Computers and Concrete

  • 제24권3호
  • /
  • Pages.185-192
  • /
  • 2019
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solution for buckling analysis of micro sandwich hollow circular plate

  • Mousavi, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Rostami, Rasoul (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2019.04.08
  • 심사 : 2019.06.17
  • 발행 : 2019.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the buckling of micro sandwich hollow circular plate is investigated with the consideration of the porous core and piezoelectric layer reinforced by functionally graded (FG)carbon nano-tube. For modeling the displacement field of sandwich hollow circular plate, the high-order shear deformation theory (HSDT) of plate and modified couple stress theory (MCST) are used. The governing differential equations of the system can be derived using the principle of minimum potential energy and Maxwell's equation that for solving these equations, the Ritz method is employed. The results of this research indicate the influence of various parameters such as porous coefficients, small length scale parameter, distribution of carbon nano-tube in piezoelectric layers and temperature on critical buckling load. The purpose of this research is to show the effect of physical parameters on the critical buckling load of micro sandwich plate and then optimize these parameters to design structures with the best efficiency. The results of this research can be used for optimization of micro-structures and manufacturing different structure in aircraft and aerospace.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. AkhavanAlavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech., A/Solid., 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  2. Arani, A.G., Amir, S., Shajari, A.R., Mozdianfard, M.R., Khoddami Maraghi, Z. and Mohammadimehr, M. (2012b), "Electro-thermal non-local vibration analysis of embedded DWBNNTs", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 226(5), 1410-1422. https://doi.org/10.1177/0954406211422619.
  3. Arani, A.G., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012a), "The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5.
  4. Arani, A.G., Mohammadimehr, M., Saidi, A.R., Shogaei, S. and Arefmanesh, A. (2011), "Thermal buckling analysis of doublewalled carbon nanotubes considering the small-scale length effect", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 225(1), 248-256. https://doi.org/10.1177/09544062JMES1975.
  5. Aydogdu, M. and Gul, U. (2018), "Buckling analysis of double nanofibers embedded in an elastic medium using doublet mechanics theory", Compos. Struct., 202, 355-363. https://doi.org/10.1016/j.compstruct.2018.02.015.
  6. Bui, T.Q., Do, T.V., Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T., Nguyen-Van, T., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B: Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  7. Bui, T.Q., Khosravifard, A., Zhang, Ch., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041.
  8. Chan, D.Q., Long, V.D. and Duc, N.D. (2019), "Nonlinear buckling and postbuckling of FGM shear-deformable truncated conical shells reinforced by FGM stiffeners", Mech. Compos. Mater., 54, 745-764. https://doi.org/10.1007/s11029-019-9780-x.
  9. Dinh Duc, N., Quoc Quan, T. and Dinh Khoa, N. (2017), "New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature", Aerosp. Sci. Technol., 71, 360-372. https://doi.org/10.1016/j.ast.2017.09.031.
  10. Do, T.V., Bui, T.Q., Yu, T.T., Pham, T.D. and Nguyena, C.T. (2017b), "Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment", J. Comput. Sci., 21, 164-181. https://doi.org/10.1016/j.jocs.2017.06.015.
  11. Do, T.V., Nguyen, D.K., Nguyen, D.D., Doan, D.H. and Bui, T.Q. (2017a), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin Wall. Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022.
  12. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., 7(2), 109-123. https://doi.org/10.12989/anr.2019.7.2.109.
  13. Eslami, M.R., Mojahedin, A., Jabbari, M. and Khorshidvand, A.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin Wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008.
  14. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38, 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X.
  15. Frikha, A., Zghala, S. and Dammak, F. (2018), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Technol., 78, 438-451. https://doi.org/10.1016/j.ast.2018.04.048.
  16. Hajmohammad, M.H., Zarei, M.S., Sepehr, M. and Abtahid, N. (2018), "Bending and buckling analysis of functionally graded annular microplate integrated with piezoelectric layers based on layerwise theory using DQM", Aerosp. Sci. Technol., 79, 679-688. https://doi.org/10.1016/j.ast.2018.05.055.
