基于非线性梯度单元的石墨烯功能梯度悬臂板力学特性

doi:10.19936/j.cnki.2096-8000.20220828.002

复合材料科学与工程 ›› 2022, Vol. 0 ›› Issue (8): 15-22.DOI: 10.19936/j.cnki.2096-8000.20220828.002

基于非线性梯度单元的石墨烯功能梯度悬臂板力学特性

张鹏程¹, 于印鑫^1*, 李恩国¹, 赵天宇², 付涛¹

1.昆明理工大学机电工程学院,昆明650500;
2.东北大学理学院,沈阳110819

收稿日期:2021-10-13 出版日期:2022-08-28 发布日期:2022-09-27
通讯作者: 于印鑫(1983-),男,博士,讲师,主要从事复合材料动力学、转子动力学研究,yxy@kust.edu.cn。
作者简介:张鹏程(1997-),男,硕士研究生,主要从事复合材料力学、结构动力学研究。
基金资助:
国家自然科学基金项目(52165014);云南省基础研究计划项目青年项目(202101AU070160)

Mechanical properties of graphene functionally graded cantilever plate based on nonlinear gradient element

ZHANG Peng-cheng¹, YU Yin-xin^1*, LI En-guo¹, ZHAO Tian-yu², FU Tao¹

1. School of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China;
2. School of Science, Northeastern University, Shenyang 110819, China

Received:2021-10-13 Online:2022-08-28 Published:2022-09-27

摘要/Abstract

摘要： 针对石墨烯功能梯度材料提出了一种基于20节点非线性梯度单元的有限元建模方法,该方法克服了传统有限元分层法无法精确拟合功能材料梯度变化和无法进行应力分析的缺点。以U形、X形和O形3种梯度分布形式的悬臂板为研究对象,分析了悬臂板静载荷下的弯曲变形、应力分布和模态特性,并与有限元分层法模型进行了对比分析和验证。研究结果表明:与非线性梯度单元法相比,传统分层法模型会导致X形悬臂板弯曲刚度和对应各阶固有频率大于实际值,而导致O形悬臂板的弯曲刚度和对应各阶固有频率小于实际值;与U形分布形式相比,X形梯度分布可以提高悬臂板弯曲刚度,提高悬臂板各阶固有频率,而O形分布形式会降低悬臂板弯曲刚度,降低各阶固有频率;非线性梯度单元法能够实现对功能梯度板厚度方向的应力求解,为功能梯度板的疲劳寿命分析提供了理论基础。

关键词: 石墨烯, 非线性梯度单元, 应力, 模态, 有限元分层法

Abstract: Aiming at the complex gradient changes of graphene-reinforced composite materials, a finite element method based on 20-node nonlinear gradient element is proposed to satisfy the analysis of the mechanical properties of complex gradient materials. In this paper, the finite element models of U-shaped, X-shaped and O-shaped gradient distribution cantilever plates are established, and the static displacement, stress and mode of the cantilever plates under the three gradient distribution forms are compared and analyzed. The method in this paper is compared and verified with the finite element layered method. The results show that compared with the nonlinear gradient element method, the traditional layered method model will cause the bending stiffness of the X-shaped cantilever plate and the corresponding natural frequencies of each order to be larger than the actual values, while the bending stiffness of the O-shaped cantilever plate and the corresponding natural frequencies of each order are smaller than the actual values. Compared with the U-shaped distribution, the X-shaped gradient distribution can improve the bending stiffness of the cantilever plate, mentioning the natural frequencies of each order of the cantilever plate, while the O-shaped distribution can reduce the bending stiffness of the cantilever plate and reduce the natural frequencies of each order. The nonlinear gradient element method can solve the stress in the thickness direction of the functionally graded plate, which provides a theoretical basis for the fatigue life analysis of the functionally graded plate.

Key words: graphene, nonlinear gradient element, stress, modal, finite element layered method

中图分类号:

TB332

张鹏程, 于印鑫, 李恩国, 赵天宇, 付涛. 基于非线性梯度单元的石墨烯功能梯度悬臂板力学特性[J]. 复合材料科学与工程, 2022, 0(8): 15-22.

ZHANG Peng-cheng, YU Yin-xin, LI En-guo, ZHAO Tian-yu, FU Tao. Mechanical properties of graphene functionally graded cantilever plate based on nonlinear gradient element[J]. COMPOSITES SCIENCE AND ENGINEERING, 2022, 0(8): 15-22.

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基于非线性梯度单元的石墨烯功能梯度悬臂板力学特性

Mechanical properties of graphene functionally graded cantilever plate based on nonlinear gradient element

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