Optimality criteria-based topology optimization of a bi-material model for acoustic–structural coupled systems

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.

[1]  Donald J. Nefske,et al.  Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice , 1982 .

[2]  Qunli Sun,et al.  Acoustic-structural coupled finite element analysis for sound transmission in human ear--pressure distributions. , 2006, Medical engineering & physics.

[3]  O. Sigmund,et al.  Filters in topology optimization based on Helmholtz‐type differential equations , 2011 .

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

[5]  Mingsian R. Bai,et al.  Application of BEM (boundary element method)‐based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries , 1992 .

[6]  H. Gea.  Topology optimization: A new microstructure-based design domain method , 1996 .

[7]  Kyung K. Choi,et al.  Design Optimization for Structural-Acoustic Problems Using FEA-BEA With Adjoint Variable Method , 2004 .

[8]  Hae Chang Gea,et al.  Optimal stiffener design for interior sound reduction using a topology optimization based approach , 2003 .

[9]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[10]  Liwen Guan,et al.  Guide-Weight method for topology optimization of continuum structures including body forces , 2013 .

[11]  Mark P. Rossow,et al.  OPTIMAL TRUSS DESIGN BASED ON AN ALGORITHM USING OPTIMALITY CRITERIA , 1977 .

[12]  Nam H. Kim,et al.  Shape sensitivity analysis of sequential structural–acoustic problems using FEM and BEM , 2006 .

[13]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[14]  Richard G. DeJong.  A Study of Vehicle Interior Noise Using Statistical Energy Analysis , 1985 .

[15]  Tetsuya Sakuma,et al.  Fast multipole boundary element method for large-scale steady-state sound field analysis, Part I setup and validation , 2002 .

[16]  M. Abolbashari,et al.  On various aspects of application of the evolutionary structural optimization method for 2D and 3D continuum structures , 2006 .

[17]  A. Craggs.  The transient response of a coupled plate- acoustic system using plate and acoustic finite elements , 1971 .

[18]  Jakob S. Jensen,et al.  Acoustic design by topology optimization , 2008 .

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

[20]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[21]  R. Kohn,et al.  Topology optimization and optimal shape design using homogenization , 1993 .

[22]  Zhan Kang,et al.  Topology optimization of damping layers for minimizing sound radiation of shell structures , 2013 .

[23]  Dejie Yu,et al.  An interval random perturbation method for structural‐acoustic system with hybrid uncertain parameters , 2014 .

[24]  Jian-Qiao Sun,et al.  Structural–acoustic optimization of sandwich cylindrical shells for minimum interior sound transmission , 2008 .

[25]  N. Kikuchi,et al.  Topological design for vibrating structures , 1995 .

[26]  George I. N. Rozvany,et al.  Structural and Multidisciplinary Optimization , 1995 .

[27]  V. Kobelev,et al.  Bubble method for topology and shape optimization of structures , 1994 .

[28]  Hualing Chen,et al.  Application of Energy Finite Element Method to High-frequency Structural-acoustic Coupling of an Aircraft Cabin with Truncated Conical Shape , 2010 .

[29]  Ashok V. Kumar,et al.  Topology optimization using B-spline finite elements , 2011 .

[30]  Wei Shyy,et al.  An Optimization-Based Approach To , 2000 .

[31]  A. Klarbring,et al.  Topology optimization of hyperelastic bodies including non-zero prescribed displacements , 2013 .

[32]  Wim Desmet,et al.  Vibro-acoustic design sensitivity analysis using the wave based method , 2011 .

[33]  Niels Olhoff,et al.  Optimal design of vibrating circular plates , 1970 .

[34]  Jianbin Du,et al.  Microstructural topology optimization with respect to sound power radiation , 2013 .

[35]  Hae Chang Gea,et al.  Optimal 3D stiffener design with frequency considerations , 1997 .

[36]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

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

[38]  Qibai Huang,et al.  Topology optimization of composite material plate with respect to sound radiation , 2011 .

[39]  Robert J. Bernhard,et al.  Structural-acoustic design at high frequency using the energy finite element method , 1999 .

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

[41]  Charbel Farhat,et al.  Sensitivity analysis and design optimization of three‐dimensional non‐linear aeroelastic systems by the adjoint method , 2003 .

[42]  L. Thompson.  A review of finite-element methods for time-harmonic acoustics , 2006 .

[43]  Niels Olhoff,et al.  Regularized formulation for optimal design of axisymmetric plates , 1982 .