复合载荷作用下带边缘大波纹膜片的非线性弯曲

采用轴对称旋转壳体的简化Reissner方程，研究了在复合载荷作用下具有硬中心的带边缘大波纹膜片的非线性弯曲问题。应用格林函数方法。将波纹膜片的非线性边值问题化为非线性积分方程进行求解。为了求解积分方程并防止发散。引入一个插值参数到迭代格式中，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。绘出了不同载荷组合下波纹膜片的特征曲线。得到的特征曲线可供设计参考。由于均布压力和中心集中载荷的共同作用。将产生比均布压力单独作用更大的挠度。提出的解决方法适应于任意轴向截面的波纹壳体。

Nonlinear Bending of Corrugated Diaphragm With Large Boundary Corrugation Under Compound Load

By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a non-deformable rigid body at the center under compound load are 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 important to prevent divergence is introduced into the iterative format. 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 \ 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 for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.