Advances in materials Research

  • 제11권4호
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  • Pages.279-298
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  • 2022
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  • 2234-0912(pISSN)
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  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
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Buckling and bending analyses of a sandwich beam based on nonlocal stress-strain elasticity theory with porous core and functionally graded facesheets

  • Mehdi, Mohammadimehr (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2021.09.12
  • 심사 : 2022.01.20
  • 발행 : 2022.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.

키워드

과제정보

The authors would like to thank the referees for their valuable comments. Also, they are thankful to thank the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work by Grant No. 891238/29.

참고문헌

  1. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070.
  2. Alavi, S.H. and Eipakchi, H. (2019), "Geometry and load effects on transient response of a VFGM annular plate: An analytical approach", Struct. Eng. Mech., Int. J., 70(2), 179-197. https://doi.org/10.12989/sem.2019.70.2.179.
  3. Altekin, M. (2020), "Combined effects of material properties and boundary conditions on the large deflection bending analysis of circular plates on a nonlinear elastic foundation", Comput. Concrete, Int. J., 25(6), 537-549. https://doi.org/10.12989/cac.2020.25.6.537.
  4. Anh, V.T.T., Bich, D.H. and Duc, N.D. (2015), "Nonlinear buckling analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads", Eur. J. Mech. - A/Solids, 50, 28-38. https://doi.org/10.1016/j.euromechsol.2014.10.004.
  5. Anitescu, C., Atroshchenko, E., Alajlan, N. and Rabczuk, T. (2019), "Artificial neural network methods for the solution of second order boundary value problems", Comput. Mater. Continua, 59(1), 345-359. https://doi.org/10.32604/cmc.2019.06641.
  6. Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V. and Sahmani, S. (2013), "Size-dependent bending, buckling and free vibration of functionally graded Timoshenko micro beams based on the most general strain gradient theory", Compos. Struct., 100, 385-397. https://doi.org/10.1016/j.compstruct.2012.12.048.
  7. Babaei, H. and Eslami, M.R. (2019), "Thermally induced large deflection of FGM shallow micro-arches with integrated surface piezoelectric layers based on modified couple stress theory", Acta Mechanica, 230, 2363-2384. https://doi.org/10.1007/s00707-019-02384-0.
  8. Bahaadini, R. and Saidi, A.R. (2018), "Aeroelastic analysis of functionally graded rotating blades reinforced with graphene nanoplatelets in supersonic flow", Aerosp. Sci. Technol., 80, 381-391. https://doi.org/10.1016/j.ast.2018.06.035.
  9. Bendenia, N., Zidour, M., Bousahla, A.N., Bourada, F., Tounsi, A., Benrahou, K.H., Bedia, E.A.A., Mahmoud, S.R. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation", Comput. Concrete, Int. J., 26(3), 213-226. https://doi.org/10.12989/cac.2020.26.3.213.
  10. Canbay, C.A., Karaduman, O., Ibrahim, P.A. and Ozkul, I. (2021), "Thermostructural shape memory effect observations of ductile Cu-Al-Mn smart alloy", Adv. Mater. Res., Int. J., 10(1), 45-56. https://doi.org/10.12989/amr.2021.10.1.045.
  11. Chen, D., Kitipornchai, S. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  12. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermo-mechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", J. Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  13. Daikh, A.A., Bensaid, I., Bachiri, A., Houari, M.S.A., Tounsi, A. and Merzouki, T. (2020), "On static bending of multilayered carbon nanotube-reinforced composite plates", Comput. Concrete, Int. J., 26(2), 137-150. https://doi.org/10.12989/cac.2020.26.2.137.
  14. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 102, 306-314. https://doi.org/10.1016/j.compstruct.2012.11.017.
  15. Duc, N.D. (2014), Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi, Vietnam.
  16. Duc, N.D. (2016a), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. - A/Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004.
  17. Duc, N.D. (2016b), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric Sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266.
  18. Duc, N.D. and Quan, T.Q. (2015), "Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation", J. Vib. Control, 21(7), 1340-1362. https://doi.org/10.1177/1077546313494114.
  19. Duc, N.D., Cong, P.H., Anh, V.M., Quang, V.D., Tran, P., Tuan, N.D. and Thinh, N.H. (2015), "Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment", Compos. Struct., 132, 597-609. https://doi.org/10.1016/j.compstruct.2015.05.072.
