Investigation of Bi-directional Evolutionary Structural Optimization and Multiple Material Topology Optimization
Date Issued
2010
Date
2010
Author(s)
Lu, Chi-Han
Abstract
This research expands and uses the optimization design system developed by Lee (2005) to carry out optimizations. It focuses on the topology optimization and takes two parts: “Bi-directional Evolutionary Optimization” and “Multi-material Topology.”
In researches of our reseach group, we majorly use Evolutionary Structural Opti-mization method (Xie et al. 1993) on topology optimizations. The ESO method uses discrete design variables 0 or 1, so it easier ditiguish the material and the void than other methods with continuous design variable. And it’s simpler, easier and more time effi-cient. But because of its simple procedure with only removing elements, it may fail in some boundary condition changed cases.
The “Bi-directional Evolutionary Structural Optimization” method is so developed. The method allows filling back elements with combing the concept of smoothing and projection, so it has more freedom than the original method. It also has allowance in ini-tial design to decrease the comsuming time of the optimization, and when applying it on optimization of support positions published by Hsu (2009), the result will be better than the former research and fit with the paper results.
The filtering radius is the most important parameter in BESO method. This research makes lots of discussions about it by examples and suggests that it should be set about half of the desired member size you want, and if the initial design exists, the member width should be larger than twice the filtering redius to avoid crashing. And too large filtering radius may cause bad topology, check in smaller radius if you feel it bad.
This research also tries to make modifications on the BESO method. First try is combing it with the inverse projection scheme to control the member and the void size. The try is successful control the member size. But the result goes similar with the to-pology with a larger filtering radius and the original BESO method. It may be more discussions about using it or not. Another try is to simplify the complex computions and procedures of the BESO method. The results of the simplified method make only a little difference with results of the original BESO method, and the method can work in BESO features.
In part of “Multi-material Topology,” this research works on ESO based methods and focuses on the researches of Shih (2008) and Hsu (2009). First, in two-material to-pology problem with initial condition of soft material in the full design domain, the combination of two-step converging, smoothing technique and the rejection ratio meth-od can make more stable results. Second, in part of the evolutionary method in multiple materials, this research finds that the method with earlier decisidng on distribution of harder material will cause worse topology, and in all methods this research compared, Hsu’s Method makes better results. Last, this research takes the material interface length into the objective function and it can make clearly material concentrated topology.
Subjects
Structural Optimization
Topology Optimization
Bi-directional Evolutionary Optimization
Multi-material Topology
Type
thesis
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