1016/J.COMPSTRUCT.2015.10.04410.1016/J.COMPSTRUCT.2015.10.044 ↗
30. Madabhusi-Raman, P., Davalos, J.F.: Static shear correction factor for laminated rectangular beams. Compos. Part B Eng. 27, 285–293 (1996). https://doi.org/10.1016/1359-8368(95)00014-310.1016/1359-8368(95)00014-3 ↗
31. Malekzadeh, P.: A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches. Appl. Math. Model. 33, 1850–1861 (2009). https://doi.org/10.1016/J.APM.2008.03.00810.1016/J.APM.2008.03.008 ↗
32. Mantari, J.L.: General recommendations to develop 4-unknowns quasi-3D HSDTs to study FGMs. Aerosp. Sci. Technol. 58, 559–570 (2016). https://doi.org/10.1016/J.AST.2016.09.00710.1016/J.AST.2016.09.007 ↗
33. Mars, J., Koubaa, S., Wali, M., Dammak, F.: Numerical analysis of geometrically non-linear behavior of functionally graded shells. Lat. Am. J. Solids Struct. 14, 1952–1978 (2017). https://doi.org/10.1590/1679-7825391410.1590/1679-78253914 ↗
34. Mian, M.A., Spencer, A.J.M.: Exact solutions for functionally graded and laminated elastic materials. J. Mech. Phys. Solids 46, 2283–2295 (1998). https://doi.org/10.1016/S0022-5096(98)00048-910.1016/S0022-5096(98)00048-9 ↗
35. Militello, C., Felippa, C.A.: A variational justification of the assumed natural strain formulation of finite elements—I. Variational principles. Comput. Struct. 34, 431–438 (1990). https://doi.org/10.1016/0045-7949(90)90267-610.1016/0045-7949(90)90267-6 ↗
36. Mindlin, R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME J. Appl. Mech. 18, 31–38 (1951)10.1115/1.4010217 ↗
37. Murthy, V.V.M.: An improved transverse shear deformation theory for laminated anisotropic plates. NASA Tech. Pap. 1903, 1–37 (1981)
38. Natarajan, S., Manickam, G.: Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite Elem. Anal. Des. 57, 32–42 (2012). https://doi.org/10.1016/J.FINEL.2012.03.00610.1016/J.FINEL.2012.03.006 ↗
39. Nguyen, T.K., Sab, K., Bonnet, G.: First-order shear deformation plate models for functionally graded materials. Compos. Struct. 83, 25–36 (2008). https://doi.org/10.1016/j.compstruct.2007.03.00410.1016/j.compstruct.2007.03.004 ↗
40. Pan, E.: Exact solution for functionally graded anisotropic elastic composite laminates. J. Compos. Mater. 37, 1903–1920 (2003). https://doi.org/10.1177/00219980303556510.1177/002199803035565 ↗
41. Panda, S., Ray, M.C.: Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite. Finite Elem. Anal. Des. 44, 493–504 (2008). https://doi.org/10.1016/J.FINEL.2008.01.00110.1016/J.FINEL.2008.01.001 ↗
42. Pandey, S., Pradyumna, S.: Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory. Eur. J. Mech. A/Solids 51, 55–66 (2015). https://doi.org/10.1016/J.EUROMECHSOL.2014.12.00110.1016/J.EUROMECHSOL.2014.12.001 ↗
43. Payette, G.S., Reddy, J.N.: A seven-parameter spectral/hp finite element formulation for isotropic, laminated composite and functionally graded shell structures. Comput. Methods Appl. Mech. Eng. 278, 664–704 (2014). https://doi.org/10.1016/j.cma.2014.06.02110.1016/j.cma.2014.06.021 ↗
44. Peng, X., Li, X.: Thermoelastic analysis of functionally graded annulus with arbitrary gradient. Appl. Math. Mech. 30, 1211–1220 (2009). https://doi.org/10.1007/s10483-009-1001-710.1007/s10483-009-1001-7 ↗
