IGABEM-based Optimization For Structural-acoustic Problems

Noise problems are increasing seriously nowadays.The optimization design of structures is an effective solution to improve its noise reduction performance,which has practical significance and social benefits.In this dissertation,an isogeometric boundary element method in acoustics is presented for topology optimization of absorbing material distribution,and subdivision surface boundary element method is used for the sound field scattering analysis.The main contents are as follows:1.The acoustic analysis and shape optimization analysis of structures based on isogeometric boundary element method are presented for two dimensions in this dissertation.The isogeometric interpolation uses the same expressions of analysis model and geometrical model.Design variables are set to be the coordinates of the control points of non-uniform rational Bsplines(NURBS)representing the structural model,the objective function is set to be the mean acoustic pressure at some computing points in a certain frequency range.We present the mathematical model of the structural acoustic optimization based on the isogeometric boundary element method(IGABEM),and the method of moving asymptotes(MMA)is applied for the shape optimization analysis of two-dimensional structures.2.FEM/FMBEM coupling analysis for 3-D acoustic structure interaction problems is presented in this dissertation.A coupling algorithm based on the finite element method(FEM)and the fast multipole boundary element method(FMBEM)is proposed to simulate the radiating and scattering problems of underwater structures.The expressions of radiated sound power on structure surface and in fluid are deduced,respectively.FEM is employed to model the structure parts and FMBEM is used to model the exterior acoustic domain.The impact of acoustic admittance on the radiating and scattering problems of the underwater structure is also researched.Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.3.An optimization approach is designed to optimize the distribution of the porous layer inside cavity,seeking to decrease the noise level or to increase the sound energy dissipated.Sound level and sound pressure level are set to be the objective functions.The Delany-Bazley-Miki empirical model is used to describe the acoustic absorption characteristics.Establishing an admittance interpolation scheme via the solid isotropic microstructure with penalization(SIMP)method,the discrete optimization is transformed into a continuous optimization problem,which can be calculated by a gradient solver.To calculate the sensitivities with respect to numbers of design variables,a fast sensitivity analysis approach is improved,based on the combination of the fast multipole method(FMM)and the adjoint variable method(AVM).A cabin numerical example is introduced to validate the optimization approach.4.An optimization approach is designed to optimize the thickness of the porous layer embedded inside a muffler,trying to maximize the transmission loss(TL).The TL value is chosen to be the objective function,which can be computed from the four-pole parameters based on the boundary element analysis.The thicknesses of the elements are the design variables,making it a continuous optimization problem.A sensitivity analysis is developed via the grouping of BEM and AVM.MMA is introduced to calculate the optimization problem.The thickness-based optimization procedure compares with the density-based one developed previously,showing extraordinary similarities in the results.Numerical examples indicate the frequency-dependency.Thus a frequency-averaged TL in the frequency band is selected as the objective function to achieve a multi-frequency optimization.5.The isogeometrie boundary element method is applied for wave scattering problems governed by Helmholtz equation.NURBS is applied to represent the geometric model and approximate physical field variables.The BurtonMiller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundaryvalue problems.FMM is applied to accelerate the solution of the system equations.IGABEM is used for 3-D shape design optimization and topology optimization of absorbing material distribution.6.The acoustic topology optimization is applied to the structural surface design of porous materials.Since the subdivision surface modeling has the advantage that the polygonal mesh model is not limited by the geometric topology and the parametric surface modeling has the overall smooth surface,and the sound field scattering analysis is carried out by the subdivision surface boundary element method.The acoustic characteristics of porous materials are simulated numerically by using the Delany-Bazley-Miki empirical model and introduced into the impedance boundary conditions of the boundary element simulation.Using SIMP method of the solid isotropic material with penalization,the density of artificial elements of porous materials was selected as the design variable,and the minimum sound pressure at the reference point was taken as the design objective.In this dissertation,the adjoint variable method is used to calculate the sensitivity of objective function to design variables.According to the gradient information,MMA is used to solve the optimal solution.The topological optimization method was verified by numerical examples,and the sound pressure attenuation caused by porous materials was observed and the optimal noise reduction effect was achieved.