Advances in concrete construction

  • 제11권4호
  • /
  • Pages.315-321
  • /
  • 2021
  • /
  • 2287-5301(pISSN)
  • /
  • 2287-531X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An analytical solution for equations and the dynamical behavior of the orthotropic elastic material

  • Ramady, Ahmed (GRC Department, Faculty of Applied studies, King Abdulaziz University) ;
  • Atia, H.A. (Mathematics Department, Arts - Rabigh& College of Sciences, King Abdulaziz University) ;
  • Mahmoud, S.R. (GRC Department, Faculty of Applied studies, King Abdulaziz University)
  • 투고 : 2020.03.05
  • 심사 : 2021.03.10
  • 발행 : 2021.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, an analytical solution of the dynamical behavior in an orthotropic non-homogeneity elastic material using for elastodynamics equations is investigated. The effects of the magnetic field, the initial stress, and the non-homogeneity on the radial displacement and the corresponding stresses in an orthotropic material are investigated. The analytical solution for the elastodynamic equations has solved regarding displacements. The variation of the stresses, the displacement, and the perturbation magnetic field have shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, and the non-homogeneity. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity.

키워드

참고문헌

  1. Abd-Alla, A.M. and Mahmoud, S.R. (2010), "Magnetothermoelastic problem in rotating non-homogeneous orthotropic hollow cylindrical under the hyperbolic heat conduction model", Meccanica, 45(4), 451-462. https://doi.org/10.1007/s11012-009-9261-8.
  2. Abd-Alla, A.M. and Mahmoud, S.R. (2012), "Analytical solution of wave propagation in non-homogeneous orthotropic rotating elastic media", J. Mech. Sci. Tech., 26(3), 917-926. https://doi.org/10.1007/s12206-011-1241-y.
  3. Abd-Alla, A.M. and Mahmoud, S.R. (2013), "On problem of radial vibrations in non- homogeneity isotropic cylinder under influence of initial stress and magnetic field", J. Vib. Control, 19(9), 1283-1293. https://doi.org/10.1177/1077546312441043.
  4. Abd-Alla, A.M., Mahmoud, S.R. and AL-Shehri, N.A. (2011b), "Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material", Appl. Math. Comput., 217(22), 8914- 8922. https://doi.org/10.1016/j.amc.2011.03.077.
  5. Abd-Alla, A.M., Mahmoud, S.R., Abo-Dahab, S.M. and Helmi, M.I.R. (2011a), "Propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field", Appl. Math. Comput., 217(9), 4321-4332. https://doi.org/10.1016/j.amc.2010.10.029.
  6. Abd-Alla, A.M., Yahya, G.A. and Mahmoud, S.R. (2013), "Radial vibrations in a non- homogeneous orthotropic elastic hollow sphere subjected to rotation", J. Comput. Theor. Nanosci., 10(2), 455-463. https://doi.org/10.1166/jctn.2013.2718.
  7. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  8. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175.
  9. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  10. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  11. Argatov, I.I. (2005), "Approximate solution of the axisymmetric contact problem for an elastic sphere", J. Appl. Math. Mech., 69(2), 275-286. https://doi.org/10.1016/j.jappmathmech.2005.03.014.
  12. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  13. Azmi, M., Kolahchi, R. and Bidgoli, M.R. (2019), "Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load", Adv. Concrete Constr., 7(1), 51-63. https://doi.org/10.12989/acc.2019.7.1.051.
  14. Bahrami, A., Ilkhani, M.R. and Bahrami, M.N. (2013), "Wave propagation technique for free vibration analysis of annular circular and sectorial membranes", J. Vib. Control, 21(9), 1866-1872. https://doi.org/10.1177/1077546313505123.
  15. Barati, M.R. (2019), "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.
  16. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.
  17. Cai, J., Lin, F., Lee, Y.T., Qian, K. and Seah, H.S. (2017), "Modeling and dynamics simulation for deformable objects of orthotropic materials", Visual Comput., 33, 1307-1318. https://doi.org/10.1007/s00371-016-1221-4.
  18. David, S.A., Balthazar, J.M., Julio, B.H.S. and Oliveira, C. (2012), "The fractional and nonlinear magneto-flexible rod", J. Phys.: Conf. Ser., 382, https://www.doi.org/10.1088/1742-6596/382/1/012056.
  19. Diana, V. and Casolo, S. (2019), "A full orthotropic micropolar peridynamic formulation for linearly elastic solids", Int. J. Mech. Sci., 160, 140-155. https://doi.org/10.1016/j.ijmecsci.2019.06.036.
  20. Dutta, G., Panda, S.K., Mahapatra, T.R. et al. (2017), "ElectroMagneto-Elastic response of laminated composite plate: A finite element approach", Int. J. Appl. Comput. Math., 3, 2573-2592. https://doi.org/10.1007/s40819-016-0256-6.
  21. Guenaneche, B., Benyoucef, S., Tounsi, A. and Adda Bedia, E. A. (2019), "Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation", Adv. Concrete Constr., 7(3), 151-166. https://doi.org/10.12989/acc.2019.7.3.151.
  22. Huang, C.S. and Ho, K.H. (2004), "An analytical solution for vibrations of a polarly orthotropic Mindlin sectorial plate with simply supported radial edges", J. Sound Vib., 273, 277-294. https://doi.org/10.1016/S0022-460X(03)00501-7.
