Structural Engineering and Mechanics

  • 제72권1호
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  • Pages.131-139
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  • 2019
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Static analysis of monoclinic plates via a three-dimensional model using differential quadrature method

  • Bahrami, Kourosh (Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University) ;
  • Afsari, Ahmad (Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University) ;
  • Janghorban, Maziar (Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University) ;
  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
  • 투고 : 2019.03.12
  • 심사 : 2019.05.17
  • 발행 : 2019.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

According to the properties of monoclinic materials, the normal and shear stresses are depending on both normal and shear strains. In the current investigation, the static analysis of monoclinic plates based on three dimensional elasticity theory is investigated. New governing equations and boundary conditions are derived for monoclinic plates and the Differential Quadrature Method (DQM) is used to solve the static problem. In our method of solution, no approximation is used and the DQM is adopted in all directions. By showing the differences between our results and the results for especially orthotropic plates, one can find that it is worth to investigate the monoclinic plates to have more accurate results.

키워드

참고문헌

  1. Amar, L.H.H., Kaci, A. and Tounsi, A. (2017), "On the sizedependent behavior of functionally graded micro-beams with porosities", Struct. Eng. Mech., 64(5), 527-541. https://doi.org/10.12989/sem.2017.64.5.527.
  2. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  3. Bacciocchi, M., Eisenberger, M., Fantuzzi, N., Tornabene, F. and Viola, E. (2016), "Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method", Compos. Struct., 156, 218-237. https://doi.org/10.1016/j.compstruct.2015.12.004.
  4. Barati, M.R. (2017), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/sem.2017.64.6.683.
  5. Batra, R., Qian, L. and Chen, L. (2004), "Natural frequencies of thick square plates made of orthotropic, trigonal, monoclinic, hexagonal and triclinic materials", J. Sound Vib., 270(4-5), 1074-1086. https://doi.org/10.1016/S0022-460X(03)00625-4.
  6. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  7. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397.
  8. Chaudhuri, R.A. (2012), "Three-dimensional singular stress/residual stress fields at crack/anticrack fronts in monoclinic plates under antiplane shear loading", Eng. Fracture Mech., 87, 16-35. https://doi.org/10.1016/j.engfracmech.2011.12.003.
  9. Dash, S., Mehar, K., Sharma, N., Mahapatra, T. R. and Panda, S. K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech., 68(6), 721-733. https://doi.org/10.12989/sem.2018.68.6.721.
  10. Ebrahimi, F. and Barati, M. R. (2018), "Wave propagation analysis of smart strain gradient piezo-magneto-elastic nonlocal beams", Struct. Eng. Mech., 66(2), 237-248. https://doi.org/10.12989/sem.2018.66.2.237.
  11. Ferreira, A. and Batra, R. (2005), "Natural frequencies of orthotropic, monoclinic and hexagonal plates by a meshless method", J. Sound Vib., 285(3), 734-742. https://doi.org/10.1016/j.jsv.2004.10.025.
  12. Ferreira, A., Fasshauer, G. and Batra, R. (2009), "Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method", J. Sound Vib., 319(3-5), 984-992. https://doi.org/10.1016/j.jsv.2008.06.034.
  13. Ghayesh, M. H. (2019), "Mechanics of viscoelastic functionally graded microcantilevers", Europe J. Mech. A Solids, 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001.
  14. Ghayesh, M. H., Farokhi, H. and Farajpour, A. (2019), "Global dynamics of fluid conveying nanotubes", J. Eng. Sci., 135, 37-57. https://doi.org/10.1016/j.ijengsci.2018.11.003.
  15. Ghayesh, M. H., Farokhi, H., Gholipour, A. and Tavallaeinejad, M. (2017), "Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams", J. Eng. Sci., 120, 51-62. https://doi.org/10.1016/j.ijengsci.2017.03.010.
  16. Ghugal, Y. M. and Sayyad, A. S. (2010), "A static flexure of thick isotropic plates using trigonometric shear deformation theory", 2(1), 79-90.
  17. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115.
  18. Janghorban, M. (2011), "Static and free vibration analysis of carbon nano wires based on Timoshenko beam theory using differential quadrature method", Latin American J Solids Struct., 8(4), 463-472. http://doi.org/10.1590/S1679-78252011000400006.
  19. Kaghazian, A., Hajnayeb, A. and Foruzande, H. (2017), "Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory", Struct. Eng. Mech., 61 (5), 617-624. https://doi.org/10.12989/sem.2017.61.5.617.
  20. Karami, B. and Janghorban, M. (2019a), "Characteristics of elastic waves in radial direction of anisotropic solid sphere, a new closed-form solution", Europe J. Mech. A Solids, 76, 36-45. https://doi.org/10.1016/j.euromechsol.2019.03.008.
