用面力边界积分方程求解断裂力学J积分

Computation of J integral based on traction boundary integral equation

证明面力边界积分方程被积函数的散度等于零 ,应用 Stokes公式 ,对平面线弹性问题 ,将面力边界积分的求解转化为边界点的位移势函数的点值计算 .应用边界积分方程的求解结果 ,推导出 J积分亦可表示为边界点的积分势函数的点值计算 ,无需进行数值积分 。

Based on testifying the integrand divergence free property of the traction boundary integral equation and Stokes' theorem, the computation of traction boundary integral equation can be transformed into the evaluation of the displacement potential function on the boundary points. As the same way, applying the results of traction boundary integral equation, J integral can be also transformed into the computation of the J integral potential function at the points. No numerical integrals are needed in the whole calculation procedure. The numerical examples presented show the scheme has a excellent accuracy.