Abstract Prestressed structures are frequently encountered in civil engineering. This paper gives a theoretical analysis of a cracked orthotropic elastic plane with initial stress. The problem of an orthotropic composite with a crack parallel to a material principal axis under initial stress along the crack line reduces to a mixed boundary value problem. It is solved using the Fourier transform. Application of boundary and continuity conditions leads to dual integral equations. An analytical solution can be obtained. Full incremental elastic field in an infinite prestressed cracked orthotropic composite is derived explicitly for linearly distributed loading on the crack faces. The fracture parameters such as incremental stress intensity factor (SIF), crack opening displacement (COD), and the energy release rate (ERR) are all obtained. The results for a prestressed isotropic elastic medium with a crack can be reduced from the present. When prestress is removed, the explicit expressions of the elastic field induced by a crack embedded in an orthotropic composite are recovered. Finally, the influence of initial stress on the elastic stress field, incremental SIF, COD and ERR for a cracked orthotropic elastic plane are presented graphically.

中文翻译：

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预应力正交各向异性材料中由 I 型裂纹引起的全增量弹性场

摘要 预应力结构在土木工程中经常遇到。本文给出了具有初始应力的裂纹正交各向异性弹性平面的理论分析。正交各向异性复合材料在沿裂纹线的初始应力下具有平行于材料主轴的裂纹的问题简化为混合边界值问题。它是使用傅立叶变换解决的。边界和连续性条件的应用导致对偶积分方程。可以得到解析解。无限预应力开裂正交各向异性复合材料中的全增量弹性场被明确推导出用于裂纹面上的线性分布载荷。获得了增量应力强度因子（SIF）、裂纹张开位移（COD）、能量释放率（ERR）等断裂参数。具有裂纹的预应力各向同性弹性介质的结果可以从现在开始减少。当去除预应力时，由嵌入在正交各向异性复合材料中的裂纹引起的弹性场的显式表达式被恢复。最后，以图形方式显示了初始应力对开裂正交各向异性弹性平面的弹性应力场、增量 SIF、COD 和 ERR 的影响。