Slide gate

The idea behind this example is to show that optimization is not reserved for high-tech or mass-produced products. It is a slide gate for a water purification plant, and it is manufactured by Gerhardt Christensen's Maskinfabrik in Denmark. The pictures below show only one quarter of the doubly symmetric gate. Its purpose is to resist a water pressure. It is supported at four bosses protruding from its sides.

It is a simple structure consisting of a plate with 90 degrees bent edges and four stiffening ribs. To avoid complicated assemblies, the dimensions of the four ribs must be identical and have quadratic profiles with side lengths equal to the bent edges of the base plate. All parts, base plate, ribs and edges, are made from the same plate thickness.

In spite of its simplicity, it is a highly specialized and somewhat expensive product. It is produced in just a single or a few copies from high-quality stainless steel with a side length of more than one meter. The material is costly and there is quite a lot of manual labor involved, in particular in the welding of the structure.

The requirements are that the lateral deflection of the sides must not exceed the compliance of the rubber lib that seals against the gate. The deflection of the middle of the gate is not important, but there is a limitation on the maximum allowed stress. The design variables of the problem are the plate thickness, the position of the ribs, and the side length of the rib profile. The objective is to minimize the weight because that will reduce the cost of the rather expensive material, facilitate the bending of the plates, and reduce the welding cost.

Initial design.	Optimized design.

The optimized structure has a weight which is less than half of the initial one, and this is more than enough to justify the optimization from an economical point of view. The optimum position of the ribs is rather surprising. They had initially been positioned so as to separate the plate into three sections of equal length in each direction. It was assumed that this would provide the optimum support of the evenly distributed load. However, the optimization process resulted in a more precise problem definition specifying that the deflection of the edge and not the overall plate was important. Thus, two of the stiffeners were moved to support the free edge of the plate. The other two ribs were moved towards the center with the same purpose. It is characteristic that even simple problems are often too complicated to retain the full overview of the interplay between the parameters.

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Last modified: november 15, 2001