In this paper, the Dual Mesh Control Domain Method (DMCDM) put forward by Reddy is applied to solve linear static, free vibration, and buckling problems of functionally graded plates modeled using the First-Order Shear Deformation Theory (FSDT). The material properties are assumed to vary continuously through the thickness of the plate according to a power-law. Formulations are presented for linear triangular (3-noded) and bilinear quadrilateral (4-noded) primal elements of arbitrary shape. The influence of the power-law exponents, length to thickness ratio, boundary conditions, and plate skewness on the numerical solution is systematically analyzed. Additionally, the numerical solutions using the DMCDM are compared against those from the Finite Element Method (FEM) to demonstrate the robustness of the DMCDM as a strong competitor to well-established numerical techniques such as the FEM.

中文翻译：

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使用双网格控制域方法对功能梯度板进行静态、自由振动和屈曲分析


在本文中，Reddy 提出的双网格控制域法 （DMCDM） 应用于解决使用一阶剪切变形理论 （FSDT） 建模的功能梯度板的线性静态、自由振动和屈曲问题。根据幂律，假设材料属性在板的厚度范围内连续变化。提出了任意形状的线性三角形（3 节点）和双线性四边形（4 节点）主元的公式。系统分析了幂律指数、长厚比、边界条件和板偏度对数值解的影响。此外，将使用 DMCDM 的数值解与有限元法 （FEM） 的数值解进行了比较，以证明 DMCDM 作为 FEM 等成熟数值技术的强大竞争对手的稳健性。