A generalized approach for efficient finite element modeling of elastodynamic scattering in two and three dimensions

• Published in: The Journal of the Acoustical Society of America 2010-09, Vol.128 (3), p.1004-1014
• Main Authors: Velichko, Alexander, Wilcox, Paul D.
• Format: Article
• Language: English
• Subjects: Acoustics; Anisotropy; Computer Simulation; Defects; Elasticity; Exact sciences and technology; Finite Element Analysis; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Models, Theoretical; Molecular Dynamics Simulation; Motion; Numerical Analysis, Computer-Assisted; Physics; Reproducibility of Results; Scattering; Signal Processing, Computer-Assisted; Solid mechanics; Structural and continuum mechanics; Three dimensional; Time Factors; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wave scattering
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.3467775

A robust and efficient technique for predicting the far-field scattering behavior for an arbitrarily-shaped defect in a generally anisotropic medium is presented that can be implemented in a commercial FE package. The spatial size of the modeling domain around the defect is as small as possible to minimize computational expense and a minimum number of models are executed. The method is based on an integral representation of a wave field in a homogeneous anisotropic medium. A plane incident mode is excited by applying suitable forces at nodes on a surface that encloses the scatterer. The scattered wave field is measured at monitoring nodes on a concentric surface and then decomposed into far-field scattering amplitudes of different modes in different directions. Example results for 2D and 3D bulk wave scattering in isotropic material and guided wave scattering are presented. Modeling accuracy is examined in various ways, including a comparison with the analytical solutions and calculation of the energy balance.