Generalized shape optimization of transient vibroacoustic problems using cut elements

Abstract

This article propose a generalized shape optimization method for transient coupled acoustic-mechanical interaction problems. The transient problem formulation allows to optimize for a broadband frequency content and the possibility to investigate transient phenomena such as pulse shaping. Throughout the work, the geometry is defined with the help of a nodal-based design field, for which its zero-level contour describes the interface between acoustic and structural domains. The approach utilizes a fixed background mesh to represent the geometry and a cut element immersed boundary method for the physical modeling. This modeling approach provides accurate solutions to the strongly coupled governing equations based on a special integration scheme. The optimization problem is solved using a gradient-based optimizer and employs a fully discrete adjoint approach for calculating the sensitivity information. A numerical examination on the accuracy of the sensitivity analysis compares the fully discrete gradients to the commonly used semidiscrete adjoint approach for transient optimization revealing the importance of consistent sensitivities. The transient design formulation is validated on a 2D benchmark problem concerning the design of a time-harmonic acoustic partitioner. The developed framework is then applied for the design of vibroacoustic pulse shaping devices to demonstrate control of a transient phenomena.

Length scale control for high-resolution three-dimensional level set–based topology optimization

“…That is, problems involving interface conditions such as multiphysics problems. In that relation, it is worth mentioning that the proposed cut element based level set design methodology recently has been successfully applied to fully coupled vibroacoustic shape optimization in two dimensions (Dilgen and Aage, 2021).…”

Topology optimization of acoustic mechanical interaction problems: a comparative review

“…a level set function, which is used to identify the acoustic and structural domains embedded inside the total computational domain Ω = Ω s ∪ Ω a as illustrated in figure 1(a). This work follows the same geometry representation as used in [19,23] meaning that the iso-level is chosen as the zero-level of the level set function and hence, that the following rule is used to determine acoustic and structural material phases…”

“…To this end, a triangulation is carried out in the identified cut Q4 elements to correctly place the integration points in the sub-elements as well as on the interface in order to integrate the coupling boundary conditions, equations 5 and 9, inside the parent Q4 element. The reader is referred to [19] for details regarding all necessary integrals. The resulting semi-discrete form of the coupled system then reads…”

“…To the best of the authors' knowledge, utilization of time-domain methods to realize wideband optimization in the frequency domain have not been demonstrated before for structural optimization of strongly coupled vibroacoustic problems. Moreover, the work utilizes the discrete adjoint method for calculating the gradients of the objective function [44,19]. A thorough explanation of the consistent sensitivity calculation through the discrete adjoint framework that involves the FFT operation, which is needed to define the objective function in frequency domain, is also among the contributions of the present work.…”

A reduced-order cutFEM approach to model complex moving sound sources

“…An alternative approach is to use a static mesh, such that the problem does not require a re-meshing step during simulation, and use techniques to enrich the mesh to include the proper source description. Several techniques to do this are known, such as the extended finite element method (XFEM) and the cut finite element method (cutFEM) [2][3][4]. The disadvantage of these methods with respect to the ALE formulation is that the DOFs will change during the simulation, since the DOFs that are covered by the source fall outside of the physical domain and will not contribute to the solution.…”