Research On The Structural Shape And Topology Optimization Approaches For Acoustic And Vibro-acoustic Problems Based On The Boundary Element Method

In order to achieve efficient noise control,methods of optimization design have been introduced to noise analysis,where shape optimization and topology optimiza-tion are the research focus in current noise analysis.The purpose of shape optimization is to improve the acoustic performance of structure by changing the geometric shape,while the object of topology optimization is to achieve vibration and noise decrease by changing the distribution of structural materials.The boundary element method(BEM)has become a powerful tool for acoustic analysis due to its unique advantages.Thus,shape optimization and topology optimization models can be effectively established by combining BEM with optimization tools,and structural acoustic performance will be significantly improved after optimization design.Isogeometric analysis(IGA)has suc-cessfully eliminated the separated state between computer-aided design and computer-aided engineering.Considering IGA's advantages such as exact geometric model and no requirement for mesh regeneration,the time of shape design significantly decreases.On the other hand,the non-uniform rational basis spline(NURBS)in IGA also builds a bridge between the structural shape change and distribution of sound absorption ma-terial(SAM)on structure surface.This dissertation is mainly based on isogeometric boundary element method(IGA BEM)to carry out shape optimization,topology opti-mization of SAM and their combined optimization in acoustic problems.In addition,topology optimization of structural materials by FEM-BEM coupled analysis is also researched.The main content includes the following four parts:Shape optimization based on isogeometric wideband fast multipole boundary element method for 2D acoustic problems.Considering 2D exterior acoustic prob-lems,the general formulations of IGA BEM are derived based on NURBS interpolation.The Burton-Miller method is used to get stable solutions under the frequency domain analysis.The hyper-singular integral is solved based on the idea of singularity can-cellation with Cauchy principal value and Hadamard principal value.The wideband fast multipole method(WFMM)is introduced to IGA BEM to achieve a balance be-tween high accuracy and high efficiency of computation in wide frequency range,and the adjoint variable method(AVM)is adopted to improve the efficiency of shape sen-sitivity analysis.Finally,shape optimization approach is established with the MM A optimization solver to carry out shape design,and thus,acoustic values at reference plane decrease.Shape optimization based on isogeometric boundary element method for 3D acoustic problems.Considering 3D exterior acoustic problems,the basic equations of IGA BEM are derived based on NURBS surface interpolation.The idea of discon-tinuous element is combined with Bezier extraction operator to improve the analysis accuracy of IGA BEM.At the same time,according to the idea of the independent in-terpolation for geometry and physical fields,a discontinuous IGA BEM is established to expand IGA BEM for multi-patches models.The AVM is also adopted to obtain the shape sensitivity with high efficiency for multi design parameters.OpenMP parallel tool is adopted to decrease the computational time for complex problems with larger scale.Finally,shape optimization approach for 3D acoustics is built with MMA optimization tool.and shape design analysis is applied to problems with complex geometry.A combined shape and topology optimization approach based on isogeometric boundary element method for 3D acoustic problems.The basic formulations of IGA BEM with impedance boundary condition are derived on the basis of SAM covered on structural surfaces.Topology optimization of continuous material's distribution is car-ried out by using SIMP material interpolation model,and the AVM is also adopted to improve the computational efficiency of topology sensitivity analysis with multi design variables.NURBS interpolation is used to connect the change of structural shape with the distribution of SAM on structure surfaces.The NURBS control points' coordinates are set as shape design parameters,and the artificial densities of SAM on NURBS el-ements are selected as topology design variables.By choosing an effective iteration scheme to combine the shape change and the distribution of SAM,a combined shape and topology optimization approach is established for 3D acoustic problems,which will achieve a better noise reduction compared with the single type of shape optimization or topology optimization.A multi-frequency topology optimization approach of structural materials based on the FEM-BEM coupled method.Considering the structure composed by two different materials,sound radiation problem caused by structural vibration is effec-tively solved based on the FEM-BEM coupled method.Combining the SIMP method with the AVM to implement efficient topology sensitivity analysis,and then,topology optimization approach of structure-acoustic system is established based on the MMA optimization tool,which will achieve efficient noise and vibration reduction for the vibro-acoustic system.The computational efficiency on multi-frequency analysis is sig-nificantly improved through sound radiation modal analysis and interpolation technol-ogy of the impedance matrix.Finally,multi-frequency topology optimization approach of structural material is set up based on the vibro-acoustic analysis.More practical re-sults will be obtained after topology optimization with frequency band analysis,which can be a better guidance for engineering practice.In this dissertation,shape optimization,topology optimization of SAM,and com-bined optimization approaches are established based on IGA BEM for acoustic prob-lems.In addition,topology optimization with frequency band analysis for structural materials is also developed based on the FEM-BEM coupled method.Structural acous-tic performance has been improved by the mentioned methods,and finally an efficient noise control will be achieved.