Topology optimization of dynamic acoustic–mechanical structures using the ersatz material model

• Published in: Computer methods in applied mechanics and engineering Vol. 372; p. 113387
• Main Authors: Hu, Jie, Yao, Song, Huang, Xiaodong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2020
• Subjects: acoustic–structure interaction; Sound transmission loss; The ersatz material model; The mixed displacement/pressure finite element formulation; Topology optimization; The mixed displacement/pressure finite element formulation; Topology optimization; acoustic–structure interaction; Sound transmission loss; The ersatz material model
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113387

Topology optimization of dynamic acoustic–mechanical structures is challenging due to the interaction between the acoustic and structural domains and artificial localized vibration modes of structures. This paper presents a floating projection topology optimization (FPTO) method based on the mixed displacement/pressure (u/p) finite element formulation and the ersatz material model. The former is able to release the need for tracking the interface boundaries explicitly between the structural and acoustic domains during the optimization process. The ersatz material model enables us to entirely avoid artificial localized vibration modes caused by the extremely high ratio between mass and stiffness. The floating projection simulates the original 0/1 constraints, and it gradually pushes the design variables toward 0 or 1 at the desired level so that the optimized element-based design can be accurately represented by a smooth design. Some 2D and 3D numerical examples, including minimizing sound pressure at the designated domain, restraining structural vibration, and maximizing sound transmission loss, are presented to demonstrate the effectiveness of the proposed topology optimization algorithm. The optimized solutions achieve the consistency of the objective function between the element-based design using the mixed formulation and the smooth design using the segregated formulation. The study suggests that the FPTO method using the ersatz material model is a promising approach for optimizing dynamic acoustic-mechanical structures. •A new topology optimization algorithm for acoustic–mechanical structures is proposed.•Topology optimization using the ersatz material model avoids any artificial local modes.•Both 2D and 3D numerical examples are presented with element-based and smooth designs.•The performance of element-based designs is consistent with that of smooth designs using the segregated formulation.