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Nonlinear analysis of functionally graded nanocomposite rotating thick disks with variable thickness reinforced with carbon nanotubes

机译：用碳纳米管增强功能梯度的功能梯度纳米复合旋转厚盘的非线性分析

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摘要

In this paper the nonlinear elasticity solution of functionally graded nanocomposite rotating thick disks with variable thickness reinforced with single-walled carbon nanotubes (SWCNTs) is presented. Four distribution types of uniaxial aligned SWCNTs are considered: uniform and three types of functionally graded (FG) distributions along radial direction of the disk. The effective material properties of the nanocomposite disk are estimated by a micro-mechanical model. The governing nonlinear equations are based on the axisymmetric theory of elasticity with the geometric nonlinearity in axisymmetric complete form. The nonlinear graded finite element method (NGFEM) based on Rayleigh-Ritz energy formulation with the Picard iterative scheme is employed to solve the nonlinear equations. The solution is considered for four different thickness profiles, namely constant, linear, concave and convex. The effects of different types of distributions and volume fractions of CNTs and various types of thickness profiles on the displacement and stresses of the rotating disks as well as comparison between linear and nonlinear responses are investigated. The achieved results show that the displacement and stress fields can be controlled by changing the type of distribution and volume fraction of CNTs as well as the thickness profile. Moreover, the difference between linear and nonlinear results are noticeable in high angular velocities; thus, for obtaining accurate results, the geometric nonlinearity must be considered.
机译：本文提出了功能梯度的单壁碳纳米管（SWCNTs）增强功能可变的纳米复合旋转厚盘的非线性弹性解。考虑了单轴排列的SWCNT的四种分布类型：沿磁盘径向的均匀分布和三种功能梯度（FG）分布。纳米复合材料圆盘的有效材料性能是通过微机械模型估算的。支配的非线性方程是基于轴对称弹性理论的，其中几何非线性为轴对称完整形式。采用基于Rayleigh-Ritz能量公式的皮卡德迭代方案的非线性梯度有限元法（NGFEM）求解非线性方程。针对四种不同的厚度轮廓（即恒定，线性，凹形和凸形）考虑了该解决方案。研究了不同类型的碳纳米管的分布和体积分数以及各种类型的厚度分布对转盘位移和应力的影响以及线性和非线性响应之间的比较。所得结果表明，可以通过改变CNT的分布类型和体积分数以及厚度分布来控制位移和应力场。此外，线性和非线性结果之间的差异在高角速度时也很明显。因此，为了获得准确的结果，必须考虑几何非线性。

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