Quadrature rules for isogeometric shell formulations: Study using a real-world application about metal forming

被引：5
作者：
Hokkanen, Jaro [1 ]
Pedroso, Dorival M. [1 ]
机构：
[1] Univ Queensland, Sch Civil Engn, St Lucia, Qld 4072, Australia
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2020年 / 363卷
关键词：
Isogeometric analysis; Quadrature rules; Reduced integration; Numerical locking; Hourglass problem; GAUSSIAN QUADRATURE; LOCKING-FREE; ELEMENT; INTEGRATION; SPLINES;
D O I：
10.1016/j.cma.2020.112904
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper studies quadrature rules for simulating large deformations of shells using isogeometric analysis. Several recently proposed rules and their effects on a real-world application known as incremental sheet forming are investigated. It is observed that, when tackling real-world applications, unexpected problems arise and, therefore, theoretical studies only with manufactured solutions are not enough for a complete verification of a method. The chosen application reveals problems with certain quadratures and that some simple stabilization strategies cannot completely suppress hourglass modes. Additionally, the effects of quadrature rules on the total computational costs are demonstrated and the influence of the maximum stable time step is assessed using a highly demanding simulation. (C) 2020 Elsevier B.Y. All rights reserved.
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页数：16
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共 29 条
[1]   Stable time step estimates for NURBS-based explicit dynamics [J].
Adam, C. ;
Bouabdallah, S. ;
Zarroug, M. ;
Maitournam, H. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 295 :581-605
[2]   Selective and reduced numerical integrations for NURBS-based isogeometric analysis [J].
Adam, C. ;
Hughes, T. J. R. ;
Bouabdallah, S. ;
Zarroug, M. ;
Maitournam, H. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 284 :732-761
[3]   Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells [J].
Adam, C. ;
Bouabdallah, S. ;
Zarroug, M. ;
Maitournam, H. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 284 :106-137
[4]   Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams [J].
Adam, C. ;
Bouabdallah, S. ;
Zarroug, M. ;
Maitournam, H. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 279 :1-28
[5]   Explicit Gaussian quadrature rules for C1 cubic splines with symmetrically stretched knot sequences [J].
Ait-Haddou, Rachid ;
Barton, Michael ;
Calo, Victor Manuel .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 290 :543-552
[6]   A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis [J].
Auricchio, F. ;
Calabro, F. ;
Hughes, T. J. R. ;
Reali, A. ;
Sangalli, G. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 249 :15-27
[7]   Gaussian quadrature rules for C1 quintic splines with uniform knot vectors [J].
Barton, Michael ;
Ait-Haddou, Rachid ;
Calo, Victor Manuel .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 322 :57-70
[8]   Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines [J].
Barton, Michael ;
Calo, Victor Manuel .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 296 :709-723
[9]   A large deformation, rotation-free, isogeometric shell [J].
Benson, D. J. ;
Bazilevs, Y. ;
Hsu, M-C ;
Hughes, T. J. R. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (13-16) :1367-1378
[10]   Isogeometric shell analysis: The Reissner-Mindlin shell [J].
Benson, D. J. ;
Bazilevs, Y. ;
Hsu, M. C. ;
Hughes, T. J. R. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) :276-289
123