Isogeometric symmetric FE-BE coupling method for acoustic-structural interaction

Abstract The problems of Acoustic-Structural Interaction (ASI) are commonly encountered in the simulation of the thin-walled structures immersed in the fluid. This interaction can affect the acoustic properties of the fluid and the dynamic characteristics of the structure. In this paper, a Non-Uniform Rational B-Splines (NURBS)-based Isogeometric Finite Element (FE) - Boundary Element (BE) symmetric coupling method is developed to study the ASI problems and the free vibration of the elastic structures submerged in the fluid. The geometry of the thin-walled structures is exactly modelled and discretized by utilizing the Isogeometric Reissner-Mindlin shell elements. This shell theory simplifies the continuity enforcement between NURBS patch boundaries. The Isogeometric Boundary Element Method (IGABEM) is applied to describe the acoustic field. In order to impose coupling constraints, a transformation equation of unknown variables on the interface between sound field and structure field is established, that is, sound pressure versus external force and particle velocity versus displacement. Different from the non-symmetric matrix obtained by the traditional direct BEM, a new variational formulation is introduced to obtain the symmetric coupling coefficient matrix, which maks this coupling approach suitable for a broad class of solvers and improves the robustness of the computation. The reliability and stability of the symmetric coupling method are verified by numerical examples considering acoustic and structural loadings. It is concluded that the symmetric coupling method possesses high accuracy, and can circumvent the limitation of traditional coupling method in solving open boundary problems.

[1]  John A. Evans,et al.  Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .

[2]  Jon Trevelyan,et al.  Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures , 2019, Computer Methods in Applied Mechanics and Engineering.

[3]  C. Zheng,et al.  FEM/wideband FMBEM coupling for structural–acoustic design sensitivity analysis , 2014 .

[4]  Y. P. Gong,et al.  A novel interface integral formulation for 3D steady state thermal conduction problem for a medium with non-homogenous inclusions , 2018, Computational Mechanics.

[5]  José A. González,et al.  Partitioned solution strategies for coupled BEM-FEM acoustic fluid-structure interaction problems , 2015 .

[6]  Olgierd Zaleski,et al.  Evaluation of hypersingular and nearly singular integrals in the Isogeometric Boundary Element Method for acoustics , 2017 .

[7]  A. Sommerfeld.  Partial Differential Equations in Physics , 1949 .

[8]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[9]  Richard W. Johnson.  Higher order B-spline collocation at the Greville abscissae , 2005 .

[10]  Chuanzeng Zhang,et al.  Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver , 2018, J. Comput. Phys..

[11]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[12]  T. Greville.  Numerical Procedures for Interpolation by Spline Functions , 1964 .

[13]  Olaf Steinbach,et al.  A fast BE‐FE coupling scheme for partly immersed bodies , 2010 .

[14]  Onur Atak,et al.  An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains , 2017 .

[15]  Delfim Soares,et al.  An optimized BEM-FEM iterative coupling algorithm for acoustic-elastodynamic interaction analyses in the frequency domain , 2012 .

[16]  Miguel C. Junger,et al.  Sound, Structures, and Their Interaction , 1972 .

[17]  Yonghong Wu,et al.  Isogeometric indirect boundary element method for solving the 3D acoustic problems , 2020, J. Comput. Appl. Math..

[18]  Michael C. H. Wu,et al.  Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials , 2015 .

[19]  Martin Ochmann,et al.  Boundary Element Acoustics Fundamentals and Computer Codes , 2002 .

[20]  S. Marburg,et al.  Computational acoustics of noise propagation in fluids : finite and boudary element methods , 2008 .

[21]  Ming-Chen Hsu,et al.  Penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches with application to composite wind turbine blades , 2019, Computer Methods in Applied Mechanics and Engineering.

[22]  Thomas-Peter Fries,et al.  Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems , 2016 .

[23]  J. Trevelyan,et al.  An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects , 2013, 1302.5305.

[24]  I. Mathews,et al.  Numerical techniques for three‐dimensional steady‐state fluid–structure interaction , 1986 .

[25]  Habibou Maitournam,et al.  Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells , 2015 .

[26]  C. Dong,et al.  Isogeometric FE-BE coupling approach for structural-acoustic interaction , 2020 .

[27]  Delfim Soares,et al.  A FEM-BEM coupling procedure to model the propagation of interacting acoustic-acoustic/acoustic-elastic waves through axisymmetric media , 2008 .

[28]  Haijun Wu,et al.  A coupling FEM/BEM method with linear continuous elements for acoustic-structural interaction problems , 2019, Applied Acoustics.

[29]  Thomas-Peter Fries,et al.  Fast Isogeometric Boundary Element Method based on Independent Field Approximation , 2014, ArXiv.

[30]  P. Kerfriden,et al.  Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth , 2017 .

[31]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[32]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[33]  Thomas-Peter Fries,et al.  Isogeometric Boundary Element Analysis with elasto-plastic inclusions. Part 1: Plane problems , 2015, ArXiv.

[34]  Lothar Gaul,et al.  Solution of FE‐BE coupled eigenvalue problems for the prediction of the vibro‐acoustic behavior of ship‐like structures , 2011 .

[35]  Toru Takahashi,et al.  A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver , 2016, 1606.02383.

[36]  Fehmi Cirak,et al.  Isogeometric FEM‐BEM coupled structural‐acoustic analysis of shells using subdivision surfaces , 2017, 1704.08491.

[37]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[38]  G. Beer,et al.  Isogeometric Boundary Element Analysis of steady incompressible viscous flow, Part 1: Plane problems , 2017 .

[39]  A. Ergin,et al.  Hydroelastic vibration analysis of plates partially submerged in fluid with an isogeometric FE-BE approach , 2019, Ocean Engineering.

[40]  N. Atalla,et al.  Finite Element and Boundary Methods in Structural Acoustics and Vibration , 2015 .

[41]  Lothar Gaul,et al.  A comparison of FE–BE coupling schemes for large‐scale problems with fluid–structure interaction , 2009 .

[42]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[43]  D. T. Wilton.  Acoustic radiation and scattering from elastic structures , 1978 .

[44]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[45]  T. Rabczuk,et al.  A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis , 2012 .

[46]  G. C. Everstine,et al.  Coupled finite element/boundary element approach for fluid–structure interaction , 1990 .