Nonlinear dynamic response of functionally graded material plates using a high‐order implicit algorithm,ZAMM - Journal of Applied Mathematics and Mechanics

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Nonlinear dynamic response of functionally graded material plates using a high‐order implicit algorithm
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-07-26 , DOI: 10.1002/zamm.202000087
Oussama Bourihane ₁ , Youssef Hilali _{1,

2} , Khadija Mhada ₃

Affiliation

In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite. To handle integrals in the case of inhomogeneous FGMs, the stress vector is split to four parts and it is written in dimensionless form. The resulting equations of motion are established using the Hamilton principle. Finite element discretization is adopted using a four‐node quadrilateral element with seven degrees of freedom per node. The resolution of the nonlinear equations is made by a high‐order implicit algorithm based on the asymptotic numerical method (ANM) techniques. Numerical comparisons of vibration natural frequencies and dynamic response of FGM plates under external loading with literature and laminate composite modeling results are presented to validate the accuracy and the performance of the proposed model.

中文翻译：

使用高阶隐式算法的功能梯度材料板非线性动力学响应

本文利用高阶隐式算法对功能梯度材料（FGM）板在外部动态载荷作用下的强迫非线性动力学行为进行了分析。该模型是使用三阶剪切变形板运动学（TSDT）开发的。与以前的作品不同，在此贡献中，配方的编写既不求助于任何均质化技术，既不遵循混合规则，也不将FGM作为层压复合材料。为了在不均匀的FGM情况下处理积分，将应力矢量分为四个部分，并以无量纲形式编写。使用汉密尔顿原理建立运动方程。使用四节点四边形元素采用有限元离散化，每个节点具有七个自由度。非线性方程的解析是通过基于渐近数值方法（ANM）技术的高阶隐式算法进行的。提出了FGM板在固有载荷下的振动固有频率和动力响应的数值比较，并结合文献和层合复合材料建模结果，验证了所提模型的准确性和性能。

更新日期：2020-07-26

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