Design Optimization with FEM

This chapter considers two types of optimization processes: one is a conventional parameter scan type, and the other is a genetic optimization process. The main purpose of the optimization study is to investigate the characteristics of the stator when the piezoelectric plates are placed at an optimum angle so that the two orthogonal bending mode frequencies are equivalent to each other. There are two main groups under consideration: geometrical and material parameters. The geometrical parameters are divided into two subgroups in terms of the elastic material: with circular cross section and with square cross section. The genetic algorithm (GA) was chosen among other optimization procedures for its multidimensionality and ease of implementation. The GA was also attractive for its capability of avoiding local optima and rapidly finding the global optimum in the searched domain. The application of GAs to ultrasonic devices presents some difficulties.