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A solution for an isotropic sector under anti-plane shear loadings

机译：反平面剪切载荷下各向同性扇形的解决方案

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摘要

In this study, the problem of an isotropic sector subjected to anti-plane shear loadings is investigated. The loadings were applied to the arc of the sector, and the radial edges of the sector were under traction-free or fixed conditions. Depending on these conditions, three problems, namely, free-free, fixed-free, and fixed-fixed edges were studied. A procedure using the finite Mellin transform combined with the Laplace transform was proposed for solving these problems. Explicit closed form solutions for the displacement and stress fields throughout the sector were obtained. The stress intensity factor (SIF) for each problem was analyzed using the obtained stress fields. It was determined that the SIF disappeared under the special condition of a fixed-fixed edge. Other special cases having anti-symmetric conditions were deduced from the derived solutions, and the results of these verified those cited in the literature as well as those obtained using finite element analysis (FEA).
机译：在这项研究中，研究了各向同性扇形承受反平面剪切载荷的问题。将载荷施加到扇形的弧上，扇形的径向边缘处于无牵引或固定状态。根据这些条件，研究了三个问题，即自由自由，固定自由和固定固定边缘。提出了使用有限梅林变换和拉普拉斯变换相结合的方法来解决这些问题。获得了整个部门中位移和应力场的显式封闭形式解决方案。使用获得的应力场分析每个问题的应力强度因子（SIF）。确定在特殊的固定边缘条件下，SIF消失了。从导出的解中推导出其他具有反对称条件的特殊情况，这些结果验证了文献中引用的结果以及使用有限元分析（FEA）获得的结果。

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