Study On Acoustic Topology Optimization Of Isogeometric Boundary Element Method With Subdivision Surface

With the continuous expansion of the scope of human automation activities,aircraft and other means of transport to bring convenience at the same time accompanied by noise problems.Noise pollution is a serious threat to people's healthy life,and the study of structural acoustic properties can effectively solve this problem,so it is an important research topic.The method based on analytic solution has obtained a solid theoretical basis in the study of simple structural acoustics,but it is difficult to apply to complex practical structures,so it is of great practical significance to carry out an effective numerical solution method.The isogeometric analysis is used to express the geometric model and numerical analysis,and the seamless combination of computer aided design(CAD)and computer aided engineering(CAE)analysis is realized.In this paper,the structural acoustic analysis is carried out by combining the subdivision surface method with the boundary element method,and the validity of the algorithm is verified by taking the acoustic scattering problem of the structure of the adhesive sound absorbing material as an example.The main contents and innovation points of the paper are as follows:(1)Subdivision curve and surface based on isogeometry technology.The subdivision surface method can construct the discrete mesh of arbitrary topology into a whole smooth surface,and avoid the problem that the non-uniform rational B-splines(NURBS)method is difficult to stitch the surface piece.Using this method,the subdivision algorithm of two-dimensional polygon is established,and the triangular Loop subdivision and Quadrilateral Catmull-Clark Subdivision algorithm are established in three-dimensional situation respectively.The control mesh of a certain subdivision series is fitted with a surface fitting operation,and the Loop mode adopts quartic box-splines interpolation,while the Catmull-Clark mode uses bi-cubic B-splines interpolation.(2)Structural Acoustic and optimization analysis based on the boundary.element method of three-dimensional subdivision surface.According to the Helmholtz Green function,the boundary integral equation for solving the acoustic scattering problem is established.The boundary integral equation is discretized by Loop and Catmull-Clark subdivision surfaces,and the boundary element equations of the system are established by collocation method.The Burton-Miller method overcomes the non-uniqueness problem of the solution,and deal with the singular integrals of each order.The mathematical model of optimization problem is established,and the sensitivity analysis is carried out by using the adjoint variable method which is independent of the design variable.Based on the Delany-Bazley-Miki empirical model,the relationship between the admittance parameters and the relative density of the sound absorbing material element is established,and the topology optimization analysis of the sound absorbing material distribution is carried out in combination with the method of moving asymptotes(MMA)algorithm.Some practical examples show that the subdivision surface boundary element method is superior to the traditional boundary element method based on Lagrangian interpolation in calculation accuracy.At the same time,the distribution of adhesive sound absorbing materials with reasonable structure surface can save consumables and reduce costs,and achieve the optimal noise reduction effect.