Given a subtle metallic disk of circular form soldered inside a tube of the same inner diameter, and applying a pressure to one part of the tube ( creating so a pressure differential ) the disk bends a little bit. We want to modulate the thickness of the disk depending on the distance from the center in order to have a constant stress ( shear stress) along the whole disk. In reality we want the disk to last as long as possible under repeating applications of differential pressure.
We are looking to find the function that gives the thickness as a function of the distance from the center. The problem can be simplyfied at first with the linear analog ( not circular but rectangular ).
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