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Bending and free vibration analysis of orthotropic in-plane functionally graded plates using a Chebyshev spectral approach

机译：使用Chebyshev光谱法对正交性在线功能梯度板的弯曲和自由振动分析

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摘要

This paper presents a Chebyshev spectral approach for the bending and free vibration analysis of orthotropic in-plane functionally graded (IPFG) plates with general boundary conditions. Material properties and distributed loadings are assumed to be varying in the plane of the plates arbitrarily. Both of them are approximated by high-order Chebyshev expansions combining with Gauss-Lobatto sampling. Then, based on the Mindline-Reissner first-order shear deformation theory, the governing equations for the bending and free vibration are derived for orthotropic IPFG plates respectively by employing the principle of minimum total potential energy and the Lagrange's equation, which are consistent for any kind of material and loading distribution. Several numerical examples, involving various boundary conditions, types of loadings, and thickness length ratios, are presented to demonstrate the accuracy and efficiency of the proposed method. The results are compared with those reported in the literature and those obtained by commercial finite element software ABAQUS. Excellent agreements are observed, demonstrating the effectiveness of the Chebyshev spectral method for the static and dynamic analysis of orthotropic IPFG plates.
机译：本文介绍了具有一般边界条件的正交内功能梯度（IPFG）板弯曲和自由振动分析的Chebyshev光谱方法。假设材料特性和分布式载荷任意在板的平面中变化。它们都是由高阶Chebyshev扩展的近似，与Gauss-Lobatto采样相结合。然后，基于思维重新指导的一阶剪切变形理论，通过采用最小总势能和拉格朗日等式的原理，分别为弯曲和自由振动的控制方程分别用于正交IPFG板，这是任何材料和装载分布。提出了几个数值示例，涉及各种边界条件，载荷类型和厚度长度比，以证明所提出的方法的准确性和效率。将结果与文献中报告的结果进行比较，由商业有限元软件ABAQUS获得的那些。观察到良好的协议，展示了Chebyshev光谱法对正交性IPFG板的静态和动态分析的有效性。

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