A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method – application to 2D acoustic scattering problems. (English) Zbl 1533.74064
Summary: In this article, an innovative method is proposed for broadband topology optimization of sound-absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single-frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound-absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large-scale problems, a reduced-order model that retains the essential structures and key properties of the original model is built using the second-order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two-dimensional numerical examples.
© 2023 John Wiley & Sons, Ltd.
© 2023 John Wiley & Sons, Ltd.
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76Q05 | Hydro- and aero-acoustics |
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
Keywords:
boundary element method; sound-absorbing material; sound barrier structure surface; reduced-order model; Helmholtz equation; sensitivity analysis method; adjoint variable method; moving asymptotes method; Hankel functionReferences:
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