嵌入无限大弹性板中圆板的热屈曲分析 1)

分析了嵌入无限大弹性板中的圆板在变温时的热屈曲问题。由于圆板的热膨胀系数与无限大弹性板的热膨胀系数不同，温度变化时圆板中会产生压应力。当压应力达到其临界值时，圆板会发生热屈曲。首先，基于弹性力学平面应力问题的基本理论，得到圆板和无限大弹性板的应力和位移；然后建立圆板热屈曲的控制微分方程，求得临界屈曲温度的解析解和数值解，着重讨论圆板和无限大弹性板的材料物性参数的关系对圆板临界屈曲温度的影响。

THERMAL BUCKLING ANALYSIS OF CIRCULAR PLATE EMBEDDED IN AN INFINITE ELASTIC PLATE 1)

This paper analyzes the thermal buckling of the circular plate embedded in an infinite elastic plate. As the temperature changes, the compressive stress will be generated in the circular plate due to the difference of the thermal expansion coefficient between the circular plate and the infinite elastic plate. When the compressive stress reaches the critical value, the thermal buckling will occur. Firstly, based on the theory of the plane stress problem of elasticity, the stress and the displacement of the circular plate and the infinite elastic plate are obtained. Then, the governing differential equation of the thermal buckling of the circular plate is derived. Analytical and numerical solutions of the critical buckling temperature are obtained. The effect of the difference of the material properties between the circular plate and the infinite elastic plate on the critical buckling temperature is discussed.