Abstract
A simple quadrilateral shell element is proposed in this work to study large deformations and large rotations of membrane/plate/shell structures. There are three merit characters in this element: locking-free; immune to mesh distortions; and robust to surface tessellations. Numerical issues in plates/shell elements such as shear-locking and thickness-locking problems are resolved, and quadrilateral area coordinates are adopted to solve the mesh distortion issues. This element can be adopted to curved shell structures, and warped deformations can be well described. Moreover, even if a shell structure cannot be easily tessellated by high quality quadrilateral polygons, it can still be discretized by a mesh consisting of high-quality triangular and quadrilateral elements, then this element can work together with a corresponding triangular element to provide accurate results on this combined mesh, and the degree-of-freedom for the discretized system is no more than several times of the number of nodes. Numerical tests validate the effectiveness, efficiency, and universality of this element in engineering scenarios.
Issue Section:
Research Papers
References
1.
Shabana
,
A. A.
, 1997
, “
Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation
,” Multibody Syst. Dyn.
,
1
(3
), pp. 339
–348
.10.1023/A:1009740800463
2.
Gerstmayr
,
J.
,
Sugiyama
,
H.
, and
Mikkola
,
A.
, 2013
, “
Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems
,” ASME J. Comput. Nonlinear Dyn.
,
8
(3
), p. 031016
.10.1115/1.4023487
3.
Otsuka
,
K.
,
Makihara
,
K.
, and
Sugiyama
,
H.
, 2022
, “
Recent Advances in the Absolute Nodal Coordinate Formulation: Literature Review From 2012 to 2020
,” ASME J. Comput. Nonlinear Dyn.
,
17
(8
), p. 080803
.10.1115/1.4054113
4.
Mikkola
,
A. M.
, and
Shabana
,
A. A.
, 2003
, “
A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications
,” Multibody Syst. Dyn.
,
9
(3
), pp. 283
–309
.10.1023/A:1022950912782
5.
Dufva
,
K.
, and
Shabana
,
A. A.
, 2005
, “
Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation
,” Proc. Inst. Mech. Eng., Part K
,
219
(4
), pp. 345
–355
.10.1243/146441905X50678
6.
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
, 2003
, “
Description of Elastic Forces in Absolute Nodal Coordinate Formulation
,” Nonlinear Dyn.
,
34
(1/2
), pp. 53
–74
.10.1023/B:NODY.0000014552.68786.bc
7.
Patel
,
M.
, and
Shabana
,
A. A.
, 2018
, “
Locking Alleviation in the Large Displacement Analysis of Beam Elements: The Strain Split Method
,” Acta Mech.
,
229
(7
), pp. 2923
–2946
.10.1007/s00707-018-2131-5
8.
Dmitrochenko
,
O.
, and
Mikkola
,
A.
, 2011
, “
Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Coordinate Formulation
,” Proc. Inst. Mech. Eng., Part K
,
225
(1
), pp. 34
–51
.10.1177/2041306810392115
9.
Matikainen
,
M. K.
,
Valkeapää
,
A. I.
,
Mikkola
,
A. M.
, and
Schwab
,
A. L.
, 2014
, “
A Study of Moderately Thick Quadrilateral Plate Elements Based on the Absolute Nodal Coordinate Formulation
,” Multibody Syst. Dyn.
,
31
(3
), pp. 309
–338
.10.1007/s11044-013-9383-6
10.
Valkeapää
,
A. I.
, 2014
, “
Development of Finite Elements for Analysis of Biomechanical Structures Using Flexible Multibody Formulations
,” Ph.D. thesis,
Lappeenranta University of Technology
,
Lappeenranta, Finland
.11.
Ebel
,
H.
,
Matikainen
,
M.
,
Hurskainen
,
V.
, and
Mikkola
,
A.
, 2017
, “
Analysis of High-Order Quadrilateral Plate Elements Based on the Absolute Nodal Coordinate Formulation for Three-Dimensional Elasticity
,” Adv. Mech. Eng.
,
9
(6
), p. 1687814017705069
.10.1177/1687814017705069
12.
Mikkola
,
A. M.
, and
Matikainen
,
M. K.
, 2006
, “
Development of Elastic Forces for a Large Deformation Plate Element Based on the Absolute Nodal Coordinate Formulation
,” ASME J. Comput. Nonlinear Dyn.
,
1
(2
), pp. 103
–108
.10.1115/1.1961870
13.
Matikainen
,
M. K.
,
Schwab
,
A. L.
, and
Mikkola
,
A. M.
, 2009
, “
Comparison of Two Moderately Thick Plate Elements Based on the Absolute Nodal Coordinate Formulation
,” Multibody Dynamics 2009, ECCOMAS Thematic Conference
, Warsaw, Poland
, June 29–July 2,
K.
Arczewski
,
J.
Fra̧czek
, and
M.
Wojtyra
, eds., pp. 1
–21
.14.
Matikainen
,
M. K.
,
Mikkola
,
A.
, and
Schwab
,
A. L.
, 2009
, “
The Quadrilateral Fully-Parametrized Plate Elements Based on the Absolute Nodal Coordinate Formulation
,” J. Struct. Mech.
,
42
(3
), pp. 138
–148
.15.
Simo
,
J. C.
, and
Rifai
,
M. S.
, 1990
, “
A Class of Mixed Assumed Strain Methods and the Method of Incompatible Modes
,” Int. J. Numer. Methods Eng.
