In this investigation, a continuum mechanics based bilinear shear deformable shell element is developed using the absolute nodal coordinate formulation (ANCF) for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the transverse gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the middle surface and the position vector gradient at a material point in the element are interpolated by bilinear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element lockings exhibited in the element are eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the continuum mechanics based bilinear shear deformable ANCF shell element proposed in this investigation.

References

References
1.
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
2.
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
3.
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
4.
Dmitrochenko
,
O.
, and
Pogorelov
,
D. Y.
,
2003
, “
Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation
,”
Multibody Syst. Dyn.
,
10
(
1
), pp.
17
43
.10.1023/A:1024553708730
5.
Dufva
,
K.
, and
Shabana
,
A. A.
,
2005
, “
Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation
,”
IMechE J. Multibody Dyn.
,
219
(
4
), pp.
345
355
.
6.
Schwab
,
A. L.
,
Gerstmayr
,
J.
, and
Meijaard
,
J. P.
,
2007
, “
Comparison of Three-Dimensional Flexible Thin Plate Elements for Multibody Dynamic Analysis: Finite Element Formulation and Absolute Nodal Coordinate Formulation
,”
Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
Las Vegas, NV
, pp.
1059
1070
.
7.
Nachbagauer
,
K.
,
Gruber
,
P.
, and
Gerstmayr
,
J.
,
2013
, “
Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples
,”
ASME J. Comput. Nonlinear Dyn.
,
8
, p.
021004
.10.1115/1.4006787
8.
Dmitrochenko
,
O.
,
Matikainen
,
M.
, and
Mikkola
,
A.
,
2012
, “
The Simplest 3- and 4-Noded Fully Parameterized ANCF Plate Elements
,”
Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
Chicago, IL
, pp.
317
322
.
9.
Valkeapää
,
A. I.
,
Yamashita
,
H.
,
Jayakumar
,
P.
, and
Sugiyama
,
H.
, “
On the Use of Elastic Middle Surface Approach in the Large Deformation Analysis of Moderately Thick Shell Structures Using Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
(submitted).
10.
Sze
,
K. Y.
,
2002
, “
Three-Dimensional Continuum Finite Element Models for Plate/Shell Analysis
,”
Prog. Struct. Eng. Mater.
,
4
(
4
), pp.
400
407
.10.1002/pse.133
11.
Vu-Quoc
,
L.
, and
Tan
,
X. G.
,
2003
, “
Optimal Solid Shells for Non-Linear Analyses of Multilayer Composites: I Statics
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
9–10
), pp.
975
1016
.10.1016/S0045-7825(02)00435-8
12.
Vu-Quoc
,
L.
, and
Tan
,
X. G.
,
2003
, “
Optimal Solid Shells for Non-Linear Analyses of Multilayer Composites: II Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
9–10
), pp.
1017
1059
.10.1016/S0045-7825(02)00336-5
13.
Mostafa
,
M.
,
Sivaselvan
,
M. V.
, and
Felippa
,
C. A.
,
2013
, “
A Solid-Shell Corotational Element Based on ANDES, ANS and EAS for Geometrically Nonlinear Structural Analysis
,”
Int. J. Num. Methods Eng.
,
95
(
2
), pp.
145
180
.10.1002/nme.4504
14.
Simo
,
J. C.
, and
Rifai
,
M. S.
,
1990
, “
A Class of Mixed Assumed Strain Methods and the Method of Incompatible Modes
,”
Int. J. Num. Methods Eng.
,
29
(
8
), pp.
1595
1638
.10.1002/nme.1620290802
15.
Andelfinger
,
U.
, and
Ramm
,
E.
,
1993
, “
EAS-Elements for Two-Dimensional, Three-Dimensional, Plate and Shell Structures and Their Equivalence to HR-Elements
,”
Int. J. Num. Methods Eng.
,
36
(
8
), pp.
1311
1337
.10.1002/nme.1620360805
16.
Dvorkin
,
E. N.
, and
Bathe
,
K. J.
,
1984
, “
A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis
,”
Eng. Comput.
,
1
(
1
), pp.
77
88
.10.1108/eb023562
17.
Bathe
,
K. J.
, and
Dvorkin
,
E. N.
,
1986
, “
A Formulation of General Shell Elements—The Use of Mixed Interpolation of Tensorial Components
,”
Int. J. Num. Methods Eng.
,
22
(
3
), pp.
697
722
.10.1002/nme.1620220312
18.
Betsch
,
P.
, and
Stein
,
E.
,
1995
, “
An Assumed Strain Approach Avoiding Artificial Thickness Straining for a Non-Linear 4-Node Shell Element
,”
Commun. Num. Methods Eng.
,
11
(
11
), pp.
899
909
.10.1002/cnm.1640111104
19.
Betsch
,
P.
,
Gruttmann
,
F.
, and
Stein
,
E.
,
1996
, “
A 4-Node Finite Shell Element for the Implementation of General Hyperelastic 3D-Elasticity at Finite Strains
,”
Comput. Methods Appl. Mech. Eng.
,
130
(
1
), pp.
57
79
.10.1016/0045-7825(95)00920-5
20.
Bischoff
,
M.
, and
Ramm
,
E.
,
1997
, “
Shear Deformable Shell Elements for Large Strains and Rotations
,”
Int. J. Num. Methods Eng.
,
40
(
23
), pp.
4427
4449
.10.1002/(SICI)1097-0207(19971215)40:23<4427::AID-NME268>3.0.CO;2-9
21.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2002
,
Concepts and Applications of Finite Element Analysis
,
4th ed.
,
Wiley
,
New York
.
22.
Bonet
,
J.
, and
Wood
,
D. R.
,
1997
,
Nonlinear Continuum Mechanics For Finite Element Analysis
,
Cambridge University Press
, Cambridge, UK.
23.
Sze
,
K. Y.
,
Liu
,
H. X.
, and
Lo
,
S. H.
,
2004
, “
Popular Benchmark Problems for Geometric Nonlinear Analysis of Shells
,”
Finite Elem. Anal. Des.
,
40
(
11
), pp.
1551
1569
.10.1016/j.finel.2003.11.001
24.
Stander
,
N.
,
Matzenmiller
,
A.
, and
Ramm
,
E.
,
1988
, “
An Assessment of Assumed Strain Methods in Finite Rotation Shell Analysis
,”
Eng. Comput.
,
6
(
1
), pp.
58
66
.10.1108/eb023760
25.
Parisch
,
H.
,
1991
, “
An Investigation of a Finite Rotation Four Node Assumed Strain Shell Element
,”
Int. J. Num. Methods Eng.
,
31
(
1
), pp.
127
150
.10.1002/nme.1620310108
26.
Matikainen
,
M. K.
,
Valkeapää
,
A. I.
,
Mikkola
,
A. M.
, and
Schwab
,
A. L.
,
2013
, “
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
You do not currently have access to this content.