  17. Jafarian Arani, A. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. http://dx.doi.org/10.12989/cac.2016.17.5.567.
  18. Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates", AIAA J., 4(1), 162-169. https://doi.org/10.2514/2.1626.
  19. Karamanli, A. and Aydogdu, M. (2019), "Buckling of laminated composite and sandwich beams due to axially varying in-plane loads", Compos. Struct., 210, 391-408. https://doi.org/10.1016/j.compstruct.2018.11.067.
  20. Kiani, Y. (2016), "Shear buckling of FG-CNT reinforced composite plates using Chebyshev-Ritz method", Compos. Part B, 105, 176-187. https://doi.org/10.1016/j.compositesb.2016.09.001.
  21. Koukouselis, A. and Mistakidis, E. (2015), "Numerical investigation of the buckling behavior of thin ferrocement stiffened plates", Comput. Concrete, 15(3), 391-410. https://doi.org/10.12989/cac.2015.15.3.391.
  22. Liu, S., Yu, T. and Bui, T.Q. (2017), "Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis", Eur. J Mech. A/Solid., 66, 446-458. https://doi.org/10.1016/j.euromechsol.2017.08.008.
  23. Liu, S., Yu, T., Lich, L.V., Yin, S. and Bui, T.Q. (2018), "Size effect on cracked functional composite micro-plates by an XIGA-based effective approach", Meccanica, 53, 2637-2658. https://doi.org/10.1007/s11012-018-0848-9.
  24. Liu, S., Yu, T., Lich, L.V., Yin, S. and Bui, T.Q. (2019), "Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis", Comput. Struct., 212,173-187. https://doi.org/10.1016/j.compstruc.2018.10.009.
  25. Ma, L.S. and Wang, T.J. (2003), "Nonlinear bending and postbuckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Solid. Struct., 40, 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5.
  26. Ma, L.S. and Wang, T.J. (2004), "Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory", Int. J. Solid. Struct., 41, 85-101. https://doi.org/10.1016/j.ijsolstr.2003.09.008.
  27. Mohammadimehr, M. and Rostami, R. (2018), "Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields", Appl. Math. Mech., 39(2), 219-240. https://doi.org/10.1007/s10483-018-2301-6.
  28. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Alavi, S.M.A., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018b), "Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., 29(3), 405-422. https://doi.org/10.12989/scs.2018.29.3.405.
  29. Mohammadimehr, M., Monajemi, A.A. and Moradi, M. (2015), "Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM", J. Mech. Sci. Technol., 29(6), 2297-2305. https://doi.org/10.1007/s12206-015-0522-2.
  30. Mohammadimehr, M., Rostami, R. and Arefi, M. (2016), "Electroelastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., 20, 513-544. https://doi.org/10.12989/scs.2016.20.3.513.
  31. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2011), "Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 225(2), 498-506. https://doi.org/10.1177/2041298310392861.
  32. Mohammadimehr, M., Shabani, Nejad, E. and Mehrabi, M. (2018a), "Buckling and vibration analyses of MGSGT doublebonded micro composite sandwich SSDT plates reinforced by CNTs and BNNTs with isotropic foam & flexible transversely orthotropic cores", Struct. Eng. Mech., 65(4), 491-504. https://doi.org/10.12989/sem.2018.65.4.491.
  33. Nguyen-Xuan, H., Thai, C.H. and Nguyen-Thoi, T. (2013), "Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory", Compos. Part B, 55, 558-574. https://doi.org/10.1016/j.compositesb.2013.06.044.
  34. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  35. Rostami, R., Irani Rahaghi, M. and Mohammadimehr, M. (2019), "Vibration control of the rotating sandwich cylindrical shell considering functionally graded core and functionally graded magneto-electroelastic layers by using differential quadrature method", J. Sandw. Struct. Mater., 1099636218824139. https://doi.org/10.1177/1099636218824139.
