A Linear Technique for Designing the Optimal Rotating Shapes

In this article, a linear and simple method was established for designing the optimal revolving objects with desired physical properties. By defining an artificial control related to the unknown generator curve, firstly, the problem was converted into an optimal control one. Then, considering a variational presentation and applying an embedding procedure, the problem was transferred into one whose unknown was an optimal Radon measure. Using two stages of approximation, we obtain the optimal control and hence the optimal generator rotating arc from the results of a finite linear programming. The accuracy and the applications of the new method were shown by some classical simulations and compared with the level set method in numerical examples.

Keywords:

Linear programming , Generator arc , Optimal rotating shape , Optimal control , Radon measure , Level set method