New Method For Stress Analysis Of Holes And Cracks

Analysis of stresses around the hole and crack tip is a classic problem of elasticity. Although numerical methods have been widely used in engineering problems, theoretical research is still being explored,(1) A simple and effective method is proposed for elastic stress analysis of an infinite plane containing a polygon hole, subjected to arbitrary loading on the hole boundaries. The inner boundary of the hole is extended to far point where magnitude of stresses is negligible, the area on the outside of the boundary consisting a half-plane body. The adjacent two half-plane bodies share a common domain, the extending boundary of one half-plane body stretching into another half-plane body. With the values of loadings on the inner boundaries of the hole known and the traction on the boundaries stretching into other half-plane bodies firstly presumed, the stress distribution with the half-plane body can be calculated using the theory of elasticity. Then, the traction on the adjacent half-plane boundary stretching into the half-pane can be calculated, and further used to calculated stress distribution with the adjacent half-plane body. As so on, the traction on two boundaries stretching into adjacent half-plane bodies can be calculated, and further modified with iteration scheme, and converge to analytical solutions. The presented method features straightforward computation process and high precision. The results of presented examples show the stresses around the hole obtained by this method agree well with those 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.(2) An effective method called the "method of pseudo-tractions" is used for the calculation of stress field around multiple holes in an elastic infinite plane. The method uses a superposition scheme to break the problem into a number of isolated-hole problems, each loaded by undetermined traction on the hole boundary. Holes interaction is accounted for by the stresses generated by an isolated hole at a location of another hole when the former is subjected to unknown traction on the hole boundary. Based on the presented method for the stress analysis of a single hole in an infinite plane, the outer domain of the hole is divided into half-planes. By considering self-consistency of unknown tractions on the boundary of half-planes and multiple holes interaction, new iteration scheme for unknowns is formulated.Accurate stress distribution at the outward-concave corner of a concave hole is not available by complex variable method. In this paper, the problem of a concave hole in an infinite plane can be considered as two convex holes by dividing the outward-concave corner into two outward-convex corner. The dividing boundary is free of load.(3) Using the "method of pseudo-tractions", the problem of a half-plane containing multiple holes can be solved. The superposition technique is used to divided the problem into a series of isolated-hole problems and one homogenous half-plane problem. The boundary of half-plane is loaded by undetermined traction, which generates stresses at a location of multiple holes. Each hole is subjected to unknown traction on the hole boundary, which cause stresses at a location of another hole and half-plane boundary. Based on the proposed method of the isolated hole problem, the outer domain of the hole is divided into half-planes. With the self-consistency of unknown tractions on the boundary of formed half-planes, interaction effects among multiple holes and half-plane boundary, new iteration scheme for unknowns is formulated.(4) In this paper, problem of foundation excavation or edge notch can be considered as a buried hole with zero depth in a half-plane, by assuming that the imaginary boundary of the hole is free of load. With enough large width, stress field in one foundation pit side can be approximately equivalent to the stress in an elastic slope.(5) Based on stress superposition principle, the problem of a finite width strip containing multiple holes or isolated hole can be considered as a series of isolated-hole problems and two homogeneous half-plane problems, The half-plane boundary, formed by one strip border, is loaded by unknown traction, which induces stresses at a location of multiple holes and another strip border. Each hole is subjected to unknown traction on the hole boundary, which cause stresses at a location of another hole and two strip borders. By considering self-consistency of unknown tractions on the boundary of half-planes dividing by the outer domain of isolated hole, and interaction effects among multiple holes and two strip borders, new iteration scheme for unknowns is formulated.(6) The results of presented examples show the stresses related to the hole or foundation pit obtained by this method compare favorably with those of finite element method, and the order of stress singularity near the corner of hole is also approximately equal to theoretical value. The amplification and retardation effects on NSIFs are also investigated. It is found that the hole arrangements and hole shape have significant effects on the nature of the amplification or retardation.(7) Crack can be modeled as a rectangle hole by assuming that the short edge of the hole approaches to zero. Based on the method of isolated hole problem, this paper studies the problem of an infinite or half-plane containing a single crack or multiple cracks. Comparison of the results of stress intensity factors with exact solutions shows that the model gives accurate results even when the cracks are closely spaced. The amplification and retardation effects on SIFs are also investigated. It is found that the crack arrangements have significant effects on the nature of the amplification or retardation.