Introducing the Optimization of Batter

Optimizing the batter involves using the weightless scaling factor when pile length is held constant. The initial design will be the optimized design from example 4.1. From there the optimization is run, simultaneously optimizing pile size and batter. The batter’s weightless scaling factor will begin at 1024 and will decrease at iterations that have only a small change in weight. The weight reduction is shown in the figure 4.3, and the corresponding weightless scaling factor, w, in each iteration can be seen in figure 4.4.

The weightless scaling factor begins very high, and is reduced gradually by taking it to the 2/3 power when the weight reduction from the previous iteration is low. Comparing Figures 4.3 and 4.4, w does not take on a weight reducing value until the fourth iteration (w » 107). This value proved to optimize batter while reducing the overall weight of the piles for several iterations. Finally, as the weight began to converge near iteration 11, w was further reduced, but the optimization became unstable at iteration 13. As explained earlier, when w becomes too low, the changes in the weightless variable (batter in this case) become too large, creating an unstable optimization. The final design, reached on iteration 12, changed the batters only slightly but was able to significantly alter the pile sizes to find an overall lighter pile design. The volume of steel was further reduced from 49,570 in3 to 46,580 in3.

2. Conclusion

Optimality Criteria is an effective method at reducing the weight of steel in piles under rigid, concrete slabs. The method has successfully reduced the weight of piles in many real-life problems, both simple and complicated. Using weightless scaling factors provides a way to optimize zero-weight gradient variables such as batter or spacing. By gradually reducing this factor exponentially when weight reductions become sufficiently small, a near-optimal final design can be reached. However, it is important to note that the final design reached is only a local minimum, not a global minimum. Thus, the initial design plays an important role in determining the final pile layout. Because of the ease of use of this optimality criteria program, varying the initial design and rerunning the program with the same loads and constraints can result in several low-weight final designs, allowing the engineer to choose between several near-optimal designs.


This work has been performed with the support of the National Science Foundation through the NSF Graduate Teaching Fellows in K-12 Education program.


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