,
29
(8
), pp. 1595
–1638
.10.1002/nme.1620290802
16.
Shabana
,
A. A.
,
Desai
,
C. J.
,
Grossi
,
E.
, and
Patel
,
M.
, 2020
, “
Generalization of the Strain-Split Method and Evaluation of the Nonlinear ANCF Finite Elements
,” Acta Mech.
,
231
(4
), pp. 1365
–1376
.10.1007/s00707-019-02558-w
17.
Dmitrochenko
,
O. N.
,
Hussein
,
B. A.
, and
Shabana
,
A. A.
, 2009
, “
Coupled Deformation Modes in the Large Deformation Finite Element Analysis: Generalization
,” ASME J. Comput. Nonlinear Dyn.
,
4
(2
), p. 021002
.10.1115/1.3079682
18.
Hyldahl
,
P.
,
Mikkola
,
A. M.
,
Balling
,
O.
, and
Sopanen
,
J. T.
, 2014
, “
Behavior of Thin Rectangular ANCF Shell Elements in Various Mesh Configurations
,” Nonlinear Dyn.
,
78
(2
), pp. 1277
–1291
.10.1007/s11071-014-1514-y
19.
Ren
,
H.
, 2015
, “
Fast and Robust Full-Quadrature Triangular Elements for Thin Plates/Shells With Large Deformations and Large Rotations
,” ASME J. Comput. Nonlinear Dyn.
,
10
(5
), p. 051018
.10.1115/1.4030212
20.
Lee
,
N. S.
, and
Bathe
,
K. J.
, 1993
, “
Effects of Element Distortion on the Performance of Isoparametric Elements
,” Int. J. Numer. Methods Eng.
,
36
(20
), pp. 3553
–3576
.10.1002/nme.1620362009
21.
Long
,
Y. Q.
,
Li
,
J.
,
Long
,
Z.
, and
Cen
,
S.
, 1999
, “
Area Coordinates Used in Quadrilateral Elements
,” Commun. Numer. Methods Eng.
,
15
(8
), pp. 533
–545
.10.1002/(SICI)1099-0887(199908)15:8<533::AID-CNM265>3.0.CO;2-D
22.
Soh
,
A. K.
,
Long
,
Y. Q.
, and
Cen
,
S.
, 2000
, “
Development of Eight-Node Quadrilateral Membrane Elements Using the Area Coordinates Method
,” Comput. Mech.
,
25
(4
), pp. 376
–384
.10.1007/s004660050484
23.
Cen
,
S.
,
Chen
,
X. M.
, and
Fu
,
X. R.
, 2007
, “
Quadrilateral Membrane Element Family Formulated by the Quadrilateral Area Coordinate Method
,” Comput. Methods Appl. Mech. Eng.
,
196
(41–44
), pp. 4337
–4353
.10.1016/j.cma.2007.05.004
24.
Long
,
Y. Q.
, and
Huang
,
M. F.
, 1988
, “
A Generalized Conforming Isoparametric Element
,” Appl. Math. Mech. Engl. Ed.
,
9
(10
), pp. 929
–936
.10.1007/BF02014599
25.
Olshevskiy
,
A.
,
Dmitrochenko
,
O.
,
Dai
,
M. D.
, and
Kim
,
C.-W.
, 2015
, “
The Simplest 3-,6-, and 8-Node Fully-Parameterized ANCF Plate Elements Using Only Transverse Slopes
,” Multibody Syst. Dyn.
,
34
(1
), pp. 23
–51
.10.1007/s11044-014-9411-1
26.
Chen
,
X. M.
,
Cen
,
S.
,
Fu
,
X. R.
, and
Long
,
Y. Q.
, 2008
, “
A New Quadrilateral Area Coordinate Method (QAC-II) for Developing Quadrilateral Finite Element Models
,” Int. J. Numer. Methods Eng.
,
73
(13
), pp. 1911
–1941
.10.1002/nme.2159
27.
Armstrong
,
M. A.
, 1983
, Basic Topology
,
Springer
,
New York
, pp. 1
–4
.28.
Wilson
,
E. L.
,
Taylor
,
R. L.
,
Doherty
,
W. P.
, and
Ghabussi
,
T.
, 1973
, “
Incompatible Displacement Models
,” Numerical and Computer Methods in Structural Mechanics
,
S. T.
Fenven
, ed.,
Academic Press
,
New York
, pp. 43
–57
.29.
Taylor
,
R. L.
,
Beresford
,
P. J.
, and
Wilson
,
E. L.
, 1976
, “
A Non-Conforming Element for Stress Analysis
,” Int. J. Numer. Methods Eng.
,
10
(6
), pp. 1211
–1219
.10.1002/nme.1620100602
30.
MacNeal
,
R. H.
, and
Harder
,
R. L.
, 1985
, “
A Proposed Standard Set of Problems to Test Finite Element Accuracy
,” Finite Elem. Anal. Des.
,
1
(1
), pp. 3
–20
.10.1016/0168-874X(85)90003-4
31.
Yamashita
,
H.
,
Valkeapää
,
A.
,
Jayakumar
,
P.
, and
Sugiyama
,
H.
, 2015
, “
Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation
,” ASME J. Comput. Nonlinear Dyn.
,
10
(5
), p. 051012
.10.1115/1.4028657
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