Topology Optimization In Coupled Structural-acoustic Systems Based On Piecewise Constant Level Set Method

The vibration response level of the structure and the noise response level of the acoustic field have always been the key issues that designers concerned.Controlling the structural vibrations and the noise of acoustic fields is also a research hotspot.Struc-tural vibration and acoustic radiation analysis is a typical vibro-acoustic problem that considers both the vibration of the structure and the response of the acoustic field,and has some important applications in aerospace,ship and other areas.The optimization design for reducing the vibration and noise of the coupled structural-acoustic systems has great practical significance.At present,topology optimization is a classical op-timization method that can thoroughly change the structural topology in the structure optimization design,which can achieve optimal performance under the prescribed con-straints,and has become the preferred method for designers.On the other hand,the boundary element method(BEM)is a high-efficiency numerical method and has unique advantages in the analysis of infinite external acoustic field problems.The piecewise constant level set(PCLS)method developed in recent years can overcome the obvious disadvantages of the traditional level set method,and has been used in the topology optimization.This dissertation combines the finite element method(FEM)and the BEM to an-alyze the vibro-acoustic problems.An improved piecewise constant level set method has been developed for the macro and micro bi-material topology optimization design of the coupled structural-acoustic systems.The vibration and noise level of the coupled structural-acoustic systems can be reduced effectively and an effective numerical anal-ysis procedure has been developed.Three main parts are included in this dissertation as follow:(1)Response and sensitivity analysis of the coupled structural-acoustic sys-tems based on the FEM/BEM.Considering the flexibility and stability of the FEM in the structure analysis and the superiority of the BEM in the exterior acoustic field analysis,in this dissertation,we use FEM for srtuctural modeling and BEM for acoustic field modeling to analyze the response of structural-acoustic systems.In view of the high-efficiency in the complex optimization problem with multiple variables,we use the adjoint variable method to obtain the sensitivity of the target function.The detailed analysis process is derived and numerical examples are given to verify the correctness of the response analysis and sensitivity analysis of structural-acoustic systems,which pro-vides the basis for the macro and micro topology optimization designs of the coupling systems.(2)Topology optimization in coupled structural-acoustic systems based on piecewise constant level set(PCLS)method.The piecewise constant level method developed in recent years has some improvements over the traditional level set method,such as the initialization is more general,holes can be created in the optimization pro-cess.This dissertation uses the PCLS method to perform the topology optimization of the coupled systems.As for the problem-dependent problem of the optimizing pa-rameter in the PCLS method,we propose a new updating formula based on sensitivity information and perform several verification examples.Finally,macro topology opti-mization desigs for minimizing the vibration and noise level of the coupled systems are realized respectively,which provides ideas for practical design of the coupled systems.(3)Microstructural topology optimization in coupled structural-acoustic sys-tems based on the improved PCLS method.On the basis of the response and sensitiv-ity analysis of the structural-acoustic systems,the structural macro-equivalent perfor-mance analysis and the sensitivity analysis of the microstructure design are performed based on the homogenization method,and the detailed process is derived.Microstruc-tural topology optimization of bi-materal in exterior acoustic-structure interaction sys-tems is realized based on the improved PCLS method,which provides a new scheme for reducing the vibration and noise level of coupled systems.