1. 82 2.667e-05 5.9667e04
2. 0008 1.08825e-07 3.2680e-05
3. We are interested in shapes with volumes that are significantly less than the volume at float. To determine these shapes, we begin by evolving the discrete unstrained design shape to its equilibrium (as defined by Problem (*)). We find that there is essentially no excess material in the strained float shape. The results are presented in Column 3 of Table 2. We then decrement the volume and compute the corresponding EM-shape, continuing until V = 0.005vd. hitidly, we must take extremely small steps, or else the solution process will diverge. We choose AU z o.ooo~vd, until v z 0.97vd. After we have computed an EM-shape with V = O%Vd, larger steps can be taken. If (Vk,Sk) is the volume and corresponding EMshape, at the start, we use (Vk,Sk) as the initial guess for the solution (Vk+r,sk+r) where Vk+r = Vk - AV. We found that the size of the volume decrement could be increased if we used linear interpolation between pairs (Vk-r,Sk-r) and (Vk,Sk) to predict the initial shape for V = &+I. In this case: steps on the order of AV z 0.005Vd could be achieved. This process was continued until we computed the solution for V = 0.005vd. As we approached V = o.o05Vd, smaller volume decrements were used. Data on the EM-shape with V = 0.005Vd is presented in Column 4 of Table 2. We then imposed the hoop constraint and computed a family of EM-shapes with decreasing hoop constraint diameter. In particular, at V = o.o%Vd, we found that station i' = 9, zia.1 = 71.11 in. We set&a*,1 - 71 and computed an EM-shape with the additional hoop constraint. We then continued to decrement zI'p,i (in steps of roughly 2 inches), until z$ì = 44. The results for z& = 44 are summarized in Column 5 of Table 2.