Analysis of 3-Dimensional Creased Cracks

A method of analysis for calculating a precise distribution of a stress intensity factor alonga front of 3D crack was improved by introducing a closed-form integral. In the present study, the crackface is discretized with number of triangular boundary elements on which the weighting function ofbody force doublet varies linearly with coordinate variables. A closed form solution of a resultant forceover an arbitrary planar-triangular area due to a presence of an isolated point force was derived andused to satisfy a stress boundary condition of a creased crack problem. In principle, arbitrary shaped3D cracks which may contain asperities and multiple creased lines in its face can be solved by presentapproach.

Analytic stress solution for a circular tunnel in half plane with a concentrated force

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

Interaction between two nanoscale elliptical holes with surface tension

In this paper, the plane problem of two elliptical nanoscale holes with surface tension is investigated. Firstly, the basic equations are given via the complex variable methods. Then, the stress boundary condition caused by surface tension is derived through the integral-form Gurtin–Murdoch model. The problem is finally solved by the conformal mapping along with the series expansion methods. The results show that the stress field decreases as the two holes become further away from each other. When the distance between the two holes is more than three times the sum of their sizes, the interaction between the two holes can be neglected. In addition, the stress field is greatly influenced by the orientation, aspect ratio and size of the holes. The positions of the maximum hoop stress are also discussed. When the two elliptical holes are put close horizontally, the hoop stress around one hole usually obtain its maximum at the endpoint close to the other hole. However, if one elliptical hole is not horizontal, the hoop stress around it will no longer attain its maximum at the endpoints. Another exception is that when one elliptical hole becomes larger, the hoop stress around the smaller hole would tend to achieve a local minimum at the endpoint close to the larger hole.

Capillary retraction of the edge of a stretched viscous sheet

Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.