对偶边界元法中对数奇异积分的计算

CALCULATION OF LOGARITHMIC SINGULARITIES INTEGRAL IN DUAL BOUNDARY ELEMENT METHODS

采用三次多项式坐标变换计算边界元积分的方法 ,对对偶边界元法中含对数奇异积分的计算进行研究。几个解析积分算例和运用对偶边界元法对二维平面裂纹问题裂尖应力强度因子的计算结果表明 。

The calculation of integrals with logarithmic singularities in dual boundary element methods have been discussed by the third degree polynomial coordinate transformation. The equations of the dual boundary element method (DBEM) are the displacement and the traction boundary integral equations. When the displacement equations is applied on one of the crack surfaces and the traction equations is applied on the other, general mixed mode crack problems can be solved in a single region boundary element formulation, with both crack surface discretized with discontinues quadratic boundary element, at the intersection between a crack and an edge where discretized semi discontinues quadratic boundary element. For the creation of the influence matrices, computation of surface integrals with logarithmic singularities must be calculated. By using the non linear co ordinate transformation and some results of analytical integral, the evaluation of stress intensity factor of two dimensional crack problems have been calculated. Numerical results show that the implementation described herein is more efficient than element subdivision for general boundary element applications.