简支梯形底扁球壳弯曲问题的准格林函数方法

Green quasifunction method for bending problem of simply-supported trapezoidal shallow spherical shells

以简支梯形底扁球壳的弯曲问题为例,详细阐明了准格林函数方法的思想。即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将简支扁球壳弯曲问题的控制微分方程化为两个互相耦合的第二类Fredholm积分方程。边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程来表示问题的边界,以克服积分核的奇异性,最后由积分方程的离散化方程组可求得径向挠度。数值结果表明,该方法具有较高的精度。

The idea of Green quasifunction method is clarified in detail by considering bending of simply-supported trapezoidal shallow spherical shells.A Green quasi-function is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The differential equation of the bending problem of simply-supported trapezoidal shallow spherical shells is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,a new normalized boundary equation can be established such that the singularity of the kernel of integral equations is overcome.Finally,the radial deflection of shell is obtained by the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.