Study on the boundary stress distribution of elliptical cavity under uniform pressure load

Abstract

By introducing the complex variable function and conformal transformation, the elliptical cavity expansion problem is transformed into the cylindrical cavity expansion problem. Combined with the least square fitting method and Von-Mises yield criterion, the elastic-plastic boundary of the elliptical section cavity under uniform load is determined. The cavity boundary displacement is solved by the mass conservation equation of the plastic zone, and the theoretical calculation model of the static elliptical cavity expansion is established. The results indicated that when the material reaches stability under the load of elliptical cavity boundary, the axis stress value increases gradually from the minor axis to the major axis of the elliptical cavity, showing a similar sinusoidal distribution. Due to this mechanical characteristic, it is more difficult to expand in the major axis direction than in the minor axis direction. With the increase of initial load, the range of stress on the boundary of elliptical cavity decreases, and the average stress on the boundary of cavity tends to a constant value. The majorminor axis ratio of elliptical cavity has significant influence on the stress field distribution of materials, while the initial cavity area has little influence. With the increase of the major-minor axis ratio, the stress rising rate gradually increases, and the stress value gap between major-minor axis gradually increases.