Design of bidirectional functionally graded plate for optimal natural frequencies

An advantage of functionally graded materials (FGMs) over laminated composites is that material properties vary continuously in an FGM but are discontinuous across adjoining layers in laminated composites. Furthermore, in an FGM material, properties can be graded in all three directions which is more difficult to achieve in laminated composites. FGMs have been used for structural optimization, e.g., bamboo is a highly optimized naturally occurring FGM [1]. FGMs with material properties varying only in the thickness direction can be manufactured by highspeed centrifugal casting [2,3], or by depositing ceramic layers on a substrate [4,5], and those with properties varying in the plane of a sheet by ultraviolet irradiation to alter the chemical composition [6]. Plate theories used to analyze deformations of an FG plate include the first-order shear deformation theory (FSDT) [7], the third-order shear deformation theory (TSDT) [8], and the compatible higher-order shear and normal deformation plate theory (HOSNDPT) [9–11]. In the FSDT and the TSDT three-dimensional constitutive relations are modified by assuming that the transverse normal stress vanishes. After solving the plate theory equations, the transverse shear and the transverse normal stresses are computed first by finding the in-plane stresses and then