有限元法求解广义热弹耦合一维热冲击问题

FINITE ELEMENT METHOD TO A GENERALIZED ONE-DIMENSIONAL THERMO-ELASTIC COUPLED PROBLEM SUBJECT TO A THERMAL SHOCK

为了避免积分变换方法在求解Lord-Shulman(L-S)型广义热弹性耦合问题时由于数值反变换所引起的计算精度降低的问题,该文应用直接有限元方法,求解了基于L-S型广义热弹性理论的窄条薄板受热冲击作用的动态响应问题,结果表明,该方法对求解L-S型广义热弹性耦合的一维问题具有很高的精度。该文给出了L-S型广义热弹性理论下的热弹耦合的控制方程,建立了L-S型的广义热弹性问题的虚位移原理,推导得到了相应的有限元方程。计算得到了窄条薄板中无量纲温度、无量纲位移及无量纲应力的分布规律,从温度分布图上可以清晰地观察到热波波前的特有属性,即热波波前处存在明显的温度梯度的突变。

In order to avoid the accuracy loss encountered in the process of numerical inversion in an integral transformation method adopted to solve generalized thermoelastic coupled problems in the context of Lord-Shulman（L-S） theory,the finite element method is used to solve a L-S type generalized thermoelastic coupled dynamic problem of a thin slim strip.The results show that the finite element method is very valid to obtain high calculation accuracy for L-S type generalized one-dimensional themoelastic coupled problem subjected to a thermal shock.The L-S type generalized thermoelastic coupled governing equations,the general form of virtual displacement principle as well as the corresponding finite element equations are formulated in this paper.The distributions of dimensionless temperature,dimensionless displacement and dimensionless stress are displayed graphically.From the distribution of temperate,the unique characteristic of heat wave can be observed clearly in the location of heat wave front where a sharp change of temperature gradient occurs.