https://doi.org/10.1140/epjp/i2019-12501-x
Regular Article
Nonlinear bending analysis of nanoplates made of FGMs based on the most general strain gradient model and 3D elasticity theory
1
Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
2
Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University, P.O. Box 1616, Lahijan, Iran
3
Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran
* e-mail: r_ansari@guilan.ac.ir
Received:
1
October
2017
Accepted:
7
January
2019
Published online:
19
April
2019
In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity theory is used for modeling the nanoplate. The governing equations are also derived in the discretized weak form using the variational differential quadrature (VDQ) method. Finally, the solution of the nonlinear bending problem is obtained by the pseudo arc-length continuation algorithm. In the numerical results, the effects of thickness-to-length scale ratio, side length-to-thickness ratio and material gradient index on the nonlinear bending response of nanoplates subject to different types of boundary conditions are analyzed. Moreover, a comparison is provided between the predictions of various strain gradient-based theories.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019
