Reproducing Kernel Approximation Method for Structural Optimization Using Genetic Algorithms

This thesis proposes the reproducing kernel approximation method for structural optimization using genetic algorithms. Firstly, geometric parameters of a structure are defined, and a parametric design program is developed to automatically generate the solid model of the structure. Then, a macro program to automatically analyze structural behaviors of the structure is developed. Analysis results are used as fitnesses of population individuals to generate reproducing kernel shape functions. Then, reproducing kernel approximations of fitnesses are developed. Genetic algorithms are used to solve the optimization problem. In genetic algorithms processes, a modified trust region approach is developed. Fitnesses of population individuals are evaluated exactly only for some specific generations. Fitnesses of population individuals for the following some generations, called the generation delay, are evaluated approximately by reproducing kernel approximations. In addition, an adaptive tournament selection scheme is developed by adjusting the tournament size to reduce approximation errors in each generation. When 90% of population individuals in a certain generation have the same fitness value, the solution of the optimization problem is found. Finally, an integrated program combining computer aided design software, finite element analysis software, reproducing kernel approximation method and genetic algorithms is developed for structural optimization. With the developed program, optimum design processes of several structural design problems are investigated. From optimum results, they show that this proposed program is reliable and results in fast and satisfactory convergent solutions.