A coupled isogeometric finite element and boundary element method with subdivision surfaces for structural -acoustic analysis of shell structures

Abstract

We demonstrate a method for simulating medium-wave acoustic scattering over elastic thin shell structures. We propose a coupled approach whereby the finite element formulation is used to describe the dynamic structural response of the shell and the boundary element method models the acoustic pressure within the infinite acoustic domain. The two methods are coupled through the relationship between acoustic velocities on the structural-fluid interface. In our approach, a conforming subdivision discretization is generated in Computer Aided Design (CAD) software which can be used directly for analysis in keeping with the idea of isogeometric analysis whereby a common geometry and analysis model is adopted. The subdivision discretization provides C1 surface continuity which satisfies the challenging continuity requirements of Kirchhoff-Love shell theory. The new method can significantly reduce the number of elements required per wavelength to gain same accuracy as an equivalent Lagrangian discretization, but the main benefit of our approach is the ability to handle arbitrarily complex geometries with smooth limit surfaces directly from CAD software. Our implementation make use of H-matrices to accelerate dense matrix computations and through this approach, we demonstrate the ability of our method to handle high-fidelity models with smooth surfaces for structural-acoustic analysis.