A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells
A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells
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DOI：
10.1631/jzus.a1500016
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发表时间：
2015-07
影响因子：
3.2
通讯作者：
Xu Liang;Hailei Kou;Guohua Liu;Lizhong Wang;Zhenyu Wang;Zhijun Wu
中科院分区：
文献类型：
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作者：
Xu Liang;Hailei Kou;Guohua Liu;Lizhong Wang;Zhenyu Wang;Zhijun Wu
设计师和研究人员有必要充分了解功能梯度材料 (FGM) 圆柱壳的机械行为。然而，尚未分析 FGM 圆柱壳在各种边界条件下的 3D 瞬态响应。本文通过提出一种集成状态空间法、微分求积法和杜宾纳拉普拉斯变换数值反演方法来解决该问题。层合板模型用于获得径向方向的瞬态解。在边缘处，考虑四种边界条件：夹紧-夹紧、夹紧-简支、夹紧-自由和简支-简支。所提出的方法和有限元（FE）方法的结果非常吻合。收敛性研究表明该方法具有较快的收敛速度。所提出的方法、实验和其他理论方法获得的固有频率彼此非常吻合。研究了载荷频率和持续时间、长度/外半径比以及（外半径-内半径）/外半径比对FGM壳体瞬态响应的影响。考虑材料属性沿径向方向变化的两个定律：第一个具有沿径向方向按指数规律变化的材料属性，而第二个具有按幂律变化的材料属性。在这两种情况下研究了功能分级指数对 FGM 壳瞬态响应的影响。本文获得的结果可以作为进一步研究的基准数据。
A good understanding of the mechanical behavior of functionally graded material (FGM) cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbina’s numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered: Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element (FE) method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the (outer radius-inner radius)/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered: the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.