DOI QR코드

DOI QR Code

Mechanical analysis of functionally graded spherical panel resting on elastic foundation under external pressure

  • Cao, Yan (School of Mechatronic Engineering and Shaanxi Key Laboratory of Non-Traditional Machining, Xi'an Technological University) ;
  • Qian, Xueming (School of Mechatronic Engineering and Shaanxi Key Laboratory of Non-Traditional Machining, Xi'an Technological University) ;
  • Fan, Qingming (School of Mechatronic Engineering and Shaanxi Key Laboratory of Non-Traditional Machining, Xi'an Technological University) ;
  • Ebrahimi, Farbod (Young Researchers and Elite Club, Tehran Branch, Islamic Azad University)
  • 투고 : 2019.06.07
  • 심사 : 2020.02.10
  • 발행 : 2020.04.25

초록

The main purpose of this study is to analyze the effects of external pressure on the vibration and buckling of functionally graded (FG) spherical panels resting of elastic medium. The material characteristics of the FG sphere continuously vary through the thickness direction based on the power-law rule. In accordance with first-order shear deformation shell theory and by the use of Ritz formulation the governing equations are presented. In this regard, the beam functions are applied in two-dimensions for different sets of boundary supports. The Winkler and Pasternak models of elastic foundations are also taken into account. In order to show the validity and applicability of the presented formulation, various comparison studies are given. Furthermore, a diverse range of numerical results is reported to check the impacts of geometrical and material parameters along with external pressure on the vibration and buckling analysis of FG spherical panels.

키워드

과제정보

연구 과제 주관 기관 : Xi'an Technological University

This paper is supported by Shaanxi Key Research and Development Plan (Grant: 2018ZDXM-GY-077), Shaanxi Natural Science Basic Research Project (Grant: S2019-JCYB-2897), Project of Joint Postgraduate Training Base of Xi'an Technological University, and Research Project of Graduate Education and Teaching Reform of Xi'an Technological University in 2017.

