Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 328, Issue -, Pages 554-564Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.09.025
Keywords
Isogeometric analysis; Quadrature rule; Dispersion analysis; Spectrum analysis
Funding
- European Union [644202]
- VMC's
- Basque Government through the BERC
- Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence [SEV-2013-0323]
- Spanish Ministry of Economy and Competitiveness [MTM2016-76329-R]
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We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two quadrature points per element to minimize the dispersion error (Barton et al., 2017 [ 1]), and they are equivalent to the optimized blending rules we recently described. Our approach further simplifies the numerical integration: instead of blending two three-point standard quadrature rules, we construct directly a single two-point quadrature rule that reduces the dispersion error to the same order for uniform meshes with periodic boundary conditions. Also, we present a 2.5-point rule for both uniform and non-uniform meshes with arbitrary boundary conditions. Consequently, we reduce the computational cost by using the proposed quadrature rules. Various numerical examples demonstrate the performance of these quadrature rules. (C) 2017 Elsevier B.V. All rights reserved.
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