Position and Thickness Optimization of Ribs for Ventilation Covering Using the Micro Genetic Algorithm with an Interpolated Smooth Objective Function

Abstract

Structures with supporting ribs are adopted in many fields of engineering. These ribs are attached to the main plate or shell to increase stiffness and reduce the stresses of a structure. Currently, much research in structural optimization has been devoted to size or thickness optimizations. In this study, the discrete positions of the ribs of a structure are optimized in addition to their thicknesses. The objective function, which is the total weight of a structure, is a continuous function with respect to the thickness of the ribs. However, it is a stepwise function of a dimensionless variable, which represents the set of positions of the ribs. Because of this stepwise objective function, the gradient method of optimization is not applicable. Therefore, we applied the micro genetic algorithm (MGA), which does not need derivatives of the objective function. To accelerate the rate of convergence, the stepwise objective function is interpolated to a smooth artificial objective function that does not alter the optimal solution.