用边界元法计算双曲线缺口圆柱的弯曲中心

Application of Boundary Element Method to Calculation of Flexural Center of Circular Cylinder with Hyperbolic Notch

使用ＳａｉｎｔＶｅｎａｎｔ 弯曲理论及调和函数的基本解，将任意截面柱体的ＳａｉｎｔＶｅｎａｎｔ 弯曲问题归为解两个非耦合的以弯曲函数Ψ（ｘ，ｙ） 和扭转函数φ（ｘ，ｙ） 为未知函数的边界积分方程．基于上述结果并通过对横截面上扭矩的计算，导出了用于计算柱体弯曲中心的理论公式．可以指出，若横向力作用于弯曲中心，则柱体只产生单一的弯曲而无附加的扭转．以双曲线缺口圆柱的ＳａｉｎｔＶｅｎａｎｔ 弯曲为例，通过对边界积分方程的离散，用边界元法对其作了计算，最后求得了柱体的扭转刚度、弯曲中心及应力分布等数值结果。

By use of the flexural theorem of Saint-Venant and the fundamental solution of harmonic function, the Saint-Venant flexural problem of a cylinder with an arbitrary cross section is reduced to two uncoupled boundary integral equations with unknown flexural function Ψ(x,y) and unknown torsion function φ(x,y) .On the basis of these results and through calculation of the torsion moment on the cross section, a theoretical formula of the flexural center is derived for the cylinder. It is shown that if the lateral force is applied at the flexural center, then only the bending but not the additional torsion will occur. In order to explain the use of the method proposed in this paper, an example of the Saint Venant flexure is calculated for a circular cylinder with a hyperbolic notch through discretion of the boundary integral equations and by use of the boundary element method. Finally, the numerical results of torsion rigidity, flexural center and the distribution of stresses of the cylinder are obtained and some results coincide well with theoretical results. Thus the present method is verified.