Body-fitted topology optimization with the Equivalent Radiated Power criterion
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The Equivalent Radiated Power (ERP) criterion focuses on the vibration of structural panels; as such , in automotive applications, it can be used to estimate the acoustic performance of vehicles without modeling the fluid as well as the computationally expensive fluid-structure coupling. As a matter of fact, such a computationally intensive effort may not even be required in an early design phase. In practice, the spatial averaging version of the ERP criterion is evaluated through a post-processing of the solution arising from an harmonic response problem of a visco-elastic body. In the broad sense, shape and topology optimization aims at finding an optimal shape among a set of admissible shapes $\mathcal{O}_{ad}$, constrained in a design space $D\subset\mathbb{R}^3$, with respect to a set of prescribed criteria. The level-set method is based on a sensitivity analysis from the shape optimization framework and is used to enforce a descent direction and advect a structural interface and also provides a clear definition of the shape. Thus we opt for a level-set based topology optimization method for the ERP minimization on three dimensional test cases. Note that it is coupled with a remeshing routine, in order to enables the reconstruction of a body-fitted mesh at each step of the iterative process. Such a choice allows us to handle naturally the topology changes and provides high quality meshes for the physical evaluations inherent to the optimization process.