Advertisement

Acta Mechanica

, Volume 230, Issue 7, pp 2363–2384 | Cite as

Thermally induced large deflection of FGM shallow micro-arches with integrated surface piezoelectric layers based on modified couple stress theory

  • Hadi BabaeiEmail author
  • M. Reza Eslami
Original Paper
  • 23 Downloads

Abstract

Based on the modified couple stress theory, nonlinear thermally induced large deflection analysis of shallow sandwich arches is studied. A functionally graded material (FGM) micro-arch with piezoelectric layers integrated into the surfaces and with immovable pinned and fixed edges is analyzed. Temperature and position dependence of the thermomechanical properties for an FGM micro-arch are taken into account. The piezo-FGM arches are subjected to different types of thermal loads such as uniform temperature, linear temperature, and heat conduction. A modified couple stress theory is combined with the uncoupled thermoelasticity assumptions to derive the governing equations of the arch by using the virtual displacement principle. The von Kármán type of geometrical nonlinearity and first-order shear deformation theory are also used to obtain the equilibrium equations. The nonlinear governing equilibrium equations of the piezo-FGM sandwich arch under different thermal loads are solved analytically. The solutions of the system of ordinary differential equations for both cases of boundary conditions are established by employing the two-step perturbation technique. Comparison is made with the existing results for the cases of FGM arch without couple stress and piezoelectric layers under uniform temperature rise, and good agreement is obtained. Also, parametric studies are proposed to show the effects of couple stress, piezoelectric layers, volume fraction index, geometrical parameters, and temperature dependence, the thermally induced deflection of the piezo-FGM sandwich arch.

