A state-based peridynamic formulation for functionally graded Kirchhoff plates

Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler-Lagrange equation and Taylor's expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young's modulus is assumed to be varied linearly through the thickness direction and Poisson's ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.