含单孔洞无限平面体弹性应力场解析逼近方法
发布时间：2018-12-12 05:24
【摘要】：基于半无限平面体顶边集中力作用下的弹力应力解析解,提出一种解析逼近方法,求解含单个任意形状凸孔洞无限平面体在孔边任意荷载作用下的弹性应力场。将n边形孔洞外域划分为顶边上作用待定面力分布的n个半无限平面体。对于每个半无限平面体的顶边,其孔口部分外力已知,而两侧延伸部分上面力未知。提出一种有效的迭代方式依次计算所有延伸边上的面力,直至收敛,同时得到孔洞外域的弹性应力场。该方法原理简单、计算过程明了;由于基于弹性力学解析解和一维高精度数值积分,其最终结果属解析逼近解。算例表明,该方法获得的工程尺度下的孔洞外域应力场与复变函数方法、有限元方法计算结果非常吻合,表明方法的有效性。同时,可计算孔洞角点处近场应力,由孔洞角点处近场应力值拟合得到的广义应力强度因子具有极高精度,且应力奇异性次数与断裂力学理论值一致。
[Abstract]:Based on the analytical solution of elastic stress under concentrated force at the top edge of a semi-infinite plane body, an analytical approximation method is proposed to solve the elastic stress field of an infinite plane body with a single convex hole with a single arbitrary shape under arbitrary loads on the edge of a hole. In this paper, the external region of an n-side hole is divided into n semi-infinite plane bodies with the force distribution of the undetermined plane acting on the top edge. For the top edge of each semi-infinite plane body, the external force of the orifice part is known, but the upper force of the two side extension part is unknown. An effective iterative method is proposed to calculate the surface forces of all the extended edges in turn until they converge and to obtain the elastic stress field outside the hole at the same time. The principle of the method is simple and the calculation process is clear, because of the analytical solution of elastic mechanics and one-dimensional high precision numerical integration, the final result is an analytical approximation solution. The numerical results show that the stress field of the external hole field obtained by the method is in good agreement with the complex variable function method, and the finite element method is in good agreement with the results obtained by the finite element method, which shows the effectiveness of the method. At the same time, the near field stress at the hole corner can be calculated. The generalized stress intensity factor fitted from the near field stress value of the hole corner has a high accuracy, and the number of stress singularities is in agreement with the theoretical value of fracture mechanics.
【作者单位】： 合肥工业大学土木与水利工程学院;合肥工业大学土木工程结构与材料安徽省重点实验室;
【分类号】：TU45
，
本文编号：2374000
[Abstract]:Based on the analytical solution of elastic stress under concentrated force at the top edge of a semi-infinite plane body, an analytical approximation method is proposed to solve the elastic stress field of an infinite plane body with a single convex hole with a single arbitrary shape under arbitrary loads on the edge of a hole. In this paper, the external region of an n-side hole is divided into n semi-infinite plane bodies with the force distribution of the undetermined plane acting on the top edge. For the top edge of each semi-infinite plane body, the external force of the orifice part is known, but the upper force of the two side extension part is unknown. An effective iterative method is proposed to calculate the surface forces of all the extended edges in turn until they converge and to obtain the elastic stress field outside the hole at the same time. The principle of the method is simple and the calculation process is clear, because of the analytical solution of elastic mechanics and one-dimensional high precision numerical integration, the final result is an analytical approximation solution. The numerical results show that the stress field of the external hole field obtained by the method is in good agreement with the complex variable function method, and the finite element method is in good agreement with the results obtained by the finite element method, which shows the effectiveness of the method. At the same time, the near field stress at the hole corner can be calculated. The generalized stress intensity factor fitted from the near field stress value of the hole corner has a high accuracy, and the number of stress singularities is in agreement with the theoretical value of fracture mechanics.
【作者单位】： 合肥工业大学土木与水利工程学院;合肥工业大学土木工程结构与材料安徽省重点实验室;
【分类号】：TU45
，
本文编号：2374000
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