The paper addresses the problem of asymmetric buckling of geometrically imperfect circular plates undergoing large axisymmetric deflections under thermal loading. The plate edge is assumed to be immovable in the radial direction and elastically restrained against bending rotation. The plate material is graded in the thickness direction and dependence of the material properties on temperature is taken into account. The governing equations are derived using the von Karman nonlinear plate theory and the concept of physically neutral surface. It is shown that, when subjected to increasing temperature, the plate initially bends into a figure of revolution and then buckles into asymmetric mode with local circumferential waves. To determine the critical temperature rise, a nonlinear eigenvalue problem is formulated by linearizing the governing equations about the axisymmetric state of equilibrium and solved using power-series expansions. The effect of temperature-dependent material properties, rotational spring stiffness and initial geometric imperfection on the critical temperature rise and buckling mode shapes is studied.

中文翻译：

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具有旋转约束边缘的不完美 FGM 圆板的非对称热屈曲

本文解决了几何不完美圆板在热载荷下发生大轴对称挠曲的不对称屈曲问题。假定板边缘在径向方向上是不可移动的并且弹性地限制弯曲旋转。板材在厚度方向上分级，并考虑了材料特性对温度的依赖性。控制方程是使用 von Karman 非线性板理论和物理中性表面的概念推导出来的。结果表明，当温度升高时，板首先弯曲成旋转图形，然后屈曲成具有局部圆周波的不对称模式。为了确定临界温升，通过线性化关于平衡轴对称状态的控制方程来制定非线性特征值问题，并使用幂级数展开求解。研究了与温度相关的材料特性、旋转弹簧刚度和初始几何缺陷对临界温升和屈曲模式形状的影​​响。