集中载荷作用下具有光滑中心波纹膜片的非线性分析

波纹膜片是一种薄壳弹性体，由于它的参数很多，又相互制约，所以使得它的设计很复杂。在大多数位移式仪器仪表中，要求波纹膜片产生至少和膜片厚度是同样数量级的弹性位移。这就要求使用薄壳的几何非线性理论进行分析。大多数学者研究波纹膜片的弯曲问题，是采用扁壳理论讨论具有浅波纹的膜片。而工程实际中，经常遇到深波纹膜片，这就要求从一般壳体大挠度方程进行求解。本文采用轴对称旋转壳体的简化Re-issner方程。研究了在中心集中载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用积分方程方法，可以获得膜片的特征关系（载荷-中心挠度关系）和应力分布。文末给出实例计算的数值结果。

Nonlinear Analysis of Corrugated Diaphragm with Plane Central Region under Concentrated Load

Corrugated diaphragm is a type of elastic thin shells. Its design is very complicated because of too many parameters that are influenced each other. In a number of instruments measuring displacements, the elastic displacement is at least the same order as its thickness, so that it is necessary to use geometrical nonlinear theory of thin shells to analyze. In most cases, only the problem of shallow corrugated diaphragm was analyzed by using the theory of shallow shells. In engineering practice, a corrugated diaphragm with deep corrugation is often encountered. The large deflection theory of shells must be used to solve such corrugated diaphragm. By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated diaphragm with plane central region under concentrated load had been investigated. The characteristic curves and the stress distribution in the plate could be obtained by means of the method of integral equation. The numerical results of an example are given.