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Isogeometric FEM‐BEM coupled structural‐acoustic analysis of shells using subdivision surfaces
Author(s) -
Liu Zhaowei,
Majeed Musabbir,
Cirak Fehmi,
N. Simpson Robert
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5708
Subject(s) - isogeometric analysis , finite element method , shell (structure) , boundary element method , helmholtz equation , subdivision , subdivision surface , discretization , polygon mesh , mathematics , helmholtz free energy , basis function , mathematical analysis , boundary (topology) , boundary value problem , computation , geometry , physics , structural engineering , engineering , algorithm , mechanical engineering , civil engineering , quantum mechanics
Summary We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin‐shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff‐Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work, the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the C 1 continuity property required for the Kirchhoff‐Love formulation and are highly efficient for the acoustic field computations. We verify the proposed isogeometric formulation through a closed‐form solution of acoustic scattering over a thin‐shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural‐acoustic analysis of shells.