经典梁理论对氮化硼纳米管弯曲变形的精确解  

Exact Solutions of the Bending Deflection of BNNTs by Classical Beam Theory

作　　者：颜建伟 程超 金超奇 YAN Jianwei;CHENG Chao;JIN Chaoq(Engineering Research&Development Centre for Underground Technology of Jiangxi Province,School ofCivil Engineering and Architecture,East China Jiaotong University,Nanchang 330013,China)

机构地区：[1]华东交通大学土木建筑学院江西省地下空间技术开发工程研究中心,南昌330013

出　　处：《现代应用物理》2023年第1期210-220,共11页Modern Applied Physics

基　　金：国家自然科学基金资助项目(20202ZDB01001,12072112)。

摘　　要：本文利用连续介质理论中的欧拉梁理论和铁木辛柯梁理论对单壁氮化硼纳米管在横向荷载作用下的剪切弯曲变形进行预测。理论中所用的氮化硼纳米管厚度分别选择层间距0.333 nm和本征厚度0.090 6 nm,并与分子动力学模拟的结果进行比较。结果表明:采用单原子材料厚度为0.090 6nm进行计算得到的结果与利用分子动力学模拟结果吻合较好;而采用层间距厚度的连续梁理论计算结果与分子动力学结果有很大偏差且明显低于分子动力学结果。这表明:经典连续介质理论适用于纳米材料领域,引入尺度参数的广义连续介质理论实质上修正了材料的弯曲刚度,使其与分子模拟结果相吻合。In this paper,the Euler beam theory and Timoshenko beam theory in continuum theory are used to predict the shear bending deflection of single walled boron nitride nanotubes(BNNTs)under lateral loading.The thickness of BNNTs used in theory was chosen as the layer spacing of 0.333 nm and the intrinsic thickness of 0.0906 nm,respectively,and compared with the results of molecular dynamics simulation.The results show that the calculated results using a single atomic material thickness of 0.0906 nm are in good agreement with those using molecular dynamics simulation.However,the calculated results of the continuous beam theory using the interlayer spacing thickness of 0.333 nm have a significant deviation from the molecular dynamics results and are significantly lower than the molecular dynamics results.This indicates that the classical continuum theory is applicable to the field of nanomaterials,and the introduction of the generalized continuum theory with scale parameters substantially corrects the bending stiffness of materials,making it consistent with molecular simulation results.

关 键 词：梁理论 分子动力学 氮化硼纳米管 弯曲变形 材料厚度 

分 类 号：O346[理学—固体力学]