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©2012 Civil-Comp Ltd |
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W.M. Vicente, R. Picelli and R. Pavanello
Department of Computational Mechanics, State University of Campinas, Brazil
Keywords: topology optimization, fluid-structure interaction, frequency response function, ESO/BESO methods.
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Multiphysics coupled systems including dynamic fluid-structure interaction (FSI) problems have hardly been studied in several fields of mechanical engineering. The finite element method (FEM) is extensively used to simulate this class of problem. FE solvers can be combined with techniques to develop a design optimized systems. One of these techniques is topology optimization. The structural topology optimization method for continuum structures [1] has gained in popularity and is used daily as a design tool both in industry and academic research. The basic idea is to find an optimal distribution of material in a structural design domain, considering an objective function. Commercial finite element packages often contain solvers for multiphysics problems, however they do not enable optimization. This paper applies a topology optimization method in order to improve the dynamic characteristics of a system. Considering a fluid-structure system, we investigate how the vibration or pressure characteristics of given examples can be improved on the basis of the structural frequency response function (FRF) using topology optimization. Frequency response optimization is of great importance in many engineering fields such as acoustics systems and fluid dynamics. This paper focuses on the mean pressure minimization in acoustic-structure coupled systems. Yoon et al. [2], proposed an alternative mixed finite element formulation for acoustic-structure interaction for topology optimization of these coupled systems.
In this paper, an evolutionary method is proposed for the solution of the same problem using the u-p standard formulation. The technique is the so called evolutionary structural optimization (ESO) was first introduced in the 1990s by Xie and Steven [3], as a gradual removal of inefficient material from the design domain. The technique is quite simple and might be easily implemented in finite element packages. A later development of the evolutionary method is called bi-directional ESO (BESO), in which elements are simultaneously removed and added in the finite element mesh. Dynamic problems were already treated with this method [4], but FRFs have not been explored with this evolutionary technique. Herewith, the BESO method is developed for FRF optimization and extended to pressure minimization in acoustic-structural systems. The possibility of removing and adding material systematically with the evolutionary method might be a helpful procedure to explicitly define the fluid-structure interfaces. However, only cases with immovable of interfaces will be considered in this paper. For this kind of problem, a sensitivity analysis was discussed. For a number of excitation frequencies the methodology presented here was capable to minimize the pressure and to converge to optimized topologies. The efficiency of the method is demonstrated for a good range of frequencies. In particular for higher frequencies a good minimization of the pressure is achieved with just a small percentage of material removed.
- 1
- M.P. Bendsoe, O. Sigmund, "Topology Optimization - Theory, Methods and Applications", Berlin, Heidelberg, Springer-Verlag, 2003.
- 2
- G.H. Yoon, J. Sondergaard, O. Sigmund, "Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation", International Journal for Numerical Methods in Engineering, 70, 1049-1075, 2007.
- 3
- Y.M. Xie, G.P. Steven, "A simple evolutionary procedure for structural optimization", Computers and Structures, 49, 885-896, 1993.
- 4
- X. Huang, Y.M. Xie, "Evolutionary topological optimization of vibrating continuum structures for natural frequencies", Computers and Structures, 88, 357-364, 2010.
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