  36. Rostami, R., Mohammadimehr, M., Ghannad, M. and Jalali, A. (2018), "Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties", Theo. Appl. Mech. Lett., 8, 97-108. https://doi.org/10.1016/j.taml.2018.02.005.
  37. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010.
  38. Safari Bilouei, B., Kolahchi, R. and Rabani Bidgoli M. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053.
  39. Sahmani, S., Ansari, R., Gholami, R. and Darvizeh, A. (2013), "Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory", Compos. Part B, 51, 44-53. https://doi.org/10.1016/j.compositesb.2013.02.037.
  40. Saidi A.R., Rasouli, A. and Sahraee, S. (2009), "Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory", Compos. Struct., 89, 110-119. https://doi.org/10.1016/j.compstruct.2008.07.003.
  41. Shen, H. and Xiang, Y. (2012), "Nonlinear vibration of nanotubereinforced composite cylindrical shells in thermal environments", Comput. Meth. Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  42. Sobhy, M. and Zenkour, A.M. (2018), "Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate", Compos. Part B, 154, 492-506. https://doi.org/10.1016/j.compositesb.2018.09.011.
  43. Sobhy, M. and Zenkour, A.M. (2019), "Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory", Compos. Struct., 220, 289-303. https://doi.org/10.1016/j.compstruct.2019.03.096.
  44. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198 (37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  45. Tornabene, F. and Reddy, J.N. (2013), "FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundation: A GDQ solution for static analysis with a posteriori stress and strain recovery", J. Ind. Inst. Sci., 93(4), 635-688.
  46. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. B Eng., 89, 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016.
  47. Tornabene, F., Fantuzzi, N., Viola, E. and Batra, R.C. (2015), "Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory", Compos. Struct., 119, 67-89. https://doi.org/10.1016/j.compstruct.2014.08.005.
  48. Tornabene, F., Liverani, A. and Caligiana, G. (2011), "FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations", Int. J. Mech. Sci., 53, 446-470. https://doi.org/10.1016/j.ijmecsci.2011.03.007.
  49. 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.
  50. 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.
  51. Yazdani, R., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of Cooper-Naghdi micro saturated porous sandwich cylindrical shells with reinforced CNT face sheets under magneto-hydro-thermo-mechanical loadings", Struct. Eng. Mech., 70(3), 351-365. https://doi.org/10.12989/sem.2019.70.3.351.
  52. Yin, S., Yu, T., Bui, T.Q., Zheng, X. and Tanaka, S. (2016), "Inplane material inhomogeneity of functionally graded plates: A higher-order shear deformation plate isogeometric analysis", Compos. Part B: Eng., 91, 273-284. https://doi.org/10.1016/j.compositesb.2016.09.008.
  53. Yu, T., Hu, H., Zhang, J. and Bui, T.Q. (2019), "Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory", Thin Wall. Struct., 138,1-14. https://doi.org/10.1016/j.tws.2018.12.006.
  54. Yu, T., Zhanga, J., Hua, H. and Bui, T.Q. (2019), "A novel sizedependent quasi-3D isogeometric beam model for twodirectional FG microbeams analysis", Compos. Struct., 211, 76-88. https://doi.org/10.1016/j.compstruct.2018.12.014.
  55. Zghal, S., Frikha, A. and Dammak, F. (2018), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B, 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037.

피인용 문헌

  1. Non-local orthotropic elastic shell model for vibration analysis of protein microtubules vol.25, pp.3, 2019, https://doi.org/10.12989/cac.2020.25.3.245
  2. Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method vol.27, pp.1, 2019, https://doi.org/10.12989/cac.2021.27.1.073
  3. Strength performance with buckling analysis of Intermediate filaments by consideration nonlocal parameters vol.28, pp.1, 2021, https://doi.org/10.12989/cac.2021.28.1.069