Viscoelastic Plate Analysis Based on Gateaux Differential

Kadıoğlu F., Tekin Özkan G.

4th International Conference on Nano and Materials Science (ICNMS), New-York, United States Of America, 7 - 09 January 2016, vol.43 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 43
  • Doi Number: 10.1051/matecconf/20164304004
  • City: New-York
  • Country: United States Of America
  • Istanbul Technical University Affiliated: Yes


In this study, it is aimed to analyze the quasi-static response of viscoelastic Kirchhoff plates with mixed finite element formulation based on the Gateaux differential. Although the static response of elastic plate, beam and shell structures is a widely studied topic, there are few studies that exist in the literature pertaining to the analysis of the viscoelastic structural elements especially with complex geometries, loading conditions and constitutive relations. The developed mixed finite element model in transformed Laplace-Carson space has four unknowns as displacement, bending and twisting moments in addition to the dynamic and geometric boundary condition terms. Four-parameter solid model is employed for modelling the viscoelastic behaviour. For transformation of the solutions obtained in the Laplace-Carson domain to the time domain, different numerical inverse transform techniques are employed. The developed solution technique is applied to several quasi-static example problems for the verification of the suggested numerical procedure.