  21. Karami, B. and Janghorban, M. (2019b), "On the dynamics of porous nanotubes with variable material properties and variable thickness", J. Eng. Sci., 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.
  22. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.
  23. Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., https://doi.org/10.1007/s00366-018-0664-9.
  24. Karami, B., Janghorban, M. and Tounsi, A. (2018b), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Sturct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  25. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin Wall Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  26. Karami, B., janghorban, M. and Tounsi, A. (2019a), "On exact wave propagation analysis of triclinic material using threedimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.
  27. Karami, B., janghorban, M. and Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  28. Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., 7(1), 51-61. https://doi.org/10.12989/anr.2019.7.1.051.
  29. Karami, B. and Shahsavari, D. (2019), "Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers", Smart Struct. Syst., 23(3), 215-225. https://doi.org/10.12989/sss.2019.23.3.215.
  30. Karami, B., shahsavari, D., janghorban, M. and Li, L. (2019c), "Influence of homogenization schemes on vibration of functionally graded curved microbeams", Compos. Struct., 216, 67-79. https://doi.org/10.1016/j.compstruct.2019.02.089.
  31. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019d), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  32. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2019e), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 233(6), 2149-2169. https://doi.org/10.1177/0954406218781680.
  33. Khetir, H., Bouiadjra, M. B., Houari, M. S. A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.
  34. Kirchoff, G. (1850), "Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe", Journal fur die reine und angewandte Mathematik (Crelle's Journal), 40, 51-88.
  35. Krishna Murty, A. (1986), "Toward a consistent plate theory", AIAA J., 24(6), 1047-1048. https://doi.org/10.2514/3.9388.
  36. Kumar, R. and Tomar, S. (2006), "Free transverse vibrations of monoclinic rectangular plates with continuously varying thickness and density", J. Appl. Mech., 11(4), 881.
  37. Lu, L., Guo, X. and Zhao, J. (2017), "A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms", J. Eng. Sci., 119, 265-277. https://doi.org/10.1016/j.ijengsci.2017.06.024.
  38. Lurie, S. and Solyaev, Y. (2018), "Revisiting bending theories of elastic gradient beams", J. Eng. Sci., 126, 1-21. https://doi.org/10.1016/j.ijengsci.2018.01.002.
  39. Malekzadeh, P. (2007), "A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates", Thin Wall Struct., 45(2), 237-250. https://doi.org/10.1016/j.tws.2007.01.011.
  40. Mindlin, R. D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  41. Rajasekaran, S. and Khaniki, H. B. (2017), "Bending, buckling and vibration of small-scale tapered beams", J. Eng. Sci., 120, 172-188. https://doi.org/10.1016/j.ijengsci.2017.08.005.
  42. 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.
  43. Shahsavari, D., Karami, B. and Li, L. (2018), "Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model", Comptes Rendus Mécanique, 346(12), 1216-1232. https://doi.org/10.1016/j.crme.2018.08.011.
  44. She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H. (2018), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., 66(6), 729-736. https://doi.org/10.12989/SEM.2018.66.6.729
  45. She, G.L., Ren, Y.R. and Yan, K.M. (2019a), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010.
  46. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.-S. (2019b), "On nonlinear bending behavior of FG porous curved nanotubes", J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  47. Singhal, P. and Bindal, G. (2012), "Generalised differential quadrature method in the study of free vibration analysis of monoclinic rectangular plates", American J. Comput. Appl. Math., 2(4), 166-173. https://doi.org/10.5923/j.ajcam.20120204.05
  48. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., 63 (3), 401-415. https://doi.org/10.12989/sem.2017.63.3.401.
  49. Soldatos, K. P. (2004), "Complex potential formalisms for bending of inhomogeneous monoclinic plates including transverse shear deformation", J. Mech. Physics Solids, 52 (2), 341-357. https://doi.org/10.1016/S0022-5096(03)00102-9
  50. Tornabene, F., Fantuzzi, N., Viola, E. and Carrera, E. (2014), "Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method", Compos. Struct., 107, 675-697. https://doi.org/10.1016/j.compstruct.2013.08.038.
  51. Yousfi, M., Atmane, H. A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66 (3), 353-368. https://doi.org/10.12989/SEM.2018.66.3.353
  52. Zemri, A., Houari, M. S. A., Bousahla, A. A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54 (4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693.