Two trigonometric quadrature formulae for evaluating hypersingular integrals
Two trigonometric quadrature formulae for evaluating hypersingular integrals
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DOI：
10.1002/nme.582
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发表时间：
2003-01
影响因子：
2.9
通讯作者：
Philsu Kim;U. J. Choi
中科院分区：
文献类型：
--
作者：
Philsu Kim;U. J. Choi
在Cauchy主值积分三角求积公式的基础上，给出了计算超奇异积分${\int\hskip-0.33cm=}_{-1}^{1} w（\tau）g（\tau）/（\tau-t）^{2} \，{\rm d}\tau$的两个三角求积公式，一个是非插值型的，一个是插值型的.该公式在实际横坐标上采用变量余弦变换和三角多项式插值。快速三项递归关系，用于评估正交权重。数值试验进行了使用目前的公式。作为应用，考虑了两个简单裂纹问题。一个是包含垂直于其边界的内部裂纹的半无限平面，另一个是受到法向和剪切力的中心裂纹板。发现本方法通常给出上级结果。版权所有© 2002年约翰威利父子有限公司。
Two trigonometric quadrature formulae, one of non‐interpolatory type and one of interpolatory type for computing the hypersingular integral ${\int\hskip-0.33cm=}_{-1}^{1} w(\tau)g(\tau)/(\tau-t)^{2} \,{\rm d}\tau$ are developed on the basis of trigonometric quadrature formulae for Cauchy principal value integrals. The formulae use the cosine change of variables and trigonometric polynomial interpolation at the practical abscissae. Fast three‐term recurrence relations for evaluating the quadrature weights are derived. Numerical tests are carried out using the current formula. As applications, two simple crack problems are considered. One is a semi‐infinite plane containing an internal crack perpendicular to its boundary and the other is a centre cracked panel subjected to both normal and shear tractions. It is found that the present method generally gives superior results. Copyright © 2002 John Wiley & Sons, Ltd.