极坐标系下扇形截面杆件扭转问题的有限差分法

The Finite Difference Method for Torsion Problem of Bars with Sectorial Cross-sections in Polar Coordinate System

导出了极坐标系下扇形截面杆件扭转问题的差分格式 ;用逐次超松驰迭代法求出了扭转应力函数差分值 .采用复化二维辛普生求积公式计算了截面的相当极惯性矩 ,求出了相应的扭转应力的差分解 ,并对张角为 2π的扇形截面计算了其裂纹尖端附近的第三型应力强度因子 .

A torsion difference scheme of the bar with sectorial cross-section is developed in polar coordinate system. Using the successive over-relaxation method, the difference values of the torsion stress function are determined. With the compound two-dimensional Simpson quadrature formula, the equivalent polar moment of inertia of the sectorial cross-section is obtained. Consequently, the difference solution to the torsion stress is given. As the field angle is 2π, the stress intensity factor of mode Ⅲ near the crack tip is calculated.