关键词: 正多边形孔洞, 对称荷载, 应力, 应力奇异性次数, 弹性理论

Abstract: A simple and effective method is proposed for elastic stress analysis of an infinite plane including a regular polygon hole, subjected to symmetrical loading on the hole boundaries. The inner boundary of the hole is extended to far point where the magnitude of stresses is negligible. The outer area of the boundary consists of a semi-infinite plane body. The adjacent two semi-infinite plane bodies share a common domain, the extending boundary of one semi-infinite plane body stretching into another. With the values of loadings on the inner boundaries of the hole known and the traction on the boundaries stretching into other semi-infinite plane bodies firstly presumed, the stress distribution within the semi-infinite plane body can be calculated using the theory of elasticity. By symmetry, the traction on the two boundaries stretching into adjacent semi-infinite plane bodies can be calculated, and further modified with iteration method, and converge to analytical solutions. The presented method features straightforward computation process and high precision. The results of presented examples show that the stresses of engineering scale thus obtained by this method agree well with ones obtamed by function of complex variable method and finite element method; and the order of stress singularity near the corner of hole is also approximately equal to theoretical value.

Key words: regular polygon hole, symmetric loading, stress, order of stress singularity, theory of elasticity