论文部分内容阅读
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。
Based on the analytical solution of elastic stress at the top edge of the semi-infinite planar body, an analytic approximation method is proposed to solve the elastic stress field of an infinite planar body with any arbitrary convex shape under any load on the hole edge. The outer domain of n-shaped holes is divided into n semi-infinite planar bodies with the distribution of forces to be determined on the top edge. For the top edge of each semi-infinite planar body, the external force of the orifice part is known, while the force on the two side extensions is unknown. An effective iterative method is proposed to calculate the surface forces on all the extended edges in turn until they converge and the elastic stress field in the outer region of the hole is obtained. The method is simple in principle and has a clear calculation process. The final result is a analytic approximation solution based on the analytical solutions of elastic mechanics and one-dimensional high-precision numerical integration. The numerical results show that the stress field in the outer domain of engineering under the engineering scale obtained by this method is in good agreement with the results of complex variable function method and finite element method, indicating the effectiveness of the method. At the same time, the near-field stress at the corner of the hole can be calculated, and the generalized stress intensity factor fitted by the near-field stress at the hole corner has a very high accuracy. The number of stress singularities is consistent with the theoretical value of fracture mechanics.