An isogeometric coupled boundary element method and finite element method for structural-acoustic analysis through loop subdivision surfaces

[摘要] This present thesis proposes a novel approach for coupling finite element and boundary element formulations using a Loop subdivision surface discretisation to allow efficient acoustic scattering analysis over shell structures. The analysis of underwater structures has always been a challenge for engineers because it couples shell structural dynamics and acoustic scattering. In the present work, a finite element implementation of the Kirchhoff-Love formulation is used for shell structural dynamic analysis and the boundary element method is adopted to solve the Helmholtz equation for acoustic scattering analysis. The boundary element formulation is chosen as it can handle infinite domains without volumetric meshes.In the conventional engineering workflow, generating meshes of complex geometries to represent the underwater structures, e.g. submarines or torpedoes, is very time consuming and costly even if it is only a data conversion process. Isogeometric analysis (IGA) is a recently developed concept which aims to integrate computer aided design (CAD) and numerical analysis by using the same geometry model. Non-uniform rational B-splines~(NURBS), the most commonly used CAD technique, were considered in early IGA developments. However, NURBS have limitations when used in analysis because of their tensor-product nature. Subdivision surfaces discretisation is an alternative to overcome NURBS limitation. The new method adopts a triangular Loop subdivision surface discretisation for both geometry and analysis. The high order subdivision basis functions have $C^1$ continuity, which satisfies the requirements of the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. The control meshes for the shell analysis and the acoustic analysis have the same resolution, which provides a fully integrated isogeometric approach for coupled structural-acoustic analysis of shells. The method is verified by the example of an acoustic plane wave which scatters over an elastic spherical shell. The ability of the presented method to handle complex geometries is also demonstrated.

[发布机构] University:University of Glasgow;Department:School of Engineering

[关键词] Isogeometric analysis, finite element method, boundary element method, structural-acoustic analysis.