Acta Mechanica

, Volume 229, Issue 5, pp 2251–2265 | Cite as

Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects

  • Mokhtar BouazzaEmail author
  • Ashraf M. ZenkourEmail author
  • Noureddine Benseddiq
Original Paper


A four-variable plate model is successfully extended here to investigate the thermal buckling analysis of advanced nanoplates. The advanced nanoplate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the nanoplate thickness. Two types of thermal loadings, uniform and nonlinear temperature rises along the nanoplate thickness are taken into consideration. The present model contains four unknown functions as against five or more in other alternative models. The through-the-thickness distributions of transverse shear stresses of the nanoplate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem-dependent shear correction factor. Comparison examples are made between results obtained via this model and those via available solutions in the literature.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of BecharBécharAlgeria
  2. 2.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Laboratory of Materials and Hydrology (LMH)University of Sidi Bel AbbesSidi Bel AbbèsAlgeria
  4. 4.Department of Mathematics, Faculty of ScienceKafrelsheikh UniversityKafrelsheikhEgypt
  5. 5.Mechanics Laboratory of Lille, CNRS UMR 8107University of Lille 1Villeneuve d’AscqFrance

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