The effect of time on the material yield stress, a^, which has been 

 observed to decrease as loading time progresses,is next considered. A 

 graphical relationship of this is presented in Figure 18 in the Design Recom- 

 mendation portion of this report. At this point, a qualitative outline is 

 presented, illustrating the origination of the graph. 



Consider the typical creep data shown in a of Figure C-1 where each 

 curve represents the strain-time relation for a given level of stress. If a parti- 

 cular time, T,, is selected and corresponding values of stress and strain are 

 plotted as shown in b of Figure C-1, an isochronous stress-strain relationship 

 results. Because time has been held constant, any curvature in the stress- 

 strain relation is due to either yielding or nonlinearity of the material. 

 Curvature arising solely from nonlinearity does not limit the yield-strength 

 of the material as previously defined, however, existing creep data for acrylic 

 does not contain unloading histories and permanent set records, thus render- 

 ing it impossible to separate the effect of nonlinearity from yielding. 

 Therefore, it was conservatively assumed that all curvature was due to 

 yielding and that the yield strength at time T^ was defined as the 0.2% 

 offset strain intersect of the isochronous stress-strain relation. Following 

 the above procedure for several different times of interest, a curve can be 

 generated as in c of Figure C-1 which establishes the yield-stress versus 

 load-time relationship. The graph of this relationship for acrylic, displayed 

 in Figure 18, was derived from creep data obtained from three sources.^ o,i 3,1 4 

 For some loading durations, creep data were nonexistent for Plexiglas G, 

 but were approximated by engineering judgments of creep data on 

 Plexiglas l-A. 



A STRESS SINGULARITY AND THE ANALYTICAL TOOL 

 (FINITE ELEMENT) 



In modeling the viewport by the finite element technique, a 

 preliminary investigation was conducted to determine an adequate number 

 of quadrilateral elements to represent the system. It can be shown by 

 variational theorems that the finite element solution approaches the exact 

 solution as the number of elements approach infinity. Of practical 

 importance, the convergence of the finite element model can be determined 

 by comparing stresses obtained from a coarse mesh with those obtained 

 from a finer mesh. In so doing, it was discovered that about 400 elements 

 was a sufficient number, such that, further increase in the number of elements 

 did not appreciably alter the numerical values of stresses at a given point. 

 This held true throughout the entire cross section except for one very notable 



48 