Keywords

Thermo-elastic deflection Sandwich arch Two-step perturbation technique Piezoelectric layer Functionally graded material Modified couple stress theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Eslami, M.R.: Buckling and Postbuckling of Beams, Plates, and Shells. Springer, Cham (2018)CrossRefzbMATHGoogle Scholar
  2. 2.
    Shen, H.S., Wang, Z.X.: Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments. Int. J. Mech. Sci. 81, 195–206 (2014)CrossRefGoogle Scholar
  3. 3.
    She, G.L., Shu, X., Ren, Y.R.: Thermal buckling and post-buckling analysis of piezoelectric FGM beams based on high-order shear deformation theory. J. Therm. Stress. 40, 783–797 (2017)CrossRefGoogle Scholar
  4. 4.
    She, G.L., Yuan, F.G., Ren, Y.R.: Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Appl. Math. Model. 47, 340–357 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Kiani, Y., Eslami, M.R.: Thermomechanical buckling of temperature-dependent FGM beams. Lat. Am. J. Solids Struct. 10, 223–246 (2013)CrossRefGoogle Scholar
  6. 6.
    Kiani, Y., Eslami, M.R.: Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation. Arch. Appl. Mech. 82, 891–905 (2012).  https://doi.org/10.1007/s00419-011-0599-8 CrossRefzbMATHGoogle Scholar
  7. 7.
    Komijani, M., Kiani, Y., Esfahani, S.E., Eslami, M.R.: Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams. Compos. Struct. 98, 143–152 (2013).  https://doi.org/10.1016/j.compstruct.2012.10.047 CrossRefGoogle Scholar
  8. 8.
    Kong, S., Zhou, S., Nie, Z., Wang, K.: Static and dynamic analysis of micro beams based on strain gradient elasticity theory. Int. J. Eng. Sci. 47, 487–498 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Asghari, M., Kahrobaiyan, M.H., Ahmadian, M.T.: A nonlinear Timoshenko beam formulation based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1749–1761 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S.: Nonlinear free vibration of size dependent functionally graded microbeams. Int. J. Eng. Sci. 50, 256–267 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Simsek, M., Reddy, J.N.: Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. Int. J. Eng. Sci. 64, 37–53 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Darijani, H., Mohammadabadi, H.: A new deformation beam theory for static and dynamic analysis of microbeams. Int. J. Mech. Sci. 89, 31–39 (2014)CrossRefGoogle Scholar
  13. 13.
    Akgoz, B., Civalek, O.: Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. Int. J. Eng. Sci. 85, 90–104 (2014)CrossRefzbMATHGoogle Scholar
  14. 14.
    Akgoz, B., Civalek, O.: Shear deformation beam models for functionally graded microbeams with new shear correction factors. Compos. Struct. 112, 214–225 (2014)CrossRefGoogle Scholar
  15. 15.
    Attia, M.A., Mahmoud, F.F.: Modeling and analysis of nanobeams based on nonlocal couple-stress elasticity and surface energy theories. Int. J. Mech. Sci. (2015).  https://doi.org/10.1016/j.ijmecsci.2015.11.002 Google Scholar
  16. 16.
    AkbarzadehKhorshidi, M., Shariati, M., Emam, S.A.: Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory. Int. J. Mech. Sci. (2016).  https://doi.org/10.1016/j.ijmecsci.2016.03.006 Google Scholar
  17. 17.
    Dehrouyeh-Semnani, A.M., Mostafaei, H., Nikkhah-Bahrami, M.: Free flexural vibration of geometrically imperfect functionally graded microbeams. Int. J. Eng. Sci. 105, 56–79 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Bradford, M.A., Uy, B., Pi, Y.L.: In-plane elastic stability of arches under a central concentrated load. J. Eng. Mech. ASCE 128, 710–719 (2002)CrossRefGoogle Scholar
  19. 19.
    Pi, Y.L., Bradford, M.A., Uy, B.: In-plane stability of arches. Int. J. Solids Struct. 39, 105–125 (2002)CrossRefzbMATHGoogle Scholar
  20. 20.
    Pi, Y.L., Bradford, M.A., Tin-Loi, F.: Nonlinear analysis and buckling of elastically supported circular shallow arches. Int. J. Solids Struct. 44, 2401–2425 (2007)CrossRefzbMATHGoogle Scholar
  21. 21.
    Pi, Y.L., Bradford, M.A.: In-plane thermoelastic behaviour and buckling of pin-ended and fixed circular arches. Eng. Struct. 32, 250–260 (2010)CrossRefGoogle Scholar
  22. 22.
    Pi, Y.L., Bradford, M.A.: Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading. Int. J. Mech. Sci. 52, 75–88 (2010)CrossRefGoogle Scholar
  23. 23.
    Pi, Y.L., Bradford, M.A.: Nonlinear thermoelastic buckling of pin-ended shallow arches under temperature gradient. J. Eng. Mech. 136, 960–8 (2010)CrossRefGoogle Scholar
  24. 24.
    Wang, M., Liu, Y.: Elasticity solutions for orthotropic functionally graded curved beams. Eur. J. Mech. A Solids 37, 8–16 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Jun, L., Guangwei, R., Jin, P., Xiaobin, L., Weiguo, W.: Free vibration analysis of a laminated shallow curved beam based on trigonometric shear deformation theory. Mech. Based Des. Struct. Mach. 42, 111–129 (2014)CrossRefGoogle Scholar
  26. 26.
    Asgari, H., Bateni, M., Kiani, Y., Eslami, M.R.: Non-linear thermo-elastic and buckling analysis of FGM shallow arches. Compos. Struct. 109, 75–85 (2014)CrossRefGoogle Scholar
  27. 27.
    Han, Q., Cheng, Y., Lu, Y., Li, T., Lu, P.: Nonlinear buckling analysis of shallow arches with elastic horizontal supports. Thin-Walled Struct. 109, 88–102 (2016)CrossRefGoogle Scholar
  28. 28.
    Bouras, Y., Vrcelj, Z.: Non-linear in-plane buckling of shallow concrete arches subjected to combined mechanical and thermal loading. Eng. Struct. 152, 413–423 (2017)CrossRefGoogle Scholar
  29. 29.
    Tsiatas, G.C., Babouskos, N.G.: Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force. Int. J. Non-Linear Mech. 92, 92–101 (2017)CrossRefGoogle Scholar
  30. 30.
    Babaei, H., Kiani, Y., Eslami, M.R.: Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method. ZAMM J. Appl. Math. Mech. (2018).  https://doi.org/10.1002/zamm.201800148 Google Scholar
  31. 31.
    Babaei, H., Kiani, Y., Eslami, M.R.: Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment. Thin-Walled Struct. 132, 48–57 (2018)CrossRefGoogle Scholar
  32. 32.
    Babaei, H., Kiani, Y., Eslami, M.R.: Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads. Acta Mech. 229, 3123–3141 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Babaei, H., Kiani, Y., Eslami, M.R.: Thermomechanical nonlinear in-plane analysis of fix-ended FGM shallow arches on nonlinear elastic foundation using two-step perturbation technique. Int. J. Mech. Des. (2018).  https://doi.org/10.1007/s10999-018-9420-y zbMATHGoogle Scholar
  34. 34.
    Brush, D.O., Almorth, B.O.: Buckling of Bars, Plates and Shells. Mc. Graw-Hill, New York (1975)CrossRefGoogle Scholar
  35. 35.
    Trinh, L.C., Nguyen, H.X., Vo, T.P., Nguyen, T.K.: Size-dependent behaviour of functionally graded microbeams using various shear deformation theories based on the modified couple stress theory. Compos. Struct. (2016).  https://doi.org/10.1016/j.compstruct.2016.07.033 Google Scholar
  36. 36.
    Shen, H.S.: Functionally Graded Materials Nonlinear Analysis of Plates and Shells. CRC Press, Boca Raton (2009)Google Scholar
  37. 37.
    Hetnarski, R.B., Eslami, M.R.: Thermal Stresses, Advanced Theory and Applications. Springer, Amsterdam (2009)zbMATHGoogle Scholar
  38. 38.
    Komijani, M., Esfahani, S.E., Reddy, J.N., Liu, Y.P., Eslami, M.R.: Nonlinear thermal stability and vibration of pre/post-buckled temperature- and microstructure-dependent functionally graded beams resting on elastic foundation. Compos. Struct. 112, 292–307 (2014)CrossRefGoogle Scholar
  39. 39.
    Kiani, Y., Rezaei, M., Taheri, S., Eslami, M.R.: Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams. Int. J. Mech. Mater. Des. 7, 185–197 (2011)CrossRefGoogle Scholar
  40. 40.
    Kiani, Y., Taheri, S., Eslami, M.R.: Thermal buckling of piezoelectric functionally graded material beams. J. Therm. Stress. 34, 835–850 (2011)CrossRefGoogle Scholar
  41. 41.
    Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)CrossRefzbMATHGoogle Scholar
  42. 42.
    Reddy, J.N.: Microstructure-dependent couple stress theories of functionally graded beams. J. Mech. Phys. Solids 59, 2382–2399 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Shen, H.S.: A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells. Wiley, Singapore (2013)CrossRefzbMATHGoogle Scholar
  44. 44.
    Babaei, H., Kiani, Y., Eslami, M.R.: Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load. J. Therm. Stress. 41, 847–865 (2018)CrossRefGoogle Scholar
  45. 45.
    Kiani, Y., Eslami, M.R.: Thermal buckling analysis of functionally graded material beams. Int. J. Mech. Mater. Des. 6, 229–238 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical Engineering Department, South Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Mechanical Engineering DepartmentAmirkabir University of TechnologyTehranIran

Personalised recommendations