Analysis on strength of the rectangular plate with an elliptical hole in case of axial loads

Abstract

In the process of designing the aviation structure, the complete study of the stress field is one of the most important problems. Incomplete study of the stress concentration field has been the cause of many disasters. In this article, an inelastic plate with a central elliptical cross section under axial load discussed. The purpose of the article is to create an analytical model in the software complex MASTRAN, the solution of which will approach the analytical solution with high accuracy, and to determine the ratio between the semi-axes of the ellipse and the value of the stress concentration. The results of the analytical solution and the analysis of the results of numerical experiment showed us that if we approximate the surface of plate with 4-node quadrilateral elements of different sizes (it is not necessary to use 8 nodes quadrilateral elements) the error compared to the analytical solution is practically equal to 0, and also if the ratio of semi-axes of the ellipse is equal to two, then the value of stress at the vertices of parabola increases 7 times. Numerical analysis showed us that, in the case of a narrow ellipse, the value of stresses at the tip is large, and it is possible that it tends to infinity when the ellipse tends to the crack. As for the second case (tensile forces act on all four edges of the plate), in the case of a normal ellipse, the stresses were concentrated along the ox axis at the right edge of the attachment.