  23. Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B: Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  24. Katariya, P. V., Panda, S. K., Hirwani, C. K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595.
  25. Kumar, A., Stickland, A.D. and Scales, P.J. (2012), "Viscoelasticity of coagulated alumina suspensions", Korea-Australia Rheology J., 24(2), 105-111. https://doi.org/10.1007/s13367-012-0012-3.
  26. Mahmoud, S.R. (2013), "On problem of Shear waves in a magneto-elastic half-space of initially stressed a non-homogeneous anisotropic material under influence of rotation", Int. J. Mech. Sci., 77(12), 269-276. https://doi.org/10.1016/j.ijmecsci.2013.10.004.
  27. Mahmoud, S.R. (2016), "An analytical solution for effect of initial stress, rotation, magnetic field and a periodic loading in thermoviscoelastic homogeneity medium with a spherical cavity", Mech. Adv. Mater. Struct., 23(1), 1-7. https://doi.org/10.1080/15376494.2014.884659.
  28. Mahmoud, S.R., Abd-Alla, A.M. and AL-Shehri, N.A. (2011a), "Effect of the rotation on plane vibrations in a transversely isotropic infinite hollow cylinder", Int. J. Modern Phys. B, 25, 3513-3528. https://doi.org/10.1142/S0217979211100928.
  29. Mahmoud, S.R., Abd-Alla, A.M. and Matooka, B.R. (2011b), "Effect of the rotation on wave motion through cylindrical bore in a micropolar porous cubic crystal", Int. J. Modern Phys. B, 25, 2713-2728. https://doi.org/10.1142/S0217979211101739.
  30. Malekzadeh, P. (2008), "Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT", Compos. Struct., 83, 189-200. https://doi.org/10.1016/j.compstruct.2007.04.007.
  31. Mehar, K., Mishra, P.K. and Panda, S.K. (2020), "Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure", Mech. Adv. Mater. Struct., 1-13 https://doi.org/10.1080/15376494.2020.1725193.
  32. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002.
  33. Othman, M. and Fekry, M. (2018), "Effect of rotation and gravity on generalized thermo- viscoelastic medium with voids", Multidisc. Model. Mater. Struct., 14(2), 322-338. https://doi.org/10.1108/MMMS-08-2017-0082.
  34. Panda, S.K. and Singh, B.N. (2013a), "Nonlinear finite element analysis of thermal post- buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007.
  35. Panda, S.K. and Singh, B.N. (2013b), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097.
  36. Panda, S.K. and Singh, B.N. (2013c), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlin. Dyn., 74, 395-418. https://doi.org/10.1007/s11071-013-0978-5.
  37. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056.
  38. Ramady, A., Mahmoud, S.R. and Atia, H.A. (2020), "A theoretical approach in 2d-space with applications of the periodic wave solutions in the elastic body", Membr. Water Treatment, 11(4), 295-30. https://doi.org/10.12989/mwt.2020.11.4.295.
  39. Singh, B.N. and Panda, S.K. (2015), "Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers", Smart Struct. Syst., 16(5), 853-872. DOI: http://dx.doi.org/10.12989/sss.2015.16.5.853.
  40. Singh, B.N., Mahapatra, T.R. and Panda, S.K. (2016a), "Nonlinear flexural analysis of single/doubly curved smart composite shell panels integrated with PFRC actuator", Eur. J. Mech.-A/Solid., 60, 300-314. https://doi.org/10.1016/j.euromechsol.2016.08.006.
  41. Singh, B.N., Mahapatra, T.R. and Panda, S.K. (2016b), "Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator", Compos. Struct., 157, 121-130. https://doi.org/10.1016/j.compstruct.2016.08.020.
  42. Singh, V.K., Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mehar, K. (2019), "Numerical and experimental nonlinear dynamic response reduction of smart composite curved structure using collocation and non-collocation configuration", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 233(5), 1601-1619. https://doi.org/10.1177/0954406218774362.
  43. Sofiyev, A.H. and Karaca, Z. (2009), "The vibration and buckling of laminated non- homogeneous orthotropic conical shells subjected to external pressure", Eur. J. Mech. A/Solid., 28, 317-328. https://doi.org/10.1016/j.euromechsol.2008.06.002.
  44. Stavsky, Y. and Greenberg, J.B. (2003), "Radial vibrations of orthotropic laminated hollow spheres", J. Acoust. Soc. Am., 113(2), 847-851. https://doi.org/10.1121/1.1536625.
  45. Theotokoglou, E.E. and Stampouloglou, I.H. (2008), "The radially non-homogeneous axisymmetric problem", Int. J. Solid. Struct., 45, 6535-6552. https://doi.org/10.1016/j.ijsolstr.2008.08.011
  46. Thije, R.H.W.T., Akkerman, R. and Huetink, J. (2007), "Large deformation simulation of anisotropic material using an updated Lagrangian finite element method", Comput. Meth. Appl. Mech. Eng., 196, 3141-3150. https://doi.org/10.1016/j.cma.2007.02.010.
  47. Timesli, A. (2020), "An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory", SN Appl. Sci., 2, 407. https://doi.org/10.1007/s42452-020-2182-9.
  48. Towfighi, S. and Kundu, T. (2003), "Elastic wave propagation in anisotropic spherical curved plates", Int. J. Solid. Struct., 40, 5495-5510. https://doi.org/10.1016/S0020-7683(03)00278-6.