具有中心弹性约束的圆膜片的非线性弯曲

Nonlinear Bending of Circular Diaphragm with a Central Elastic Constraint

本文应用ｖｏｎＫａｒｍａｎ薄板理论．求解了具有中心弹性约束的圆薄板在均布横向力作用下的非线性弯曲问题。在求解其幂级数解中，文中采用了与物理意义相联系的嵌套的牛顿迭代法，使计算时间大为减少。其所得结果为这类敏感弹性元件的应用提供了可靠的数据。

From the von Karman plate theory, the nonlinear bending problem of the central elastic constraint supported circular thin plate/diaphragm under uniformly distributed pressure in lateral haw been researched in this paper. We use the Newton's iterative methods connected to the physical meaning to solve the power series solutions of the problems so that the calculations can be much more reduced. The obtained results are used to provide reliable date for the design of this type of the sensitive elastic elements.