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

[1]  Chongmin Song,et al.  The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics , 1997 .

[2]  J. Wolf,et al.  The scaled boundary finite-element method – a primer: derivations , 2000 .

[3]  Géza Seriani,et al.  3-D large-scale wave propagation modeling by spectral element method on Cray T3E multiprocessor , 1998 .

[4]  Seymour V. Parter,et al.  On the Legendre–Gauss–Lobatto Points and Weights , 1999, J. Sci. Comput..

[5]  D. Komatitsch,et al.  Introduction to the spectral element method for three-dimensional seismic wave propagation , 1999 .

[6]  Beth A. Wingate,et al.  A generalized diagonal mass matrix spectral element method for non-quadrilateral elements , 2000 .

[7]  Spectral schemes on triangular elements , 2001 .

[8]  C. Brezinski.  Interpolation and Extrapolation , 2001 .

[9]  Jens Markus Melenk,et al.  On condition numbers in hp -FEM with Gauss-Lobatto-based shape functions , 2002 .

[10]  J. Rose,et al.  Guided wave dispersion curves for a bar with an arbitrary cross-section, a rod and rail example. , 2003, Ultrasonics.

[11]  J. Wolf,et al.  The scaled boundary finite element method , 2004 .

[12]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[13]  Andrew Deeks,et al.  Use of higher‐order shape functions in the scaled boundary finite element method , 2006 .

[14]  Chongmin Song,et al.  Development of a fundamental‐solution‐less boundary element method for exterior wave problems , 2006 .

[15]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[16]  Tim Warburton,et al.  An explicit construction of interpolation nodes on the simplex , 2007 .

[17]  Marek Krawczuk,et al.  Wave propagation modelling in 1D structures using spectral finite elements , 2007 .

[18]  Alessandro Reali,et al.  Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS , 2008 .

[19]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[20]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[21]  Chongmin Song,et al.  The scaled boundary finite element method in structural dynamics , 2009 .

[22]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[23]  T. Hughes,et al.  Efficient quadrature for NURBS-based isogeometric analysis , 2010 .

[24]  F. Tin-Loi,et al.  A unified 3D‐based technique for plate bending analysis using scaled boundary finite element method , 2012 .

[25]  Saeed Shojaee,et al.  Free vibration analysis of thin plates by using a NURBS-based isogeometric approach , 2012 .

[26]  U. Gabbert,et al.  Comparison of different higher order finite element schemes for the simulation of Lamb waves , 2012 .

[27]  Hauke Gravenkamp,et al.  The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method. , 2012, The Journal of the Acoustical Society of America.

[28]  Hauke Gravenkamp,et al.  A numerical approach for the computation of dispersion relations for plate structures using the Scaled Boundary Finite Element Method , 2012 .

[29]  T. Rabczuk,et al.  A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis , 2012 .

[30]  R. Echter,et al.  A hierarchic family of isogeometric shell finite elements , 2013 .

[31]  Hauke Gravenkamp,et al.  The computation of dispersion relations for three-dimensional elastic waveguides using the Scaled Boundary Finite Element Method , 2013 .

[32]  Hauke Gravenkamp,et al.  The computation of dispersion relations for axisymmetric waveguides using the Scaled Boundary Finite Element Method. , 2014, Ultrasonics.

[33]  Gao Lin,et al.  Scaled boundary isogeometric analysis for 2D elastostatics , 2014 .

[34]  J. Foley,et al.  Accurate solutions of wave propagation problems under impact loading by the standard, spectral and isogeometric high-order finite elements. Comparative study of accuracy of different space-discretization techniques , 2014 .

[35]  Roland Wüchner,et al.  A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis , 2014 .

[36]  Fabian Bause,et al.  On the computation of dispersion curves for axisymmetric elastic waveguides using the Scaled Boundary Finite Element Method , 2014 .

[37]  Sven Klinkel,et al.  A NURBS based hybrid collocation–Galerkin method for the analysis of boundary represented solids , 2015 .

[38]  Hauke Gravenkamp,et al.  Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the Scaled Boundary Finite Element Method , 2015, J. Comput. Phys..

[39]  Sven Klinkel,et al.  The weak substitution method – an application of the mortar method for patch coupling in NURBS‐based isogeometric analysis , 2015 .

[40]  Barbara Wohlmuth,et al.  Isogeometric mortar methods , 2014, 1407.8313.

[41]  Sven Klinkel,et al.  Hybrid collocation-Galerkin approach for the analysis of surface represented 3D-solids employing SB-FEM , 2015 .

[42]  S. Natarajan,et al.  Isogeometric analysis enhanced by the scaled boundary finite element method , 2015 .

[43]  Hauke Gravenkamp,et al.  Modeling ultrasonic waves in elastic waveguides of arbitrary cross-section embedded in infinite solid medium , 2015 .

[44]  Wim Desmet,et al.  A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics , 2016 .

[45]  W. Dornisch,et al.  An efficient and robust rotational formulation for isogeometric Reissner–Mindlin shell elements , 2016 .

[46]  B. H. Nguyen,et al.  An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems , 2016 .

[47]  Ralf Müller,et al.  Dual and approximate dual basis functions for B-splines and NURBS – Comparison and application for an efficient coupling of patches with the isogeometric mortar method , 2017 .

[48]  Hauke Gravenkamp,et al.  Efficient wave propagation simulation on quadtree meshes using SBFEM with reduced modal basis , 2017 .

[49]  Onur Atak,et al.  A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces , 2017 .

[50]  Hauke Gravenkamp,et al.  A semi‐analytical curved element for linear elasticity based on the scaled boundary finite element method , 2017 .

[51]  Sven Klinkel,et al.  Implicit dynamic analysis using an isogeometric Reissner–Mindlin shell formulation , 2017 .