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Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods

Navazi, H. M ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijmecsci.2008.08.010
  3. Publisher: 2008
  4. Abstract:
  5. An exact solution is presented for the nonlinear cylindrical bending and postbuckling of shear deformable functionally graded plates in this paper. A simple power law function and the Mori-Tanaka scheme are used to model the through-the-thickness continuous gradual variation of the material properties. The von Karman nonlinear strains are used and then the nonlinear equilibrium equations and the relevant boundary conditions are obtained using Hamilton's principle. The Navier equations are reduced to a linear ordinary differential equation for transverse deflection with nonlinear boundary conditions, which can be solved by exact methods. Finally, by solving some numeral examples for simply supported plates, the effects of volume fraction index and length-to-thickness ratio are studied. It is shown that there is no bifurcation point for simply supported functionally graded plates under compression. The behavior of near-boundary areas predicted by the shear deformation theory and the classical theory is remarkably different. © 2008 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Beams and girders ; Bending (deformation) ; Boundary conditions ; Boundary value problems ; Deformation ; Linear equations ; Nonlinear analysis ; Ordinary differential equations ; Plates (structural components) ; Shear deformation ; Analytical methods ; Bifurcation points ; Classical theories ; Cylindrical bending ; Exact methods ; Exact solutions ; Functionally graded plate ; Functionally graded plates ; Hamilton's principles ; Linear ordinary differential equations ; Material properties ; Navier equations ; Nonlinear boundary conditions ; Nonlinear equilibrium equations ; Nonlinear strains ; Postbuckling ; Power laws ; Shear deformation theories ; Simply supported ; Thickness ratios ; Transverse deflections ; Volume fraction indices ; Von Karman ; Nonlinear equations
  8. Source: International Journal of Mechanical Sciences ; Volume 50, Issue 12 , 2008 , Pages 1650-1657 ; 00207403 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0020740308001252?via%3Dihub