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Precision and Accuracy in Generating Globally Optimum Shapes 235increases, at the same time computational times get longer and longer. With a large number ofoptimization variables, locating the global minimum also becomes difficult. As the designertries to obtain a more precise definition, he or she becomes less sure of the accuracy of the results.One may repeat the optimization process many times and designate the design havingthe lowest cost as the global optimum design. However, because of the long computationaltimes this approach is not feasible. Another way to overcome this difficulty is to start optimizationby choosing only a few design variables and finding the optimum design. In thiscase, the reliability of locating globally optimum design will be high, even though precisionwill be low. Then, the designer keeps increasing the number of variables and finding the optimumdesign. With the assumption that the difference between the optimum designs will notbe large as the number of design variables is increased, one may observe convergence to themost precise global optimum design.6. Results and DiscussionsOne of the problems that we considered in this study is the optimal design of an eccentricallyloaded plate restrained at one end and loaded at the other (Figure 3). One segment of theborder on the right is fixed in length and subject to 200MP a pressure. The left border isdefined by a line between two keypoints; the lower one is fixed, while the upper one is freebut restrained to move in the vertical direction. The problem is to find the optimum shape ofthis plate as stated above.Firstly, five keypoints were used to describe the boundary and using their coordinates as designvariables the best shape was found. Figure 4 shows the optimal shape with its finiteelement mesh. Because the number of design variables was low, the optimum design couldbe obtained with high reliability. Then, optimization process was repeated using seven andnine moving keypoints resulting in the optimum designs shown in figures 5 and 6. The lateralareas of the optimum shapes defined by five, seven, and nine keypoints turned out tobe 37.100, 36.313, and 35.903 cm 2 , respectively. Consequently, with a higher number of keypoints,we could obtain a better definition of shape and also find an optimum configurationwith a lower cost. Although reliability of the solution is low when the number of design variablesis large, because optimum designs defined by a high number of keypoints approximatethe more reliable optimum designs defined by lower number of keypoints, the reliability isensured.Figure 3.The design problemIn order to ensure the accuracy at which the cost was calculated, convergence of the F E solutionwas frequently checked during the optimization process. If the change in the magnitudeof the maximum stress was greater than 1% when F E analysis was carried out using one