Stiffener layout optimization to maximize natural frequencies of a structure using evolution strategies and geometry algorithms

Abstract

Structural dynamics modification (SDM) is a tool to improve dynamic characteristics of a structure, more specifically of a baseline structure, by adding or deleting auxiliary (modifying) structures. In this research, stiffener layout optimization to maximize natural frequencies of a baseline structure was considered as part of structural dynamics modification, where the lengths as well as the positions of stiffeners were chosen as design variables. However, non-matching interface nodes problem that the nodes of stiffeners do not match those of the baseline structure inevitably occurs during the optimization process. In order to handle this problem without adjusting node positions, i.e. remeshing, and to satisfy interface kinematic compatibility conditions systematically, localized Lagrange multipliers were utilized and an eigenproblem solving method for the stiffened baseline structure was proposed by using an eigen reanalysis technique for topological modifications. In stiffener layout optimization problems, most of the previous researches considering the position and/or the length of the stiffener as design variables dealt with baseline structures having just simple convex shapes such as a square or rectangle. The reason was because concave shape structures have difficulties in formulating the geometric constraint that the stiffener should be fully placed within the baseline structure. In this research, a new geometric constraint handling technique, which can define both convex and concave feasible stiffener positioning regions and measure a degree of geometric constraint violation, was proposed by using geometry algorithms. Evolution strategies (ESs) and differential evolution (DE) were utilized as optimization tools. In addition, the constraint-handling technique of EVOSLINOC (EVOlution Strategies for scalar optimization with Llnear and NOnlinear Constraints) was utilized to solve constrained optimization problems. The developed methodologies for stiffener ...