  20. Duc, N.D., Bich, D.H. and Cong, P.H. (2016c), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Thermal Stresses, 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194.
  21. Duc, N.D., Nguyen, P.D. and Khoa, N.D. (2017a), "Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin-Wall. Struct., 117, 178-189. https://doi.org/10.1016/j.tws.2017.04.013.
  22. Duc, N.D., Tuan, N.D., Tran, P. and Quan, T.Q. (2017b), "Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads", Mech. Adv. Mater. Struct., 24(4), 318-329. https://doi.org/10.1080/15376494.2016.1142024.
  23. Duc, N.D., Tuan, N.D., Tran, P. and Quan, T.Q. (2017c), "Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads", Mech. Adv. Mater. Struct., 24(4), 318-329. https://doi.org/10.1080/15376494.2016.1142024.
  24. Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018a), "Nonlinear dynamic response of FGM porous plates on elastic foundation subjected to thermal and mechanical loads using the first order shear deformation theory", J. Appl. Computat. Mech., 4(4), 245-259. https://doi.org/10.22055/jacm.2018.23219.1151.
  25. Duc, N.D., Seung-Eock, K. and Chan, D.Q. (2018b), "Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT", J. Thermal Stresses, 41(3), 331-365. https://doi.org/10.1080/01495739.2017.1398623.
  26. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008.
  27. Ebrahimi, F., Seyfi, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., Int. J., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  28. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Mathe. Modell., 40(5-6), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  29. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  30. Eringen, A.C. (1983), "On direrential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  31. Gao, X.-L. (2015), "A new Timoshenko beam model incorporating microstructure and surface energy effects", Acta Mechanica, 226, 457-474. https://doi.org/10.1007/s00707-014-1189-y.
  32. Ghayesh, M.H., Farajpour, A. and Farokhi, H. (2020), "Effect of flow pulsations on chaos in nanotubes using nonlocal strain gradient theory", Commun. Nonlinear Sci. Numer. Simul., 83, 105090. https://doi.org/10.1016/j.cnsns.2019.105090.
  33. Ghorbanpour, A.A., Shokravi, M., Mohammadimehr, M. (2009), "Buckling analysis of a double-walled carbon nanotube embedded in an elastic medium using the energy method", J. Solid Mech., 1(4), 289-299.
  34. Guo, H., Zhuang, X. and Rabczuk, T. (2019), "A deep collocation method for the bending analysis of Kirchhoff plate", Comput. Mater. Continua, 59(2), 433-456. https://doi.org/ 10.32604/cmc.2019.06660.
  35. Hadji, L. and Bernard, F. (2020), "Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation", Adv. Mater. Res., Int. J., 9(1), 63-98. https://doi.org/10.12989/amr.2020.9.1.063.
  36. Jomehzadeh, E., Noori, H.R. and Saidi, A.R. (2011), "The size-dependent vibration analysis of micro-plates based on a modified couple stress theory", Physica E: Low-dimens. Syst. Nanostruct., 43(4), 877-883. https://doi.org/10.1016/j.physe.2010.11.005.
  37. Karami, B. and Shahsavari, D. (2020), "On the forced resonant vibration analysis of functionally graded polymer composite doubly-curved nanoshells reinforced with graphene-nanoplatelets", Comput. Methods Appl. Mech. Eng., 359, 112767. https://doi.org/10.1016/j.cma.2019.112767.
  38. Lam, D., Yang, F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  39. Li, Q., Wu, D., Gao, W. Tin-Loi, F. (2020), "Size-dependent instability of organic solar cell resting on Winkler-Pasternak elastic foundation based on the modified strain gradient theory", Int. J. Mech. Sci., 177, 105306. https://doi.org/10.1016/j.ijmecsci.2019.105306.
  40. Ma, H.M., Gao, X.-L. and Reddy, J.N. (2008), "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007.
  41. Merzouki, T., Ahmed, H.M.S., Bessaim, A., Haboussi, M., Dimitri, R. and Tornabene, F. (2022), "Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory", Mathe. Mech. Solids, 27(1), 66-92. https://doi.org/10.1177/10812865211011759.
  42. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431.
  43. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2010), "Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory", J. Mech. Sci. Technol., 24(6), 1289-1299. https://doi.org/10.1007/s12206-010-0331-6.
  44. Mohammadimehr, M., Nejad, E.S. and Mehrabi, M. (2018), "Buckling and vibration analyses of MGSGT double-bonded micro composite sandwich SSDT plates reinforced by CNTs and BNNTs with isotropic foam & flexible transversely orthotropic cores", Struct. Eng. Mech., Int. J., 65(4), 491-504. https://doi.org/10.12989/sem.2018.65.4.491.
  45. Murmu, T. and Adhikari, S. (2010), "Nonlocal transverse vibration of double-nanobeam-systems", J. Appl. Phys., 08, 083514. https://doi.org/10.1063/1.3496627.
