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提出一种简单有效的计算方法,求解对称荷载作用下含正多边形孔洞无限平面体的弹性应力解。将孔洞内边界向两侧延伸至应力可忽略的远处,其外侧构成半无限平面体。相邻两个半无限平面体有一个公共域,其中一个半无限平面体顶边延伸至相邻两个半限平面体体内。孔洞内边界上面力是已知的,延伸至两相邻半无限平面体体内的顶边上面力可先假设,由弹性理论求出半无限平面体体内应力,再计算相邻半无限平面体顶边上面力,根据对称性得到本半无限平面体顶边上面力改进值,迭代求解直至收敛。该方法具有计算过程简单、精度高等优点。算例分析表明,该方法求解的工程尺度下孔洞周边应力场与复变函数方法、有限元方法计算结果吻合,拟合计算的孔边角点处应力奇异性次数与理论解基本一致。
A simple and effective calculation method is proposed to solve the elastic stress solution of an infinite planar body with regular polygon holes under the symmetrical load. The inner boundary of the hole is extended to the far side where the stress is negligible on both sides, and the outer side of the hole forms a semi-infinite plane body. The two adjacent semi-infinite planar bodies have a common domain, and the top of one semi-infinite planar body extends into the adjacent two semi-restricted body. The force above the inner boundary of the hole is known, and the force above the top edge in two adjacent semi-infinite planar bodies can be assumed first. The stress in the semi-infinite plane body is calculated by elasticity theory, and then the adjacent semi- Edge force, according to the symmetry of the top half of the infinite planar body to improve the value of the top edge, iterative solution until convergence. The method has the advantages of simple calculation process and high accuracy. The case study shows that the stress field around the hole is in agreement with the complex variable function method and the finite element method calculated by this method. The number of stress singularities at the edge of the hole calculated by the method is basically consistent with the theoretical solution.