Analysis of anisotropic gradient elastic shear deformable plates

S. M. Mousavi*, J. N. Reddy, J. Romanoff

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

21 Citations (Scopus)


In this paper, Reddy’s third-order shear deformable plate theory is employed for the analysis of centrosymmetric anisotropic plate structures within strain gradient elasticity. The general three-dimensional anisotropic gradient theory is reduced to a two-dimensional formulation for the analysis of thick plate structures. The third-order shear deformation theory (TSDT) takes into account quadratic variation of the transverse shear strains of the plate and does not require shear correction factors. In order to investigate the case of small strains but moderate rotations, the von Kármán strains are considered. The TSDT is also simplified to anisotropic Kirchhoff plate theory within gradient elasticity. To study specific material properties in more detail, the (Kirchhoff and TSDT) gradient plate theory of general anisotropy is simplified to the more practical case of orthotropic plates. It is observed that the gradient theory provides the capability to capture the size effects in anisotropic plate structures. As case studies, the bending and buckling behaviors of the simply supported orthotropic (Kirchhoff and TSDT) plates are studied. Variationally consistent boundary conditions are also discussed. Finally, analytical solutions are presented for the bending and buckling of simply supported orthotropic Kirchhoff plates. The effects of internal length scales on deflections and buckling loads are presented.

Original languageEnglish
Pages (from-to)3639-3656
Number of pages18
Issue number12
Early online date19 Jul 2016
Publication statusPublished - Dec 2016
MoE publication typeA1 Journal article-refereed


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