Isogeometric Boundary Element Method For Acoustic Sensitivity Analysis And Shape Optimization

The optimization of acoustic structures is very important as nowadays the noise problem becomes increasingly serious. The traffic noise pollution can be reduced ef-fectively by erecting barriers between the noise source and the zone to be protected. In order to improve the performance of a noise barrier, different shapes of barriers should be investigated. The shape optimization will not only improve the quality of acoustic structures, but also achieve significant economic and social benefits.In optimization process, building a valid connection between structural geometry description and analysis is a key step. Isogeometric analysis (IGA), instead of the con-ventional time-consuming mesh and remesh strategy, is a suitable choice for shape op-timization because it is convenient for shape control. Non-Uniform Rational B-Splines(NURBS), are chosen as basic functions to represent accurate structural geometry and approximate field variables. Compared with the traditional Lagrange polynomial-based interpolation, geometric errors can be removed completely in IGA. Furthermore, when the position of the control point is set as a parameter of structural shape control in IGA,shape changes can flexibly realize. This advantage plays an important role in the shape optimization process.This dissertation presents an isogeometric boundary element method in acoustics and a related sensitivity-based shape optimization algorithm for acoustic structures. The main contents are as follows:(1) An isogeometric fast multipole boundary element method in two dimensional acoustics is presented. The isogeometric boundary integral equations are formulated based on NURBS interpolation. An IGA version of the subtracting and adding back technique is adopted to eliminate singularities, in which the Cauchy principal value and the Hadamard finite part integral methods are also used. The fast multipole method(FMM) is applied to improve the overall computational efficiency.(2) The shape sensitivities in two dimensional acoustics are computed using the isogeometric fast multipole boundary element method. The sensitivity formulations are obtained by differentiating boundary integral equations with respect to control points based on isogeometric discretization. The direct differentiation method is adopted in this study because of its accuracy and convenience.(3) A sensitivity-related shape optimization algorithm is proposed based on the iso-geometric fast multipole boundary element method in two dimensional acoustics. Shape sensitivity can specify the optimal direction for shape design when it is coupled with a gradient-based optimization solver, such as method of moving asymptotes (MMA).The shape optimization of the ?-shaped sound barrier is used to study the performance of the presented algorithm on the improvement of noise reduction.(4) An isogeometric boundary element method in three dimensional acoustics and a related sensitivity analysis method are presented. The structure geometry is built by NURBS surface. In sensitivity analysis, the control points are selected as design vari-ables, and the direct differentiation method is used. The boundary integral equations and its sensitivity boundary integral equations are formulated under isogeometric dis-cretization. The similar technique is adopted to eliminated the singularities in boundary integral equations.