特性参数与温度相关的二维广义热弹问题的动态响应

基于Green-Lindsay广义热弹性理论,研究了材料特性参数与温度相关、受热冲击作用的半无限大体的二维热弹动态响应问题。采用了有限元法,对得到的非线性有限元方程在时域中进行了直接求解,得到了无量纲的温度、位移、应力等物理量的分布规律。结果表明:各物理量的幅值随时间的增大而增大,且其非零值仅处在一个有限的区间内;与温度相关的特性参数对各物理量有显著影响,体现在各物理量的幅值随之降低。

Characteristic Parameter and Dynamic Response of Temperature Related Two Dimensional Generalized Thermo-elastic Problem

Based on the Green-Lindsay generalized thermal-elasticity theory,research the material characteristic parameter and two dimensional thermo-elastic dynamic response problems of semi-infinite body which related temperature and under the function of thermal shock.Propose the control equation of problem and due to the material characteristic is related with temperature,it cause the control equation presents nonlinearity.In order to solve this nonlinear control equation,it adopts the finite element method.By the mean of derivation,obtain the nonlinear finite element equation and direct solve the obtained nonlinear finite element equation in the time domain,then obtain the dimensionless distribution rule of each physical quantity such as temperature,displacement and stress.In the calculation,examine the change rule of each physical quantity along with time and temperature related material characteristic parameter,the results show that the amplitude of each physical quantity increases along with the increase of time and its nonzero value only locates within a finite interval;the temperature related characteristic parameter has great influence on each physical quantity and it is reflected in the tendency that the amplitude of each physical quantity decreases along with it.