摘要
在带两个松弛时间参数的广义热弹性线性理论(Green和Lindsay理论)意义上,研究含一个球形空腔的功能梯度球形各向同性无限大弹性介质中,热弹性位移、应力和温度的求解方法.空腔表面无应力,但承受一个随时间变化的热冲击荷载作用.在Laplace变换域中,给出了一组矢量-矩阵微分方程形式的基本方程,并用特征值方法求解.应用Bellman方法进行数值逆变换.计算了位移、应力和温度,并给出相应的图形.结果表明,材料热物理性质的变化,对荷载响应的影响非常强烈.并与对应的均匀材料进行了比较和分析.
The determination of thermoelastic displacement, stresses and temperture in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory） are concerned with. The surface of the cavity is stress free and is subjected to a time dependent thermal shock. The basic equations were written in the form of a vector-matrix differenial equation in the Laplace transform domain which was then solved by eigenvalue approach. The numerical inversion of the transforms was carried out using Bellman method. The displacement, stresses and temperature were computed and presented graphically. It is found that the variation of thermo-physical properties of a material strongly influences the response to loading. A comparative study with the corresponding homogeneous material has also been made.
出处
《应用数学和力学》
CSCD
北大核心
2008年第10期1147-1160,共14页
Applied Mathematics and Mechanics
