Isogeometric FE-BE coupling approach for structural-acoustic interaction

Abstract

This paper introduces two NURBS (Non-Uniform Rational B-Splines)-based Isogeometric FE (Finite Element)-BE (Boundary Element) coupling approaches, i.e. DCM (Directed Coupling Method) and SICM (Symmetric-Iterative Coupling Method), to solve the structural-acoustic interaction problems. IGA (IsoGeometric Analysis) can eliminate the substantial geometrical errors and time-consuming meshing steps. Meanwhile, CAD (Computer Aided Design) only makes use of surface representations to model geometrical objects, which is naturally combined with BEM (Boundary Element Method). Therefore, the IGABEM (Isogeometric Boundary Element Method) simulates the acoustic domain described by the Helmholtz equation, while structures are discretized by using the Isogeometric Reissner-Mindlin shell elements that only require C0-continuity across the element boundaries, which simplifies the continuity enforcement between patch boundaries. The main strategy of two coupling approaches is to establish the transformation of interface boundary conditions, that is, the sound pressure is converted to the force boundary conditions of shell structure. The reliability and accuracy of DCM are verified by analytical solutions or Lagrange-based coupling method. By using the model with six identical bi-quartic NURBS patches, the geometric singularity of the spherical surface is eliminated, and the accuracy is significantly improved. It is found that the interaction between the fluid and structure is closely related to the physical properties of the fluid. Compared with Lagrange model, IGA method has much higher accuracy and convergence. SICM method is introduced for the first time to deal with the structure-sound interaction problem. Although SICM fails near the natural frequency of the structure, it has the advantage of generating symmetric coupling matrix, which greatly reduces the dimension of the matrix. Finally, a complex toroidal shell subjected to the mixed structural-acoustic loads, including the plane acoustic wave and the concentrated load, is investigated.