高阶梯度对纳米纤维应变分布的影响

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (4): 404-409.

高阶梯度对纳米纤维应变分布的影响

崔宏伟徐凯宇

1.上海大学上海市应用数学和力学研究所,上海 200072; 2.上海大学理学院,上海 200444

出版日期:2009-08-30 发布日期:2009-08-30
通讯作者: 徐凯宇(1956～)，男，教授，博士生导师，研究方向为微纳米力学、半导体材料力学. E-mail:kyxu@staff.shu.edu.cn
基金资助:
上海市基础研究重点资助项目（04JC14034）

Influence of High-Order Gradient on Strain Distribution of Nanofibers

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. College of Sciences, Shanghai University, Shanghai 200444, China

Online:2009-08-30 Published:2009-08-30

摘要/Abstract

摘要：

研究纳米纤维受拉力作用时静态应变的轴向分布规律.根据弹性梯度理论,提出一个新的本构模型.讨论高阶应变梯度对纳米纤维轴向应变分布的影响.忽略轴向应变高阶小量,通过基本方程和变分原理得到平衡控制方程,再通过变分法和残余权值法，导出全部的经典和非经典边界条件.得到的解析计算结果显示出高阶应变梯度对尺度和边界效应的影响.

关键词: 纳米纤维；高阶应变梯度；变分法；应变分析

Abstract:

This paper studies the static strain properties of a gradient nanofiber in tension. A new constitutive model based on gradient elasticity is proposed. The influence of high-order gradient of strain on static analysis of nanofibers is discussed. After neglecting the higher infinitesimal strain along nanofiber’s longitudinal direction, the governing equation of equilibrium is obtained with combination of the basic equation and a proposed variational principle. By using both variational and weighted residuals methods, all classical and nonclassical boundary conditions are determined. Some influences of high-order gradient of stain on size and boundary effects are identified and assessed by analytical expressions. 

Key words: nanofibers; high-order gradient; variational method; strain analysis

中图分类号:

O343.9

崔宏伟徐凯宇. 高阶梯度对纳米纤维应变分布的影响[J]. 上海大学学报(自然科学版), 2009, 15(4): 404-409.

CUI Hong-Wei, XU Kai-Yu. Influence of High-Order Gradient on Strain Distribution of Nanofibers[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(4): 404-409.