Functionally graded materials is a potential alternative to traditional fiber reinforced composite materials since they have continuously varying material properties which does 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 is obtained by using 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 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.

中文翻译：

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功能梯度基尔霍夫板的基于状态的近场动力学公式

功能梯度材料是传统纤维增强复合材料的潜在替代品，因为它们具有不断变化的材料特性，不会引起应力集中。在这项研究中，提出了功能梯度基尔霍夫板的基于状态的近场动力学模型。新公式的运动方程是通过使用欧拉-拉格朗日方程和泰勒展开获得的。该公式通过考虑几个基准问题来验证，包括承受横向载荷的夹板和承受横向载荷和倾斜载荷的简支板。选择材料属性，使得杨氏模量假设在厚度方向上线性变化，泊松比恒定。