波纹膜片的非线性稳定

应用轴对称旋转扁壳的基本方程,研究了在任意载荷作用下各种边界条件的波纹膜片的非线性稳定问题。采用格林函数方法,将扁壳的非线性微分方程组化为非线性积分方程组。再使用展开法求出格林函数,即将格林函数展开成特征函数的级数形式,积分方程就成为具有退化核的形式,从而容易得到非线性代数方程组。应用牛顿法求解非线性代数方程组时,为了保证迭代的收敛性,选取位移作为控制参数,逐步增加位移,求得相应的载荷。作为算例,首先研究了带中心平台三波纹膜片的局部失稳现象,然后讨论了由于缺陷的存在,波纹膜片有可能出现的极值点失稳,这是一种类似扁球壳的总体失稳现象。解答可供波纹膜片的设计参考。

NONLINEAR STABILITY OF CORRUGATED DIAPHRAGMS

By using the large deflection theory of axisymmetric shallow shells of revolution, the nonlinear stability of a corrugated diaphragm under arbitrary load and boundary conditions is investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations using Green’s function. To solve the integral equations, expansion method is used to obtain Green’s function. Then the integral equations are reduced to the form with degenerate core by expanding Green’s function into a series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton’s iterative method is utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, the central deflection is taken as the control parameter. Corresponding loads are obtained by increasing deflection step by step. As a numerical example, the local instability phenomenon of corrugated diaphragm with plane central region and three corrugations is studied. The snapping instability of corrugated diaphragm because of existence of defect is discussed, which is analogous to the total instability phenomenon in shallow spherical shells. The present work is expected to be useful for design of corrugated diaphragms.