均布载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用格林函数方法，波纹膜片的非线性边值问题化为了非线性积分方程的求解。为了求解积分方程并防止发散，一个插值参数被引入到迭代格式中。计算表明，当载荷很小时，任何插值参数值均能保证迭代的收敛性，取插值参数值接近或等于1获得较快的收敛速度，而当载荷较大时，插值参数值不能取得过大。绘出了波纹膜片的特征曲线，得到的特征曲线可供设计参考。可以断言，当载荷不大时，特征曲线是近似线性的，随着载荷的增大，特征曲线开始向上弯曲，明显偏离线性。本文中提出的解决方法适应于任意轴向截面的波纹壳体。

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

Using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated diaphragm with a plane central region under uniform load is investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so-called interpolated parameter being important to prevent divergence is introduced into the iterative scheme. Computation shows that when loads are small, any value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate, when loads are large, interpolated parameter cannot be taken too large in order to assure convergence. The characteristic curves of the corrugated diaphragm are given. The obtained characteristic curves are available for reference to design. It can be concluded that when loads are small, the characteristic curves are approximately linear, when loads are large, the characteristic curves become bent upward and are obviously nonlinear. The solution method in this paper can be applied to corrugated shells of arbitrary diametral sections.