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Nonlinear bending and post-buckling behaviors of FG small-scaled plates based on modified strain gradient theory using Ritz technique

  • Ghannadpour, S. Amir M. (Faculty of New Technologies Engineering, Shahid Beheshti University) ;
  • Khajeh, Selma (Faculty of New Technologies Engineering, Shahid Beheshti University)
  • Received : 2021.10.14
  • Accepted : 2022.04.12
  • Published : 2022.10.25
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Abstract

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

Keywords

References

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