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Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

机译:任意角度防滑楔中二维斯托克斯流奇点的解析解

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摘要

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.
机译:提出了一种分析方法,该方法可以找到由任意角度的楔形中的斯托克斯流的基本奇异点生成的流。具体来说,我们针对点应力小波奇异性并满足楔形两个壁上的无滑移边界条件而生成的流的流函数求解双谐方程。该方法易于适应任何其他奇异类型,充分考虑了在楔形角处出现的任何先验奇异性。该方法也适用于弹性固体的平面应变/应力问题,其中双谐波方程还控制着艾里应力函数。

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