  46. Namayandeh, M.J., Mohammadimehr, M., Mehrabi, M. and Sadeghzadeh-Attar, A. (2020), "Temperature and thermal stress distributions in a hollow circular cylinder composed of anisotropic and isotropic materials", Adv. Mater. Res., Int. J., 9(1), 15-32. https://doi.org/10.12989/amr.2020.9.1.015.
  47. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93(12), 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028.
  48. Nejadi, M.M. and Mohammadimehr, M. (2020), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, Int. J., 25(3), 215-224. https://doi.org/10.12989/cac.2020.25.3.215.
  49. Nguyen, T.N., Ngo, T.D. and Nguyen-Xuan, H. (2017a), "A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation", Comput. Methods Appl. Mech. Eng., 326, 376-401. https://doi.org/10.1016/j.cma.2017.07.024.
  50. Nguyen, T.N., Thai, C.H., Luu, A.T., Nguyen-Xuan, H. and Lee, J. (2017b), "NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells", Comput. Methods Appl. Mech. Eng., 326, 376-401. https://doi.org/10.1016/j.cma.2019.01.011.
  51. Nguyen, L.B., Thai, C.H., Duong-Nguyen, N. and Nguyen-Xuan, H. (2021), "A size-dependent isogeometric approach for vibration analysis of FG piezoelectric porous microplates using modified strain gradient theory", Eng. Comput. https://link.springer.com/article/10.1007/s00366-021-01468-7.
  52. Nguyen-Thanh, V.M., Zhuang, X. and Rabczuk, T. (2020), "A deep energy method for finite deformation hyperelasticity", Eur. J. Mech. - A/Solids, 80, 103874. https://doi.org/10.1016/j.euromechsol.2019.103874
  53. Polizzotto, C. (2001), "Nonlocal elasticity and related variational principles", Int. J. Solids Struct., 38(42-43), 7359-7380. https://doi.org/10.1016/S0020-7683(01)00039-7.
  54. Pradhan, S.C. (2009), "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", Phys. Lett. A, 373(45), 4182-4188. https://doi.org/10.1016/j.physleta.2009.09.021.
  55. Rabia, B., Daouadji, T.H. and Abderezak, R. (2020), "Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis", Adv. Mater. Res., Int. J., 9(4), 265-287. https://doi.org/10.12989/amr.2020.9.4.265.
  56. Rahi, M.J., Firoozjaee, A.R. and Dehestani, M. (2021), "Simplified numerical method for nonlocal static and dynamic analysis of a graphene nanoplate", Adv. Mater. Res., Int. J., 10(1), 1-22. https://doi.org/10.12989/amr.2021.10.1.001.
  57. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  58. Ren, H., Zhuang, X. and Rabczuk, T. (2020a), "A higher order nonlocal operator method for solving partial differential equations", Comput. Methods Appl. Mech. Eng., 367, 113132. https://doi.org/10.1016/j.cma.2020.113132.
  59. Ren, H., Zhuang, X. and Rabczuk, T. (2020b), "A nonlocal operator method for solving partial differential equations", Comput. Methods Appl. Mech. Eng., 358, 112621. https://doi.org/10.1016/j.cma.2020.112621.
  60. Samaniego, E., Anitescu, C., Goswami, S., Nguyen-Thanh, V.M., Guo, H., Hamdia, K., Zhuang, X. and Rabczuk, T. (2020), "An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications", Comput. Methods Appl. Mech. Eng., 362, 112790. https://doi.org/10.1016/j.cma.2019.112790.
  61. Shooshtari, A. and Razavi, S. (2015), "Nonlinear vibration analysis of rectangular magneto-electro-elastic thin plates", J. Eng., 28, 139-147. https://doi.org/10.5829/idosi.ije.2015.28.01a.18.
  62. Thai, C.H., Ferreira, A.J.M. and Nguyen, H. (2018), "Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory", Compos. Struct., 192, 274-288. https://doi.org/10.1016/j.euromechsol.2018.07.012.
  63. Vu-Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Software, 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005.
  64. Wang, K.F. and Wang, B.L. (2011), "Vibration of nanoscale plates with surface energy via nonlocal elasticity", Phys. E: Low-dimens. Syst. Nanostruct., 44(2), 448-453. https://doi.org/10.1016/j.physe.2011.09.019.
  65. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  66. Yang, J., Jia, X.L. and Kitipornchai, S. (2008), "Pull-in instability of nano-switches using nonlocal elasticity theory", J. Phys. D: Appl. Phys., 41, 035103. https://doi.org/10.1088/0022-3727/41/3/035103.
  67. 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-thermomechanical loadings", Struct. Eng. Mech., Int. J., 70(3), 351-365. https://doi.org/10.12989/sem.2019.70.3.351.
  68. Yazdani, R. and Mohammadimehr, M. (2019), "Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution", Comput. Concrete, Int. J., 24(6), 499-511. https://doi.org/10.12989/cac.2019.24.6.499.
  69. Zenkour, A.M. and Sobhy, M. (2013), "Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler-Pasternak elastic substate medium", Phys. E: Low-dimens. Syst. Nanostruct., 53, 251-259. https://doi.org/10.1016/j.physe.2013.04.022.