实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学解

AN ANALYTICAL SOLUTION OF A SOLID CYLINDER SUBJECTED TO THERMAL SHOCK UNDER DYNAMIC THERMOELASTIC AXISYMMETRIC PLANE STRAIN CONDITION

利用分离变量法 ,成功地给出了各向同性实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学问题的解析解 .运用此方法 ,可以避免积分变换且易于实现数值计算 .在数值结果中 ,与拟静态问题和均匀热冲击情形进行了比较 ,表明惯性项对中心处应力响应影响不大 ,而热传导的过程能大大减低中心处的热应力 .

By using the separation of variables method, the analytical solution of a solid cylinder subjected to thermal shock at the external surface for thermoelastic axisymmetric plane strain dynamic problems is performed successfully. By means of the present method, integral transform can be avoided and the numerical results are easily completed.Comparisons between the present study's and quasi-static problems as well as the uniform thermal shock are also made. It is concluded that the inertial term has little influence on the thermal stresses at the center, while the heat conduction process can greatly depress the thermal stresses at the center.