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Title Stiffener layout optimization to maximize natural frequencies of a structure using evolution strategies and geometry algorithms
Author Lee, Joon-Ho
Type KAIST Ph.D. Dissertation
Year of Pub. 2005
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 LInear and NOnlinear Constraints) was utilized to solve constrained optimization problems. The developed methodologies for stiffener layout optimization problems were applied to various baseline structures in both 2D and 3D. From numerical simulations, the proposed geometric constraint handling technique was verified and proved that the technique can easily be applied to baseline structures in not only convex but also concave shapes, even with a protrusion or interior holes. The proposed technique using geometry algorithms is not limited to stiffener layout optimization problems. The technique can also be applied to other research areas that are related to sound and vibration and need numerical optimization techniques for better designs such as absorptive material arrangement optimization, position optimization of supports, dampers and mounts, etc., where geometric constraints are inevitably involved.