Bézier based shape parameterization in high speed mandrel design

The optimization of bi-dimensional profiles of axisymmetric parts is one of the most commonly addressed problems in engineering. Shafts are a typical example of this basic shape. This work is concerned with the use of Genetic Algorithms (GAs), Finite Elements (FE) and rational Bézier curves for the optimization of high speed mandrels. The design variables of the problem are the weights of the nodes of the Bézier boundary curves used to define the finite element discretization. These values are generated by the GA and handled by a mesh generator which defines a candidate solution to the problem. The value of the natural frequencies for each individual is evaluated. For a given set of values of cross-sectional areas and resulting natural frequencies, the value of the fitness function of an individual is obtained. Is this case of a constrained optimization problem The binary-coded generational GA uses a Gray code, rank-based selection, and elitism. The paper briefly summarizes the basis of the GAs formulation and describes how to use refined genetic operators. The mixed pure cylindrical and Bézier shaped model boundary is discretized by using a beam FEM (Finite Element Method) model. Some selected parts of the boundary are modeled by using curves, in order to allow easy meshing and adaptation of the boundary to optimization process. A numerical examples is presented and discussed in detail, showing that the proposed combinedtechnique is able to optimize the shape of the domains with minimum computational effort. The improvement in confront with the original multiple-cylinder shape is significant, without violating the restrictions imposed to the model.