弹性板边界元中计算边界高阶导数的渐近收敛积分方程

本文针对板弯曲边界元方法中计算边界曲率等高阶导数项时边界积分方程中出现的高阶奇异积分项,通过对未知挠曲函数作渐近展开并加以适当摄动,获得了渐近收敛的边界积分方程。采用这一方法计算板边界上的曲率分布,获得了满意的数值结果。

The Asymptotically Convergent Integration Technique for Calculating the Higher-order Derivatives at Boundary in Kirchhoff Plate Problems

By introducing the concept of asymptotic perturbation, a convergent boundary integral equation approach for calculating the higher-order derivatives at boundary in Kirchhoff plate bending problems is presented, which effectively solves the problem of so-called hyper-singular kernal functions appearing in such integral equations. Satisfactory numerical results are obtained by applying the technique to the calculation of curvature terms at plate boundary.