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Nonlinear Bending Analysis of Functionally Graded CNT-Reinforced Shallow Arches Placed on Elastic Foundations
Acta Mechanica Solida Sinica ( IF 2.2 ) Pub Date : 2019-09-24 , DOI: 10.1007/s10338-019-00141-3
Yuanyuan Zhang , Bo Zhang , Huoming Shen , Yuxing Wang , Xin Zhang , Juan Liu

This research explores the nonlinear bending behaviors of functionally graded carbon nanotube-reinforced (FG-CNTR) shallow arches with unmovable simply supported ends and clamped–clamped ends; these arches are subjected to a uniform radial pressure and rest on a nonlinear elastic foundation. The temperature-dependent material properties of the arches are considered. Within the framework of Reddy shear deformation theory possessing von Kármán nonlinearity, the motion equations and boundary conditions for the FG-CNTR arches are determined by the Euler–Lagrange variational principle. Then, a two-step perturbation technique is adopted to determine the load–deflection relationship analytically. To verify the validity of the developed model and related perturbation solutions, a numerical investigation is conducted for shallow arches with five distribution patterns of carbon nanotube (CNT) reinforcements uniaxially aligned in the axial direction. Finally, the influences of various factors, including the elastic foundation, layout type, and volume fraction of CNTs and geometric factors, on the nonlinear behaviors of FG-CNTR shallow arches are examined. The obtained results show that the load–deflection curves exhibit less snap-through instability as the CNT volume fraction increases. The transverse shear stress versus the thickness of FG-CNTR shallow arches is markedly affected by the layout type and content of reinforcements.

中文翻译:

弹性基础上功能梯度CNT加固浅拱的非线性弯曲分析

这项研究探讨了功能梯度碳纳米管增强(FG-CNTR)浅拱形的非线性弯曲行为,该拱形具有固定的固定端和固定的固定端。这些拱门承受均匀的径向压力,并置于非线性弹性基础上。考虑了拱形的随温度变化的材料特性。在具有vonKármán非线性的Reddy剪切变形理论的框架内,根据Euler–Lagrange变分原理确定FG-CNTR拱的运动方程和边界条件。然后,采用两步摄动技术来解析地确定载荷-挠度关系。为了验证开发的模型和相关摄动解的有效性,对浅拱门进行了数值研究,该浅拱门具有沿轴向单轴排列的五个碳纳米管(CNT)增强材料分布图案。最后,研究了各种因素,包括碳纳米管的弹性基础,布局类型,体积分数和几何因素,对FG-CNTR浅拱的非线性行为的影响。获得的结果表明,随着CNT体积分数的增加,载荷-挠度曲线的搭接不稳定性较小。FG-CNTR浅拱的横向剪应力与厚度之间的关系受钢筋的布置类型和含量的影响很大。研究了碳纳米管的体积分数和几何因素对FG-CNTR浅拱的非线性行为。获得的结果表明,随着CNT体积分数的增加,载荷-挠度曲线的搭接不稳定性较小。FG-CNTR浅拱的横向剪应力与厚度之间的关系受钢筋的布置类型和含量的影响很大。研究了碳纳米管的体积分数和几何因素对FG-CNTR浅拱的非线性行为。获得的结果表明,随着CNT体积分数的增加,载荷-挠度曲线的搭接不稳定性较小。FG-CNTR浅拱的横向剪应力与厚度之间的关系受钢筋的布置类型和含量的影响很大。
更新日期:2019-09-24
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