Stress state in an elastic bent plane with two identical circular holes

Résumé

The paper presents a comparison between the stress states obtained in an elastic bent plane with two identical circular holes. The plane is bent in a manner that the neutral axis of the plane is normal to the axis formed by the two centres of the holes, in the middle point. For the analytical solution the elastic potential is obtained as a sum between the elastic potential of the compact plane and an auxiliary potential, having a form given by Jeffery. The boundary conditions were imposed to the resulting potential. The plane is loaded with a linear distributed force. For the analysis with finite elements, the load was applied using two concentrated couples. The effect of the two holes is strictly locally and does not depend on the loading mode, reflecting the Saint-Venant principle. The fact is confirmed by the perfect agreement between the plots of the stresses, obtained by the analytical and numerical methods. The principal shearing plots are especially useful as they may be obtained experimentally as well, by photoelastic method, namely isochromatics curves. Finally, theoretically and numerically isochromatics are compared to the experimental ones obtained by Mesmer, cited by Frocht.