45. Phung-Van, P., Nguyen-Thoi, T., Luong-Van, H., Lieu-Xuan, Q.: Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT. Comput. Methods Appl. Mech. Eng. 270, 15–36 (2014). https://doi.org/10.1016/J.CMA.2013.11.01910.1016/J.CMA.2013.11.019 ↗
46. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752 (1984). https://doi.org/10.1115/1.316771910.1115/1.3167719 ↗
47. Reddy, J.N.: A generalization of two-dimensional theories of laminated composite plates. Commun. Appl. Numer. Methods 3, 173–180 (1987). https://doi.org/10.1002/cnm.163003030310.1002/cnm.1630030303 ↗
48. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)10.1201/b12409 ↗
49. Reese, S.: A large deformation solid-shell concept based on reduced integration with hourglass stabilization. Int. J. Numer. Methods Eng. 69, 1671–1716 (2007). https://doi.org/10.1002/nme.182710.1002/nme.1827 ↗
50. Reinoso, J., Blázquez, A.: Geometrically nonlinear analysis of functionally graded power-based and carbon nanotubes reinforced composites using a fully integrated solid shell element. Compos. Struct. 152, 277–294 (2016). https://doi.org/10.1016/j.compstruct.2016.05.03610.1016/j.compstruct.2016.05.036 ↗
51. Shariyat, M., Alipour, M.M.: A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations. Int. J. Mech. Sci. 87, 60–71 (2014). https://doi.org/10.1016/J.IJMECSCI.2014.05.03210.1016/J.IJMECSCI.2014.05.032 ↗
52. Shen, H.-S.: Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Eng. Struct. 25, 487–497 (2003). https://doi.org/10.1016/S0141-0296(02)00191-810.1016/S0141-0296(02)00191-8 ↗
53. Shi, G.: A new simple third-order shear deformation theory of plates. Int. J. Solids Struct. 44, 4399–4417 (2007). https://doi.org/10.1016/j.ijsolstr.2006.11.03110.1016/j.ijsolstr.2006.11.031 ↗
54. Shiyekar, S.M., Lavate, P.: Flexure of power law governed functionally graded plates using ABAQUS UMAT. Aerosp. Sci. Technol. 46, 51–59 (2015). https://doi.org/10.1016/J.AST.2015.06.02110.1016/J.AST.2015.06.021 ↗
55. Simo, J.C., Rifai, M.S.: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Eng. 29, 1595–1638 (1990). https://doi.org/10.1002/NME.162029080210.1002/NME.1620290802 ↗
56. Simo, J.C., Rifai, M.S., Fox, D.D.: On a stress resultant geometrically exact shell model. Part IV: variable thickness shells with through-the-thickness stretching. Comput. Methods Appl. Mech. Eng. 81, 91–126 (1990). https://doi.org/10.1016/0045-7825(90)90143-A10.1016/0045-7825(90)90143-A ↗
57. Sze, K.Y., Liu, X.H., Lo, S.H.: Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elem. Anal. Des. 40, 1551–1569 (2004). https://doi.org/10.1016/J.FINEL.2003.11.00110.1016/J.FINEL.2003.11.001 ↗
58. Tanov, R., Tabiei, A.: Simple correction to the first-order shear deformation shell finite element formulations. Finite Elem. Anal. Des. 35, 189–197 (2000). https://doi.org/10.1016/S0168-874X(99)00069-410.1016/S0168-874X(99)00069-4 ↗
59. Thai, S., Thai, H.-T., Vo, T.P., Reddy, J.N.: Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis. Eng. Struct. 150, 905–917 (2017). https://doi.org/10.1016/J.ENGSTRUCT.2017.07.07310.1016/J.ENGSTRUCT.2017.07.073 ↗
60. Timoshenko, S., Gere, J.M.: Mechanics of Materials. Van Nostrand Reinhold Co, New York (1972)
61. Trabelsi, S., Frikha, A., Zghal, S., Dammak, F.: 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 (2019). https://doi.org/10.1016/J.ENGSTRUCT.2018.10.04710.1016/J.ENGSTRUCT.2018.10.047 ↗
