Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Eslami, M.R.: Buckling and Postbuckling of Beams, Plates, and Shells. Springer, Cham (2018)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  5. Kiani, Y., Eslami, M.R.: Thermomechanical buckling of temperature-dependent FGM beams. Lat. Am. J. Solids Struct. 10, 223–246 (2013)

    Article  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  14. Akgoz, B., Civalek, O.: Shear deformation beam models for functionally graded microbeams with new shear correction factors. Compos. Struct. 112, 214–225 (2014)

    Article  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  19. Pi, Y.L., Bradford, M.A., Uy, B.: In-plane stability of arches. Int. J. Solids Struct. 39, 105–125 (2002)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  24. Wang, M., Liu, Y.: Elasticity solutions for orthotropic functionally graded curved beams. Eur. J. Mech. A Solids 37, 8–16 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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

    MATH  Google Scholar 

  34. Brush, D.O., Almorth, B.O.: Buckling of Bars, Plates and Shells. Mc. Graw-Hill, New York (1975)

    Book  Google Scholar 

  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. Shen, H.S.: Functionally Graded Materials Nonlinear Analysis of Plates and Shells. CRC Press, Boca Raton (2009)

    Google Scholar 

  37. Hetnarski, R.B., Eslami, M.R.: Thermal Stresses, Advanced Theory and Applications. Springer, Amsterdam (2009)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  40. Kiani, Y., Taheri, S., Eslami, M.R.: Thermal buckling of piezoelectric functionally graded material beams. J. Therm. Stress. 34, 835–850 (2011)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  42. Reddy, J.N.: Microstructure-dependent couple stress theories of functionally graded beams. J. Mech. Phys. Solids 59, 2382–2399 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Shen, H.S.: A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells. Wiley, Singapore (2013)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  45. Kiani, Y., Eslami, M.R.: Thermal buckling analysis of functionally graded material beams. Int. J. Mech. Mater. Des. 6, 229–238 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, South Tehran Branch, Islamic Azad University, Tehran, Iran

    Hadi Babaei

  2. Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran

    M. Reza Eslami

Authors
  1. Hadi Babaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Reza Eslami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Babaei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babaei, H., Eslami, M.R. Thermally induced large deflection of FGM shallow micro-arches with integrated surface piezoelectric layers based on modified couple stress theory. Acta Mech 230, 2363–2384 (2019). https://doi.org/10.1007/s00707-019-02384-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-019-02384-0

Keywords

Search

Navigation