论文部分内容阅读
将含单孔洞无限平面体弹性应力场解析逼近方法进行推广,求解无限平面体内含多个任意排列、任意形状凸多边形孔洞在内边界上作用任意荷载下的弹性应力场。基于应力叠加原理,将含m个孔洞的无限平面体应力场视为m个仅含单个孔洞(称隔离孔洞)的无限平面体在洞口内边界上作用虚拟面力产生的应力场的叠加。对于每个隔离孔洞,其内边界上虚拟面力会在其他隔离孔洞内边界位置产生附加面力;一个孔洞内边界上由其他隔离孔洞产生的附加面力与其上虚拟面力之和最终等于实际作用外力。提出一种迭代方法求解所有隔离孔洞内边界上虚拟面力直至收敛,进而得到多孔洞外域弹性应力解。算例分析表明该方法获得的工程尺度范围的孔洞外域应力场与有限元法计算结果吻合良好;同时可计算孔洞边角处极近场应力,据此拟合得到应力奇异性次数与广义应力强度因子。该方法原理与计算过程简单,由于基于弹性力学解析解和高精度数值积分,其最终结果属解析逼近解。
The analytic approximation method for the elastic stress field of an infinite planar body with single hole is generalized to solve the elastic stress field under arbitrary load acting on the inner boundary of a polygonal hole with arbitrary shape and arbitrary shape in an infinite plane body. Based on the principle of stress superposition, the stress field of an infinite planar body with m holes is considered as the superposition of the stress field caused by the virtual surface force acting on an infinite planar body containing only a single hole (called an isolated hole). For each isolation hole, the virtual surface force on the inner boundary will generate additional surface force at the boundary position within the other isolation hole. The sum of the additional surface force generated by the other isolation holes in one hole boundary and its virtual surface force finally equals to the actual External forces. An iterative method is proposed to solve the virtual surface forces on all the inner boundaries of isolated voids until convergence, and then the elastic stress solution of the outer voids in the multi-holes is obtained. The case study shows that the stress field in the outer scale of the engineering scale obtained by this method is in good agreement with the finite element method. In addition, the near-field stress at the corner of the hole can be calculated, and the number of stress singularities and the generalized stress intensity factor. The principle of the method and the calculation process are simple. Due to the analytical solutions based on elastic mechanics and high-precision numerical integration, the final result is analytic approximate solution.