A Reissner-Mindlin Plate Model for Functionally Graded Materials

The concept of functionally graded materials (FGM) was proposed in 1984 by material scientists in the Sendai area of Japan. During twenty years of development, it has been efficiently applied to many industries. Moreover, it is a potential structural material for high-temperature environments. This material is composed of two or more constituents whose volume fractions change continuously as functions of position.

Functionally graded plate models have been studied with analytical and numerical methods. The significant advantage of FG plate over a laminated plate is to eliminate failure modes at interfaces. Several researchers have analyzed the behavior of thick FG plates. They proposed models that take into account the transversal shear effect, by using the five sixth correction factor. However, this factor is not appropriate to the FG plate analysis because of the position dependences of the FGM properties. Number of studies used the higher-order shear deformation theory to deal with this problem.

In this paper, a Reissner-Mindlin plate model for calculation of functionally graded materials is proposed. Identification of transverse shear factors is investigated through this model. The transverse shear stresses are derived by using energy considerations from the expression of membrane stresses. Using the transverse shear factor thus obtained, a numerical analysis is performed on a simply supported FG rectangular plate whose elastic properties are isotropic at each point and vary through the thickness according to a power law distribution. The numerical results of a static analysis are compared with available solutions from previous studies.