Skip to main content
SpringerLink
Log in

Time-dependent static analysis of viscoelastic Mindlin plates by defining a time function

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

This paper presents a new method for bending analysis of moderately thick viscoelastic plates using elasticity responses at asymptotic times. The displacement vector is approximated utilizing two functions of geometrical parameters and one function of time parameter with an unknown coefficient. The unknown coefficient of time function is determined by solving an implicit equation having little computational cost. Numerical results are compared with other existing results to show the accuracy and efficiency of the present method. Also, the effects of geometrical parameters and material properties on the time-dependent central deflection of viscoelastic Mindlin plates are considered for the first time.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Akbarov, S.D., Yahnioglu, N., Kutug, Z.: On the three dimensional stability loss problem of the viscoelastic composite plate. Int. J. Eng. Sci. 39, 1443–1457 (2001)

    Article  Google Scholar 

  • Alibeigloo, A.: Effect of viscoelastic interface on three-dimensional static and vibration behavior of laminated composite plate. Composites, Part B 75, 17–28 (2015)

    Article  Google Scholar 

  • Amoushahi, H., Azhari, M.: Static and instability analysis of moderately thick viscoelastic plates using a fully discretized nonlinear finite strip formulation. Composites, Part B 56, 223–231 (2014)

    Article  Google Scholar 

  • Donolato, C.: Analytical and numerical inversion of the Laplace–Carson transform by a differential method. Comput. Phys. Commun. 145, 298–309 (2002)

    Article  MathSciNet  Google Scholar 

  • Eisenträger, J., et al.: Application of the first order shear deformation theory to the analysis of laminate glasses and photovoltaic panels. Int. J. Mech. Sci. 96–97, 163–171 (2015)

    Article  Google Scholar 

  • Hon, J.W., Kim, J.S., Nguyen, S.N., Cho, M.: Improved viscoelastic analysis of laminated composite and sandwich plates with an enhanced first-order shear deformation theory. J. Appl. Mech. 83, 1–10 (2016)

    Google Scholar 

  • Jafari, N., Azhari, M.: Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple hp cloud method. Eng. Comput. 33(5), 1451–1471 (2016)

    Article  Google Scholar 

  • Jafari, N., Azhari, M.: Bending analysis of moderately thick arbitrarily shaped plates with point supports using simple hp cloud method. Iran. J. Sci. Technol., Civ. Eng. Trans. 41(4), 361–371 (2017a)

    Article  Google Scholar 

  • Jafari, N., Azhari, M.: Stability analysis of arbitrarily shaped moderately thick viscoelastic plates using Laplace–Carson transformation and a simple hp Cloud method. Mech. Time-Depend. Mater. 21(3), 365–381 (2017b)

    Article  Google Scholar 

  • Jafari, N., Azhari, M., Heidarpour, A.: Local buckling of rectangular viscoelastic composite plates using finite strip formulations. Mech. Adv. Mat. Struct. 21, 263–272 (2014)

    Article  Google Scholar 

  • Jafari, N., Azhari, M., Boroomand, B.: Large deformation analysis of moderately thick viscoelastic plates. Math. Comput. Simul. 163, 146–167 (2019)

    Article  MathSciNet  Google Scholar 

  • Naumenko, S., et al.: Closed and approximate analytical solution for rectangular Mindlin plates. Acta Mech. 147, 153–172 (2001)

    Article  Google Scholar 

  • Nguyen, S.N., Lee, J., Cho, M.: Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories. Int. J. Aeronaut. Space Sci. 13(4), 458–467 (2012)

    Article  Google Scholar 

  • Nguyen, S.N., Lee, J., Cho, M.: Efficient higher-order zig-zag theory for viscoelastic laminated composite plates. Int. J. Solids Struct. 62, 174–185 (2015)

    Article  Google Scholar 

  • Saadatpour, M.M., Azhari, M., Bradford, M.A.: Analysis of general quadrilateral orthotropic thick plates with arbitrary boundary conditions by the Rayleigh-Ritz method. Int. J. Numer. Methods Eng. 54, 1087–1102 (2002)

    Article  Google Scholar 

  • Sladek, J., Sladek, V., Zhang, Ch.: Local integral equation method for viscoelastic Reissner-Mindlin plate. Comput. Mech. 41, 759–768 (2008)

    Article  Google Scholar 

  • Temel, B., Sahan, M.F.: Transient analysis of orthotropic viscoelastic thick plates in the Laplace domain. Eur. J. Mech. A, Solids 37, 96–105 (2013)

    Article  Google Scholar 

  • Zenkour, A.M., Allam, M.N.M., Sobhy, M.: Bending response of a fiber-reinforced viscoelastic composite plate resting on elastic foundation. Arch. Appl. Mech. 81, 77–96 (2011)

    Article  Google Scholar 

  • Zhang, N.H., Cheng, C.J.: Nonlinear mathematical model of viscoelastic thin plates with its applications. Comput. Methods Appl. Mech. Eng. 16(5), 307–319 (1998)

    MATH  Google Scholar 

  • Zhuang, X.Y., Huang, R.Q., Zhu, H.H., Askes, H., Mathisen, K.: A new and simple locking-free triangular thick plate element using independent shear degrees of freedom. Finite Elem. Anal. Des. 75, 1–7 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Nasrin Jafari & Mojtaba Azhari

Authors
  1. Nasrin Jafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mojtaba Azhari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mojtaba Azhari.

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

Jafari, N., Azhari, M. Time-dependent static analysis of viscoelastic Mindlin plates by defining a time function. Mech Time-Depend Mater 25, 231–248 (2021). https://doi.org/10.1007/s11043-019-09437-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-019-09437-w

Keywords

Search

Navigation