Efficient finite element modeling of elastodynamic scattering

Paul D. Wilcox; Alexander Velichko

doi:10.1117/12.815454

8 April 2009 Efficient finite element modeling of elastodynamic scattering

Paul D. Wilcox, Alexander Velichko

Proceedings Volume 7295, Health Monitoring of Structural and Biological Systems 2009; 72951D (2009) https://doi.org/10.1117/12.815454
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2009, San Diego, California, United States

Abstract

The scattering of elastic waves by defects is the physical basis of ultrasonic NDE. Although analytical models exist for some canonical problems, the general case of scattering from an arbitrarily-shaped defect requires numerical methods such as finite elements (FE). In this paper, a robust and efficient FE technique is presented that is based on the premise of meshing a relatively small domain sufficient to enclose the scatterer. Plane waves are then excited from a particular direction by a numerical implementation of the Helmholtz-Kirchhoff integral that uses an encircling array of uni-modal point sources. The scattered field displacements are recorded at the same points and the field decomposed into plane waves of different modes at different angles. By repeating this procedure for different incident angles it is possible to generate the scattering- or S-matrix for the scatterer. For a given size of scatterer, all the information in an S-matrix can be represented in the Fourier domain by a limited number of complex coefficients. Thus the complete scattering behavior of an arbitrary-shaped scatterer can be characterized by a finite number of complex coefficients, that can be obtained from a relatively small number of FE model executions.

Citation Download Citation

Paul D. Wilcox and Alexander Velichko "Efficient finite element modeling of elastodynamic scattering", Proc. SPIE 7295, Health Monitoring of Structural and Biological Systems 2009, 72951D (8 April 2009); https://doi.org/10.1117/12.815454

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