轴对称平面应变问题的广义热弹性解

超常传热条件下,热扰动在介质内以有限速度传播,导致材料的热力学行为较在常规传热下具有很大的不同.本文围绕轴对称平面应变问题展开研究,借助于Laplace正逆变换及其极限特性以及贝塞尔函数的渐近公式,推导了基于不同广义热弹性理论模型下轴对称平面应变问题的热弹性解,并对包含圆孔的无限大轴对称结构在内表面受热冲击作用的广义热弹性行为进行了分析.研究发现,当热扰动以有限速度传播时,各物理场的分布呈现阶段性分布,且在波前位置处,温度场和应力场存在阶跃现象;对于各物理场的描述,L-S和G-N理论给出相近的结果,而G-L理论则在描述位移场和应力场的分布时给出了反常的结果.利用本文推导得到的热弹性解可以清楚地获取各物理场与特征参量之间的函数关系,并可以准确地捕捉到波前的阶跃行为,便于超常传热行为的理论分析.

Generalized thermoelastic solutions for the axisymmetric plane strain problem

Thermal disturbance propagates in the elastic medium with a finite speed during the transient heat transfer, which leads to the thermal-mechanical behavior of materials being significantly different than that of conventional heat transfer. The axisymmetric plane strain problem is investigated in this paper, the generalized thermoelastic solutions for different generalized thermoelasticity are derived by means of the Laplace transform and its limit theorem and the asymptotic formulas of Bessel functions. A case of an infinite axisymmetric medium with a cylindrical hole under thermal shock is analyzed. It is pointed out that each of physical field has a phased distribution when the propagation of thermal disturbance with a finite speed, and both the temperature and stresses have jumps at the location of thermal elastic wavefront and thermal wavefront. The L-S and G-N theories predict similar patterns for the distributions of displacement, temperature and stresses in the transient thermal shock problem, but for G-L theory a Dirac-delta-type result for the stresses is predicted and the displacement is discontinuous at both the wavefronts.