非局部Kelvin粘弹性直杆受轴向拉力作用的应变分析  

Strain Analysis of Nonlocal Viscoelastic Kelvin Bar in Tension

作　　者：赵雪川[1] 雷勇军[1] 周建平[1] 

机构地区：[1]国防科技大学航天与材料工程学院,长沙410373

出　　处：《应用数学和力学》2008年第1期62-68,共7页Applied Mathematics and Mechanics

基　　金：Project supported by the Science Foundation ofNational University of Defense Technology(No.JC0601-01)

摘　　要：在Kelvin粘弹性体模型中引入非局晨应力应变关系,得到了粘弹性体的非局部本构方程,研究了符合该种本构关系的直杆受到轴向拉力作用的应变响应问题.首先通过变换将应变响应的求解问题转化为Volterra积分方程形式,然后采用对称的指数型核函数,利用Neumann级数展开求解了Volterra积分方程,得到了直杆的应变场.数值算例的计算结果显示了直杆受轴向拉力作用后的蠕变过程,当时间趋近无穷大时,计算结果则退化为非局部弹性计算结果.Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity was obtained and the strain response of a bar in tension was studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the close form solution of strain field of the bar was obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.

关 键 词：非局部理论 Kelvin粘弹性体 Neumann级数 杆 应变分析 

分 类 号：O345[理学—固体力学]