波纹壳的格林函数方法

Method of Green's Function of Corrugated Shells

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具有型面锥度的浅波纹壳的非线性弯曲问题· 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· 在算例中,研究了具有球面度的浅波纹壳的弹性特征· 结果表明,由于型面锥度的引入,特征曲线发生显著变化,随着荷载的增加。

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green’s function. To solve the integral equations, expansion method was used to obtain Green’s function. Then the integral equations were reduced to the form with degenerate core by expanding Green’s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton’s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example, elastic characteristic of shallow corrugated shells with spherical taper was studied. Calculation results show that characteristic of corrugated shells changes remarkably.The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.