point, namely, a minute region in tlie neighborhood of the low-pressure face 

 corner. At this particular location all stresses were becoming exceedingly 

 higher as the number of elements were increased. Further subdivision in 

 this corner revealed that these stresses were becoming arbitrarily high, 

 suggesting that the corner point stresses would approach infinitely high 

 values if the subdividing process continued. In witness of this phenomenon. 

 Figure C-2 portrays the computed effective stress as a surface over the cross 

 section of a typical viewport in which the corner has been finely subdivided. 

 This representation readily depicts the singular nature of this stress concen- 

 tration as a Dirac spike. It was hypothesized that this spike has physical 

 significance and that it is not simply an error emanating from the numerical 

 technique involved. In support of this contention, it was observed that all 

 experimental viewports exhibited a minute permanent plastic deformation 

 at this corner even for moderate loads. 



Taking the cue from experimental observations, the corner of the 

 analytical model was "rounded" in an attempt to model the plastic deform- 

 ation occurring in the actual viewport. Furthermore, care was taken to 

 determine what effect various amounts of "rounding" had on the resulting 

 stresses. It was discovered that the percentage of area removed did not alter 

 stress values significantly providing the percentage of deformation (percentage 

 of area removed) was greater than about 0.02%. Figure C-3 illustrates this 

 relationship where it is seen that the relative maximum effective stress 

 stabilizes for deformation percentages above 0.02%, independent of the mesh 

 size. In view of this, it was hypothesized that in a physical case the viewport 

 would deform approximately 0.02% to relieve the Dirac spike stress concen- 

 tration. This contention was supported by the percentage of deformation 

 measured in the viewport shown in Figure 4 of this report. 



In summary, the philosophy to be adopted in comparing the 

 analytical and experimental results is that, under initial loading, the actual 

 viewport will undergo minute local yielding which results in deformation at 

 the low-pressure face corner, to relieve itself of the spiked stress concentra- 

 tion. This results in a "modified" structure which, when analyzed, does not 

 display the Dirac spike stress concentration, but rather a realistic stress 

 concentration with some finite value. Thus, from the analytical standpoint, 

 the initial yielding problem is dismissed by beginning the analysis with the 

 modified structure (deformed corner). Accordingly, the failure definition 

 applies to the modified structure for both fixed and free boundary condition. 



49 



