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首页> 外文期刊>International Journal of Solids and Structures >Non-axisymmetric warping of a heavy circular plate on a flexible ring support
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Non-axisymmetric warping of a heavy circular plate on a flexible ring support

机译：柔性环形支撑上的厚圆形板的非轴对称翘曲

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摘要

In this paper, we study the deformation and stability of a circular plate under its own weight and supported by a flexible concentric ring. Both bilateral and unilateral supports are considered. Von Karman's plate model is adopted to formulate the equations of motion. A nonlinear Galerkin's method based on two sets of assumed functions is used to discretize and solve the governing equations. Vibration method is used to predict the stability of the deformations. The linear analysis conducted previously predicts that the deformation is always axisymmetric. The current nonlinear analysis, however, shows that the axisymmetric deformation may become unstable when the dimensionless load, i.e., a ratio between the weight per unit area and the flexural rigidity of the plate, reaches a critical value. At this critical load, a stable non-axisymmetric deformation of the form cos nθ emerges following a pitch-fork bifurcation, where the integer n depends on the stiffness and the radius of the ring support. When the load increases further, more than one stable non-axisymmetric deformation may coexist. In a stable non-axisymmetric deformation with bilateral support, tension on the ring support may develop when the load reaches another critical value. In this situation, the circular plate will separate from the supporting ring in part of the angular region if the bilateral support is replaced by a unilateral one. The deformation with unilateral support is in general larger than the one with bilateral support.
机译：在本文中，我们研究了圆形板在自重作用下并由柔性同心环支撑的变形和稳定性。同时考虑了双边和单方面的支持。采用冯·卡曼（Von Karman）的平板模型来制定运动方程。基于两组假定函数的非线性Galerkin方法用于离散化和求解控制方程。振动法用于预测变形的稳定性。先前进行的线性分析预测变形始终是轴对称的。然而，当前的非线性分析表明，当无量纲载荷即板的单位面积重量与抗弯刚度之比达到临界值时，轴对称变形可能变得不稳定。在此临界载荷下，齿叉分叉后出现cosnθ形式的稳定的非轴对称变形，其中整数n取决于环支撑的刚度和半径。当载荷进一步增加时，可能会存在不止一种稳定的非轴对称变形。在带有双侧支撑的稳定的非轴对称变形中，当载荷达到另一个临界值时，环形支撑上可能会产生拉力。在这种情况下，如果将双侧支撑替换为单侧支撑，则圆形板将在部分角度区域中与支撑环分离。单侧支撑​​的变形通常要大于双侧支撑的变形。

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