On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems

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• 作者：Hauke Gravenkamp^a ; ^{hauke.gravenkamp@uni-due.de} ; Sundararajan Natarajan^b ; Wolfgang Dornisch^c
• 关键词：Isogeometric analysis ; Scaled boundary finite element method ; Wave propagation ; Spectral elements ; NURBS
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：315
• 期：Complete
• 页码：867-880
• 全文大小：413 K
• 卷排序：315

文摘

We discuss the application of non-uniform rational B-splines (NURBS) in the scaled boundary finite element method (SBFEM) for the solution of wave propagation problems at rather high frequencies. We focus on the propagation of guided waves along prismatic structures of constant cross-section. Comparisons are made between NURBS-based discretizations and high-order spectral elements in terms of the achievable convergence rates. We find that for the same order of shape functions, NURBS can lead to significantly smaller errors compared with Lagrange polynomials. The difference becomes particularly important at very high frequencies, where spectral elements are prone to instabilities. Furthermore, we analyze the behavior of NURBS for the discretization of curved boundaries, where the benefit of exact geometry representation becomes crucial even in the low-frequency range.