16 April 2013 The selection of spectral element polynomial orders for high frequency numerical wave propagation
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Understanding the propagating elastic wave characteristics in materials is the foundation for quantitative Nondestructive Testing methods based on wave propagation such as guided wave ultrasonic and acoustic emission. The conventional finite element formulation requires very fine meshing and small time steps to prevent the dispersion pollution at high frequencies. The spectral finite elements reduce the required degrees of freedoms and the computation of time integration for dynamic finite element models via using high order orthogonal polynomials to define the locations of nodal coordinates. In this study, the advantage of spectral elements over conventional finite elements for frequencies up to 400 kHz is demonstrated on plane stress model of a structural steel plate. The excitation frequency is varied from 60 kHz to 400 kHz. The Legendre orthogonal polynomials with the orders of 3, 4 and 5 are selected. The required h refinements (i.e. element size) to eliminate the numerical error for three polynomial orders are identified. The results provide a guide for selecting the element sizes for different polynomial orders. The validity of the spectral element formulation is demonstrated via comparison with conventional finite element results.
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Zahra Heidary, Zahra Heidary, Didem Ozevin, Didem Ozevin, } "The selection of spectral element polynomial orders for high frequency numerical wave propagation", Proc. SPIE 8694, Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2013, 86941F (16 April 2013); doi: 10.1117/12.2009243; https://doi.org/10.1117/12.2009243

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