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Thermal postbuckling analysis of FG-CNTRC plates with various shapes and temperature-dependent properties using the VDQ-FEM technique
Aerospace Science and Technology ( IF 5.6 ) Pub Date : 2020-07-20 , DOI: 10.1016/j.ast.2020.106078
R. Ansari , R. Hassani , R. Gholami , H. Rouhi

Using the ideas of variational differential quadrature and finite element methods (VDQ and FEM), a novel numerical approach is developed in this paper to investigate the postbuckling behavior of plates with arbitrary shape under the action of thermal load within the framework of higher-order shear deformation theory (HSDT). It is considered that the plates are made of functionally graded carbon nanotube reinforced composite (FG-CNTRC). By the proposed approach, the thermal postbuckling behavior of plates with arbitrary-shaped cutout can be modeled. The rule of mixture is utilized to obtain the effective material properties of nanocomposite which are considered to be temperature-dependent. To implement the proposed method that can be named as VDQFEM, the variational temperature-dependent formulation of problem is first developed. This formulation is presented using novel vector-matrix relations with the aim of utilizing in programming in an efficient way. In the context of VDQFEM, the space domain of plate is first transformed into a number of finite elements. In the next step, the VDQ discretization technique is implemented within each element. Then, the assemblage procedure is performed to derive the set of matricized governing equations which is finally solved by means of the pseudo arc-length continuation algorithm. One of the main novelties of present approach is proposing an efficient way based on mixed-formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used higher-order shear deformable plate model. Quadrilateral plate, skew plate, annular plate, square plate with rectangular hole and rectangular plate with circular hole under different boundary conditions including CCCC, SSSS, CSCS and CCSS (S: simply-supported, C: clamped) are considered in the numerical example. First, validation studies are presented in terms of critical buckling temperature of CNTRC rectangular plates with various CNT distribution patterns. It is shown that the proposed method has the advantages of standard VDQ technique including fast convergence rate, being locking-free and simple implementation. Moreover, it is capable of considering polygon and concave domains. Also, the effects of geometrical properties, volume fraction and distribution pattern of CNTs and temperature-dependency of material properties on the thermal postbuckling of plates are studied.



中文翻译:

使用VDQ-FEM技术对具有不同形状和温度相关特性的FG-CNTRC板进行热后屈曲分析

利用变分求积和有限元方法(VDQ和FEM)的思想,本文开发了一种新颖的数值方法来研究在高阶剪切框架内热载荷作用下任意形状的板的后屈曲行为。变形理论(HSDT)。认为这些板由功能梯度的碳纳米管增强复合材料(FG-CNTRC)制成。通过提出的方法,可以对具有任意形状切口的板的热后屈曲行为进行建模。利用混合规则来获得被认为是温度依赖性的纳米复合材料的有效材料性能。为了实现所提出的可以称为VDQFEM的方法,首先开发了与温度有关的变问题公式。使用新颖的矢量矩阵关系来表示此公式,目的是以一种有效的方式在编程中加以利用。在VDQFEM中,首先将板的空间域转换为多个有限元。下一步,在每个元素中实施VDQ离散化技术。然后,执行组装过程以导出矩阵化的控制方程组,最后通过伪弧长连续算法对其进行求解。本方法的主要新颖性之一是提出一种基于混合配方的有效方法,以适应所使用的高阶剪切变形板模型在元素公共边界上的一阶导数的连续性。四边形板,斜板,环形板,在数值示例中考虑了在不同边界条件下包括CCCC,SSSS,CSCS和CCSS(S:简单支撑,C:夹紧)的带矩形孔的矩形板和带圆形孔的矩形板。首先,对具有各种CNT分布模式的CNTRC矩形板的临界屈曲温度进行了验证研究。结果表明,该方法具有标准的VDQ技术的优点,具有收敛速度快,无锁,实现简单等优点。而且,它能够考虑多边形和凹形区域。此外,研究了碳纳米管的几何特性,体积分数和分布模式以及材料特性的温度依赖性对板的热后屈曲的影响。

更新日期:2020-07-20
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