TOPOLOGY OPTIMIZATION OF PERIODIC STRUCTURES FOR COUPLED ACOUSTIC-STRUCTURE SYSTEMS

Abstract. This work applies the topology optimization technique to an acoustic-structure coupled system with periodic geometry constraint in order to obtain the optimal layout of the design domain for the minimization of the pressure frequency response in the acoustic fluid. The displacement-pressure formulation (u–p) is used for the finite element analysis of the coupled system and external harmonic excitations are applied in the system. The design domain of the coupled system is considered to be composed of identical unit cells. A periodic geometry constraint is applied in the design domain considering the fluid-structure interaction and the objective function. Appling the modified bi-directional evolutionary structural optimization (BESO) technique to the system, the design domain is evolving towards the optimal topology of the unit cells through removing/adding material accordingly to the sensitivity analysis. The influence of the total number of unit cells composing the periodic structure and the aspect ratio of the unit cells are investigated in the minimization of the objective function. In order to show the capability and efficiency of the proposed formulation, two acoustic-structure systems are optimized for several cell configurations, different aspect ratios of the periodic unit cells and excitation frequencies.

[1]  Yi Min Xie,et al.  Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures , 2016 .

[2]  Yi Min Xie,et al.  Evolutionary topological optimization of vibrating continuum structures for natural frequencies , 2010 .

[3]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[4]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[5]  O. Sigmund.  Materials with prescribed constitutive parameters: An inverse homogenization problem , 1994 .

[6]  Yi Min Xie,et al.  Evolutionary Structural Optimization , 1997 .

[7]  Jakob S. Jensen,et al.  Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation , 2007 .

[8]  Yi Min Xie,et al.  Evolutionary topology optimization for natural frequency maximization problems considering acoustic-structure interaction , 2015 .

[9]  M. Wang,et al.  Level set based topology optimization of vibrating structures for coupled acoustic-structural dynamics , 2014 .

[10]  Renato Pavanello,et al.  Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems , 2015 .

[11]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[12]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[13]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[14]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[15]  Yi Min Xie,et al.  Optimal design of periodic structures using evolutionary topology optimization , 2008 .

[16]  Yi Min Xie,et al.  Evolutionary Structural Optimization Method , 2010 .

[17]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[18]  Yi Min Xie,et al.  Topology optimization of frequency responses of fluid–structure interaction systems , 2015 .

[19]  Y. Xie,et al.  AN IMPROVED BI-DIRECTIONAL EVOLUTIONARY TOPOLOGY OPTIMIZATION METHOD FOR FREQUENCIES , 2010 .

[20]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Continuum Structures: Methods and Applications , 2010 .

[21]  N. Olhoff,et al.  Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium , 2010 .

[22]  J. Sethian,et al.  Structural Boundary Design via Level Set and Immersed Interface Methods , 2000 .

[23]  Y. Xie,et al.  Comparing optimal material microstructures with optimal periodic structures , 2013 .

[24]  Niels Olhoff,et al.  Minimization of sound radiation from vibrating bi-material structures using topology optimization , 2007 .