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首页> 外文期刊>International Journal of Aerospace Sciences >Non-Linear Bending Analysis of Moderately Thick Functionally Graded Plates Using Generalized Differential Quadrature Method
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Non-Linear Bending Analysis of Moderately Thick Functionally Graded Plates Using Generalized Differential Quadrature Method

机译:中厚功能梯度板的非线性弯曲的广义差分求积法

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Linear and non-linear bending analysis of moderately thick functionally graded (FG) rectangular plates with different boundary conditions are presented using generalized differential quadrature (GDQ) method. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Based on the first-order shear deformation theory and Von Karman type non-linearity, the governing system of equations include a system of thirteen partial differential equations (PDEs) in terms of unknown displacements, forces and moments. To derive linear system of equations, non-linear terms are omitted in former equations. Presence of all plate variables in the governing equations provides a simple procedure to satisfy different boundary conditions. Successive application of the GDQ technique to the governing equations resulted in a system of non-linear algebraic equations. The Newton–Raphson iterative scheme is then employed to solve the resulting system of non-linear equations. Illustrative examples are presented to demonstrate accuracy and rapid convergence of the presented GDQ technique. Accuracy of the results for both displacement and stress components are verified with comparing the present results with those of analytical and finite element methods. It is found that the theory can predict accurately the displacement and stress components even for small number of grid points.
机译:使用广义差分正交积分法(GDQ),对具有不同边界条件的中厚功能梯度(FG)矩形板进行了线性和非线性弯曲分析。假定板的弹性模量根据幂定律分布在成分的体积分数方面变化。基于一阶剪切变形理论和Von Karman型非线性,方程的控制系统包括13个偏微分方程组(PDE),它们的位移,力和力矩未知。为了导出方程的线性系统,在先前的方程中省略了非线性项。控制方程中所有板变量的存在提供了满足不同边界条件的简单程序。 GDQ技术在控制方程中的连续应用导致了一个非线性代数方程组。然后,采用牛顿-拉夫森迭代方案来求解非线性方程组。给出了说明性示例以证明所提出的GDQ技术的准确性和快速收敛性。通过将当前结果与分析方法和有限元方法的结果进行比较,可以验证位移和应力分量结果的准确性。发现该理论即使在网格点数量较少的情况下也可以准确预测位移和应力分量。

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