Floating Projection Topology Optimization of Functionally Graded Porous Infill Structures for Acoustic-Mechanical Coupled Systems

Porous structures have been widely studied due to its low stiffness-to-weight ratio and excellent sound insulation and absorption, and the research revealed that functionally graded changes in shape and numbers of pores in porous structures can enhance the mechanical and acoustic performance. This paper presents a new topology optimization approach for dynamic acoustic-mechanical structures with functionally graded porous infill, which is realized by the Helmholtz PDE-filter with a variable radius. The floating projection topology optimization method (FPTO) based on the mixed displacement/pressure (u/p) finite element formulation and the ersatz material model are used to overcome the potential difficulties in topology optimization of acoustic-mechanical interaction, such as the interaction between the different physic domains and artificial localized vibration modes of structures. The 0/1 constraints of the design variables are simulated by the floating projection constraint so that the final smooth topological design have a clear topology. Some interesting 2D and 3D numerical examples show that the proposed method with different acoustic constraints and filter radius can generate different targeted functionally graded porous infill structures to obtain the desired mechanical stiffness and acoustic properties. The results also show that the presented method can make the material to be distributed evenly within the design domain, considering the requirements of topological configuration size and the resistance of uncertain external loads in engineering applications.