Topology optimization problems for reflection and dissipation of elastic waves

This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three material phases: a host material and scattering and/or absorbing inclusions. The capabilities of the optimization algorithm are demonstrated with two numerical examples in which the reflection and dissipation of ground-borne wave pulses are maximized.

[1]  M. Petyt,et al.  Ground vibration in the vicinity of a strip load: An elastic layer on an elastic half-space , 1993 .

[2]  Eleftherios N. Economou,et al.  Classical vibrational modes in phononic lattices: theory and experiment , 2005 .

[3]  L. H. Olesen,et al.  A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow , 2004, physics/0410086.

[4]  Jakob S. Jensen,et al.  Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide , 2005 .

[5]  Gregory M. Hulbert,et al.  Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics , 2006 .

[6]  A. G. Striz,et al.  On using genetic algorithms for optimum damper placement in space trusses , 2004 .

[7]  D. Tortorelli,et al.  Design sensitivity analysis: Overview and review , 1994 .

[8]  Jakob S. Jensen,et al.  Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends , 2004 .

[9]  A. Chopra,et al.  Perfectly matched layers for time-harmonic elastodynamics of unbounded domains : Theory and finite-element implementation , 2003 .

[10]  Ole Sigmund,et al.  Inverse design of phononic crystals by topology optimization , 2005 .

[11]  Eugène Dieulesaint,et al.  Elastic Waves in Solids II , 2000 .

[12]  Steven J. Cox,et al.  Maximizing Band Gaps in Two-Dimensional Photonic Crystals , 1999, SIAM J. Appl. Math..

[13]  P. Einziger,et al.  Effectiveness of acoustic power dissipation in lossy layers , 2004 .

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

[15]  G. Cheng,et al.  Design of cellular structures for optimum efficiency of heat dissipation , 2005 .

[16]  C. Jog.  Topology design of structures subjected to periodic loading , 2002 .

[17]  I. Takewaki,et al.  Optimal damper placement for planar building frames using transfer functions , 2000 .

[18]  Gilles A. Francfort,et al.  A Numerical Algorithm for Topology and Shape Optimization , 1993 .

[19]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.