62. Vel, S.S., Batra, R.C.: Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J. Sound Vib. 272, 703–730 (2004). https://doi.org/10.1016/S0022-460X(03)00412-710.1016/S0022-460X(03)00412-7 ↗
63. Vu-Quoc, L., Tan, X.G.: Optimal solid shells for non-linear analyses of multilayer composites. I. Statics. Comput. Methods Appl. Mech. Eng. 192, 975–1016 (2003). https://doi.org/10.1016/S0045-7825(02)00435-810.1016/S0045-7825(02)00435-8 ↗
64. Wali, M., Hajlaoui, A., Dammak, F.: Discrete double directors shell element for the functionally graded material shell structures analysis. Comput. Methods Appl. Mech. Eng. (2014). https://doi.org/10.1016/j.cma.2014.05.01110.1016/j.cma.2014.05.011 ↗
65. Wali, M., Hentati, T., Jarraya, A., Dammak, F.: Free vibration analysis of FGM shell structures with a discrete double directors shell element. Compos. Struct. 125, 295–303 (2015). https://doi.org/10.1016/J.COMPSTRUCT.2015.02.03210.1016/J.COMPSTRUCT.2015.02.032 ↗
66. Wilson, E.L., Taylor, R.L., Doherty, W.P., Ghaboussi, J.: Incompatible displacement models. Numer. Comput. Methods Struct. Mech. (1973). https://doi.org/10.1016/B978-0-12-253250-4.50008-710.1016/B978-0-12-253250-4.50008-7 ↗
67. Woo, J., Meguid, S.A.: Nonlinear analysis of functionally graded plates and shallow shells. Int. J. Solids Struct. 38, 7409–7421 (2001). https://doi.org/10.1016/S0020-7683(01)00048-810.1016/S0020-7683(01)00048-8 ↗
68. Woodward, B., Kashtalyan, M.: Performance of functionally graded plates under localised transverse loading. Compos. Struct. 94, 2254–2262 (2012). https://doi.org/10.1016/J.COMPSTRUCT.2012.02.01210.1016/J.COMPSTRUCT.2012.02.012 ↗
69. Yang, Q.J., Hayman, B.: Prediction of post-buckling and ultimate compressive strength of composite plates by semi-analytical methods. Eng. Struct. 84, 42–53 (2015). https://doi.org/10.1016/j.engstruct.2014.11.01310.1016/j.engstruct.2014.11.013 ↗
70. Yu, T.T., Yin, S., Bui, T.Q., Hirose, S.: A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates. Finite Elem. Anal. Des. 96, 1–10 (2015). https://doi.org/10.1016/J.FINEL.2014.11.00310.1016/J.FINEL.2014.11.003 ↗
71. Zenkour, A.M.: Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Arch. Appl. Mech. 77, 197–214 (2007). https://doi.org/10.1007/s00419-006-0084-y10.1007/s00419-006-0084-y ↗
72. Zghal, S., Frikha, A., Dammak, F.: Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures. Compos. Struct. 176, 1107–1123 (2017). https://doi.org/10.1016/j.compstruct.2017.06.01510.1016/j.compstruct.2017.06.015 ↗
73. Zghal, S., Frikha, A., Dammak, F.: Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels. Compos. Part B Eng. 150, 165–183 (2018a). https://doi.org/10.1016/J.COMPOSITESB.2018.05.03710.1016/J.COMPOSITESB.2018.05.037 ↗
74. Zghal, S., Frikha, A., Dammak, F.: Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures. Appl. Math. Model. 53, 132–155 (2018b). https://doi.org/10.1016/J.APM.2017.08.02110.1016/J.APM.2017.08.021 ↗
75. Zhao, X., Liew, K.M.: Geometrically nonlinear analysis of functionally graded shells. Int. J. Mech. Sci. 51, 131–144 (2009). https://doi.org/10.1016/J.IJMECSCI.2008.12.00410.1016/J.IJMECSCI.2008.12.004 ↗
76. Zhong, Z., Shang, E.: Closed-form solutions of three-dimensional functionally graded plates. Mech. Adv. Mater. Struct. 15, 355–363 (2008). https://doi.org/10.1080/1537649080197752810.1080/15376490801977528 ↗