Static Analysis of Thick Functionally Graded Plates with Different Property Distribution Functions

Functionally graded materials (FGM) have long been used to manufacture plates with desired stiffness and strength variation. Several plate theories have been used before to investigate mechanical behavior of FGM plates. However, in most of the published work, only the power law transverse material variation (P-FGM) was considered. In the present work, the third-order shear deformation theory is utilized to investigate bending behavior of other classes of FGM plates. The sigmoid variation and the exponential variation of properties are considered, in addition to the power law variation. First, the displacement distribution within the thick plate volume is presented. Then, the plate response governing equations are derived. The final matrix equation is formed using a Navier-type expansion of the unknown displacements. The model is verified by comparisons of the calculated nondimensional maximum displacement with the available published results. The model is used to investigate the shear deformation effect on the bending behavior of the plate for different values of plate aspect ratio, thickness ratio, and constituents’ elastic modulus ratio. Then, a comparison between the results of the three types of property variation is made. This comparison shows that the stiffening effect due to the incorporation of the shear deformation is less pronounced in the S-FGM than in the more commonly used P-FGM plates. Results also present the range of plate aspect ratio and thickness ratio for which this effect is more significant.