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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Closed-form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti-plane shear
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Closed-form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti-plane shear

机译：正交各向异性弹性带在任意反平面剪切力作用下垂直于边缘的裂纹的封闭形式解

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摘要

A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading.For four frequently encountered constraint edges,i.e.free-free,clamped-clamped,free-clamped,orclamped-free edges,the Fourier series method isused to reduce triple series equations,and then toa mixed boundary value problem associated witha mode-III crack for each case toa singular integral equation. Closed-form solutions are derived for the resulting equations,and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading.Numerical results of the stress intensity factors for an eccentric,central,and edge crack are shown graphically for the case of uniform loading at the crack faces.Obtained formulae for determining stress intensity factors can be taken asa benchmark of numerical evaluations.The derived results are also applicable toan isotropic elastic strip withan anti-plane shear crack normal to the edges.
机译：在反平面剪切载荷作用下，分析了一条有限宽的正交各向异性弹性条。针对四个经常遇到的约束边，即自由边，夹紧边，自由夹紧边或自由边，采用傅里叶级数法简化了三级方程组然后，对于每种情况，与奇异积分方程有关的与III型裂纹相关的混合边值问题。得出方程式的封闭形式解，并得出计算任意变化载荷下内部裂纹和边缘裂纹的应力强度因子的公式。偏心，中心和边缘裂纹的应力强度因子的数值结果为裂纹面均匀受力情况下的图形化显示。获得的确定应力强度因子的公式可作为数值评估的基准。推导的结果也适用于具有垂直于边缘的抗平面剪切裂纹的各向同性弹性带。

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