Topology Optimization of Fluid-Loaded Shells by Minimizing the Acoustic Coupling to the Fluid Domain

Abstract

Topology optimization of fluid-loaded shells is presented. A finite element model with shallow shell elements is developed using strain-based formulation. The considered elements are quadrilateral, where each node has five degrees of freedom to account for in-plane and out-of-plane deflections as well as rotations. The developed model was integrated in the optimization algorithm aiming at minimizing the coupling between the flexible shell and the adjacent fluid domain. The model is exercised to generate closed-form expressions of the sensitivities in order to enhance the topology optimization process. The Method of Moving Asymptotes is used along with the sensitivity expressions to predict the successive iterations. The fluid-structure coupling was manifested in the coupling matrix in the finite element model. The results of the finite element–based topology optimization were validated using ANSYS® commercial package. Radial loads with fixed-fixed as well as axial loads with fixed-free boundary conditions were implemented. Different values of minimum permissible shell wall thickness were developed. Numerical examples show that considerable attenuations are attained for the selected structural modes in the order of 9–12 dB for the radial as well as the axial excitation cases. Reducing the minimum permissible thickness from 35% of the original thickness to 15% has shown tremendous effect on the attenuation at the targeted modes for the different load cases in the order of 12 dB. The presented model and design methodology can be invaluable in the design of various critical cylindrical structures that must satisfy strict vibration and noise radiation require- ments.