This paper presents an incremental elastic-plastic finite element solution to the problem of small scale yieldmg near a crack in plane strain for a non-hardening material. Emphasis is placed on the design of finite elements which allow accurate reproduction, m a numerical solution, of the detailed structure of the near crack tip stress and strain fields, as understood from previous analytical studies of crack tip singularities. Numerical results are presented for: location of the elastic-plastic boundary, angular distribution of the strength of the strain singularity, crack tip opening displacemeat, stress distribution ahead of the crack, and angular variation of stresses at the tip. The latter results verify Rice's prediction of the Prandtl field in provldmg the limiting stress distribution as r ~ 0.

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A finite-element elastic analysis is made of a skull. Measurements were made of the geometry and thickness of a skull. The skull was then idealized with a doubly curved and arbitrary triangular shell element. Results suggest that the skull is well built for resistance to front loads. The importance of using a composite material through the thickness of the shell was established. On the basis of tensile cracking at maximum elastic stress, loads of 3500 lb and 1400 lb were predicted for the first cracking of the skull due to front and side loading, respectively.

An initial study has been made of a method for optimizing finite element grids. This method is based on the minimum potential energy where the nodal point positions are also treated as independent variables. Necessary conditions have been obtained for the optimized grids. Case studies demonstrate the procedure for a one-dimensional tapered bar under axial load and for a two-dimensional square membrane subjected to a parabolic tensile stress. The optimized grids were observed to give improved stress estimates.

This paper summarizes progress in the development of finite element methods for three-dimensional elasticplastic stress analysis in fracture mechanics. The work is directed toward the study of stress states near flaws such as a part-through crack in a pressure vessel wall, and emphasis is placed on the large scale plastic yielding range The development of a computer program with large computing capabilities is described. Special near crack tip elements and general isoparametric elements are employed in problems with two crack configurations. Preliminary results are given for the elastic analysis of a through crack and for the elastic-plastic analysis of a part-through semi-elliptical crack in a plate.