Nonlinear Analyses of the Stress Field near a Crack or Hole in a Plate.

Two methods for obtaining a complete stress field about a hole or crack in a plate were developed. Emphasis was placed on the effect of including the nonlinear terms in the strain-displacement equations. An analytical theory for a nonlinear crack problem was presented along with a nonlinear finite element approach to the problem of a plate with a centrally located hole. The plate was loaded in tension and the two-dimensional solution was based on an incremental theory of plane stress. Elaborate programs were written making use of the modern computer to solve the lengthy algebraic statements associated with the plate containing cracks and cutouts subjected to a loaded condition. Appropriate verification curves were plotted indicating the deviation between existing linear theories and the presented theories utilizing nonlinear considerations. These curves indicated the inaccuracy of linear solutions in the immediate crack-tip vicinity and also near a hole boundary. Complete stress fields were obtained for the two methods and corresponding stress curves were plotted. Author