Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment
Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment
复制标题
热环境中功能梯度材料板瞬态行为的新型半解析解
DOI：
10.3390/ma12244084
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发表时间：
2019-12-02
期刊：
影响因子：
3.4
通讯作者：
Leng, Jianxing
中科院分区：
文献类型：
--
作者：
Cao, Zeng;Liang, Xu;Leng, Jianxing
本文的主要目的是提出一个半解析算法的功能梯度材料板（FGM板）的瞬态行为，同时考虑面内位移的影响和温度变化的影响。基于考虑面内位移影响的经典板理论，利用汉密尔顿原理导出了运动系统的平衡方程。在这里，我们提出了一种新的，准确的，有效的半解析方法，结合傅立叶级数展开，拉普拉斯变换，其数值反演和微分求积法（DQM）来模拟瞬态行为。本文通过与半解析固有频率结果和文献结果的比较，验证了所提出的方法。动力响应的计算结果与Navier法和有限元法的计算结果吻合较好。利用不同数量的采样点的收敛性研究表明，该过程可以快速收敛，并且少量的采样点可以实现高精度。在两端的各种边界条件，材料梯度折射率，和温度变化的影响进行了进一步研究。从详细的参数研究中可以看出，峰值位移随着边缘自由度、材料梯度指数和温度变化的增加而增加。
The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.