Bending analysis of anisotropic functionally graded plates based on three-dimensional elasticity

ABSTRACT

Although theories of plates are accurate enough to use for thin plates, the three-dimensional elasticity analysis is needed to study the thick plates, which increases the computational efforts. The present paper introduces a simple solution for anisotropic functionally graded plates using differential quadrature method (DQM). Regarding anisotropy, Poisson’s ratio assumes to be constant. Also, Young’s and shear moduli are depended on coordinate perpendicular to the middle surface of the plate. By rewriting the governing elasticity relations in terms of displacement functions, governing equations of the problem are obtained. Using DQM leads to a decrease in the number of required mesh, and also, the convergence of the model is less time-consuming. The comparison between the results of the proposed method with those of finite element analysis and current complicated models shows a good agreement. In addition, the effects of grading index and the thickness on displacement and strain and stress distributions have been studied.

KEYWORDS:

• Three-dimensional elasticity solution
• functionally graded material (FGM)
• anisotropic material
• differential quadrature method (DQM)
• finite element method (FEM)

Disclosure statement

No potential conflict of interest was reported by the authors.