참고문헌

  1. ACI 228.2R-13. (2013), "Nondestructive test methods for evaluation of concrete in structures", American Concrete Institute Report, Farmington Hills, U.S.A.
  2. Akgoz, B., and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  3. Alijani, F., Amabili, M., Karagiozis, K., and Bakhtiari-Nejad, F. (2011), "Nonlinear vibrations of functionally graded doubly curved shallow shells", J. Sound Vib., 330(7), 1432-1454. https://doi.org/10.1016/j.jsv.2010.10.003.
  4. Ansari, R., and Torabi, J. (2016), "Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading", Compos. Part B Eng., 95, 196-208. https://doi.org/10.1016/j.compositesb.2016.03.080.
  5. Ansari, R., Torabi, J., and Shojaei, M. F. (2016), "Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method", Europe J. Mech. A/Solids, 60, 166-182. https://doi.org/10.1016/j.euromechsol.2016.07.003.
  6. Bich, D. H., and Van Tung, H. (2011), "Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects"., J Non-Linear Mech., 46(9), 1195-1204. https://doi.org/10.1016/j.ijnonlinmec.2011.05.015.
  7. Bich, D. H., Van Dung, D., and Nam, V. H. (2013), "Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells", Compos. Struct., 96, 384-395.https://doi.org/10.1016/j.compstruct.2012.10.009
  8. Bich, D. H., and Phuong, N. T. (2013), "Buckling Analysis of Functionally Graded Annular Spherical Shells and Segments Subjected to Mechanic Loads", VNU J. Sci. Mathematics-Physics, 29(3), https://js.vnu.edu.vn/MaP/article/view/869.
  9. Civalek, O., and Ulker, M. (2004), "Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates", Struct. Eng. Mech., 17(1), 1-14. https://doi.org/10.12989/sem.2004.17.1.001.
  10. Civalek, O. (2006), "Free vibration analysis of composite conical shells using the discrete singular convolution algorithm", Steel Compos. Struct., 6(4), 353. https://doi.org/10.12989/scs.2006.6.4.353.
  11. Civalek, O. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25(1), 127-130. https://doi.org/10.12989/sem.2007.25.1.127.
  12. Civalek, O., and Acar, M. H. (2007), "Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations", J. Pressure Vessels Piping, 84(9), 527-535. https://doi.org/10.1016/j.ijpvp.2007.07.001.
  13. Civalek, O. (2008), "Vibration analysis of conical panels using the method of discrete singular convolution", Communications Numerical Methods Eng., 24(3), 169-181. https://doi.org/10.1002/cnm.961.
  14. Darilmaz, K. (2017), "Static and free vibration behaviour of orthotropic elliptic paraboloid shells", Steel Compos. Struct., 23(6), 737-746. https://doi.org/10.12989/scs.2017.23.6.737.
  15. Foroughi, H., and Azhari, M. (2014), "Mechanical buckling and free vibration of thick functionally graded plates resting on elastic foundation using the higher order B-spline finite strip method", Meccanica, 49(4), 981-993. https://doi.org/10.1007/s11012-013-9844-2.
  16. Foroutan, K., Shaterzadeh, A., and Ahmadi, H. (2018), "Nonlinear dynamic analysis of spiral stiffened functionally graded cylindrical shells with damping and nonlinear elastic foundation under axial compression", Struct. Eng. Mech., 66(3), 295-303. http://dx.doi.org/10.12989/sem.2018.66.3.295.
  17. Ganapathi, M. (2007), "Dynamic stability characteristics of functionally graded materials shallow spherical shells", Compos. Struct., 79(3), 338-343. https://doi.org/10.1016/j.compstruct.2006.01.012.
  18. Ghannad, M., Nejad, M. Z., Rahimi, G. H., and Sabouri, H. (2012), "Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials", Struct. Eng. Mech., 43(1), 105-126. https://doi.org/10.12989/sem.2012.43.1.105.
  19. Hasrati, E., Ansari, R., and Torabi, J. (2018), "A novel numerical solution strategy for solving nonlinear free and forced vibration problems of cylindrical shells", Appl. Math. Modelling, 53, 653-672. https://doi.org/10.1016/j.apm.2017.08.027.
  20. Heydarpour, Y., Aghdam, M. M., and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200.https://doi.org/10.1016/j.compstruct.2014.06.023.
  21. 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., 21(2), 373-394. https://doi.org/10.12989/scs.2016.21.2.373.
  22. Kar, V. R., and Panda, S. K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. http://dx.doi.org/10.12989/sem.2015.53.4.661.
  23. Karroubi, R., and Irani-Rahaghi, M. (2019), "Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis", Appl. Math. Mech., 40(4), 563-578. https://doi.org/10.1007/s10483-019-2469-8.
  24. 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., 22(2), 301-321. https://doi.org/10.12989/scs.2016.22.2.301.
  25. Loy, C. T., Lam, K. Y., and Reddy, J. N. (1999), "Vibration of functionally graded cylindrical shells", J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X.
  26. Mao, Y. Q., Fu, Y. M., Chen, C. P., and Li, Y. L. (2011), "Nonlinear dynamic response for functionally graded shallow spherical shell under low velocity impact in thermal environment", Appl. Math. Modelling, 35(6), 2887-2900. https://doi.org/10.1016/j.apm.2010.12.012.
  27. Mercan, K., Demir, C., and Civalek, O. (2016), "Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique", Curved Layered Struct., 3(1), 2353-7396. https://doi.org/10.1515/cls-2016-0007.
  28. Naghsh, A., Saadatpour, M. M., and Azhari, M. (2015), "Free vibration analysis of stringer stiffened general shells of revolution using a meridional finite strip method", Thin-Walled Struct., 94, 651-662. https://doi.org/10.1016/j.tws.2015.05.015.
  29. Patel, B. P., Gupta, S. S., Loknath, M. S., and Kadu, C. P. (2005), "Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory", Compos. Struct., 69(3), 259-270. https://doi.org/10.1016/j.compstruct.2004.07.002.
  30. Shahsiah, R., Eslami, M. R., and Naj, R. (2006), "Thermal instability of functionally graded shallow spherical shell", J. Thermal Stresses, 29(8), 771-790. https://doi.org/10.1080/01495730600705406.
  31. Shen, H. S., and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  32. Sofiyev, A. H., Hui, D., Huseynov, S. E., Salamci, M. U., and Yuan, G. Q. (2016), "Stability and vibration of sandwich cylindrical shells containing a functionally graded material core with transverse shear stresses and rotary inertia effects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(14), 2376-2389. https://doi.org/10.1177/0954406215593570.
  33. Song, M. K., Kim, S. H., and Choi, C. K. (2006), "Enhanced finite element modeling for geometric non-linear analysis of cable-supported structures", Struct. Eng. Mech., 22(5), 575-598. https://doi.org/10.12989/sem.2006.22.5.575.
  34. Striz, A. G., Chen, W. L., and Bert, C. W. (1997), "Free vibration of plates by the high accuracy quadrature element method", J. Sound Vib., 202(5), 689-702. https://doi.org/10.1006/jsvi.1996.0846.
  35. Su, Z., Jin, G., Shi, S., Ye, T., and Jia, X. (2014a), "A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions", J. Mech. Sci., 80, 62-80. https://doi.org/10.1016/j.ijmecsci.2014.01.002.
  36. Su, Z., Jin, G., Shi, S., and Ye, T. (2014b), "A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints", Compos. Struct., 111, 271-284. https://doi.org/10.1016/j.compstruct.2014.01.006
  37. Su, Z., Jin, G., and Ye, T. (2014c), "Free vibration analysis of moderately thick functionally graded open shells with general boundary conditions", Compos. Struct., 117, 169-186. https://doi.org/10.1016/j.compstruct.2014.01.006.
  38. Thomas, B., and Roy, T. (2016), "Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures", Acta Mechanica, 227(2), 581-599. https://doi.org/10.1007/s00707-015-1479-z.
  39. Torabi, J., and Ansari, R. (2018), "Thermally induced mechanical analysis of temperature-dependent FG-CNTRC conical shells", Struct. Eng. Mech., 68(3), 313-323. http://dx.doi.org/10.12989/sem.2018.68.3.313.
  40. Torabi, J., and Ansari, R. (2018), "A higher-order isoparametric superelement for free vibration analysis of functionally graded shells of revolution", Thin-Walled Struct., 133, 169-179. https://doi.org/10.1016/j.tws.2018.09.040.
  41. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Methods Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  42. Wang, Q., Pang, F., Qin, B., and Liang, Q. (2018), "A unified formulation for free vibration of functionally graded carbon nanotube reinforced composite spherical panels and shells of revolution with general elastic restraints by means of the Rayleigh-Ritz method", Polymer Compos., 39(S2), E924-E944. https://doi.org/10.1002/pc.24339.
  43. Wu, Y., Xing, Y., and Liu, B. (2018), "Analysis of isotropic and composite laminated plates and shells using a differential quadrature hierarchical finite element method", Compos. Struct., 205, 11-25. https://doi.org/10.1016/j.compstruct.2018.08.095
  44. Xie, X., Zheng, H., and Jin, G. (2015), "Free vibration of four-parameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions", Compos. Part B Eng., 77, 59-73. https://doi.org/10.1016/j.compositesb.2015.03.016.
  45. Ye, T., Jin, G., and Su, Z. (2014), "Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions", Compos. Struct., 116, 571-588. https://doi.org/10.1016/j.compstruct.2014.05.046.