非均布面内变温下环形薄板的热屈曲

The Thermal Buckling of Annular Plates under a Nonuniformly Distributed Inplane Temperature

本文研究了内外周边完全夹紧的各向同性环板在面内非均匀温度场作用下的热弹性稳定性问题。由薄板大变形理论建立了环板热屈曲问题的数学模型,并简化为一个偶合的二阶非线性常微分方程边值问题,重点讨论和求解了非线性方程在其平凡解处的线性化问题,得到了反映环板失稳特性的临界温度曲线。在给定几何参数下,数值计算表明这些曲线是非常近似的直线;当温度分布均匀时,临界曲线退化为一些临界点。

This paper deals with the thermal buckling of a thin, isotropic annular plate with tightly clamped periphery under a nonuniformly distributed inplane temperature. On the basis of the theory of the thin plates with large deflections, the mathematical model for this problem is established and then simplified into a system of 2-order nonlinear ordinary differential equations. A theoretical analysis is performed on the linearized equations of the nonlinear ones, and critical temperature curves charaterizing the unstability of the annular plate are obtained. For some given geometric parameters, the critical temperature curves obtained by means of a numerical method are approximately liner. They will retrograde into some critical points when temperature is uniformly distributed.