Abstract

The performance of the absolute nodal coordinate formulation (ANCF) tetrahedral element in the analysis of liquid sloshing is evaluated in this paper using a total Lagrangian nonincremental solution procedure. In this verification study, the results obtained using the ANCF tetrahedral element are compared with the results of the ANCF solid element which has been previously subjected to numerical verification and experimental validation. The tetrahedral-element model, which allows for arbitrarily large displacements including rotations, can be systematically integrated with computational multibody system (MBS) algorithms that allow for developing complex sloshing/vehicle models. The new fluid formulation allows for systematically increasing the degree of continuity in order to obtain higher degree of smoothness at the element interface, eliminate dependent variables, and reduce the model dimensionality. The effect of the fluid/container interaction is examined using a penalty contact approach. Simple benchmark problems and complex railroad vehicle sloshing scenarios are used to examine the performance of the ANCF tetrahedral element in solving liquid sloshing problems. The simulation results show that, unlike the ANCF solid element, the ANCF tetrahedral element model exhibits nonsmoothness of the free surface. This difference is attributed to the gradient discontinuity at the tetrahedral-element interface, use of different meshing rules for the solid- and tetrahedral-elements, and the interaction between elements. It is shown that applying curvature-continuity conditions leads, in general, to higher degree of smoothness. Nonetheless, a higher degree of continuity does not improve the solution accuracy when using the ANCF tetrahedral elements.

References

1.
Ibrahim
,
R. A.
,
2005
,
Liquid Sloshing Dynamics: Theory and Applications
,
Cambridge University Press
,
Cambridge, UK
.
2.
Ibrahim
,
R. A.
,
2015
, “
Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems
,”
ASME J. Fluids Eng.
,
137
, p.
090801
.10.1115/1.4029544
3.
Ibrahim
,
R. A.
,
Pilipchuk
,
V. N.
, and
Ikeda
,
T.
,
2001
, “
Recent Advances in Liquid Sloshing Dynamics
,”
ASME Appl. Mech. Rev.
,
54
(
2
), pp.
133
199
.10.1115/1.3097293
4.
Dodge
,
F. T.
, and
Kana
,
D. D.
,
1966
, “
Moment of Inertia and Damping of Liquid in Baffled Cylindrical Tanks
,”
J. Spacecr. Rockets.
,
3
(
1
), pp.
153
155
.10.2514/3.28408
5.
Kana
,
D. D.
,
1987
, “
A Model for Nonlinear Rotary Slosh in Propellant Tanks
,”
J. Spacecr. Rockets.
,
24
(
2
), pp.
169
177
.10.2514/3.25891
6.
Kana
,
D. D.
,
1989
, “
Validated Spherical Pendulum Model for Rotary Liquid Slosh
,”
J. Spacecr. Rockets.
,
26
(
3
), pp.
188
195
.10.2514/3.26052
7.
Pinson
,
L. D.
,
1964
, “
Longitudinal Spring Constants for Liquid Propellant Tanks with Ellipsoidal Tanks
,”
NASA
,
Washington, DC
, Report No. NASA TN D-2220.
8.
Sumner
,
I. E.
,
1965
, “
Experimentally Determined Pendulum Analogy of Liquid Sloshing in Spherical and Oblate-Spherical Tanks
,” NASA, Washington, DC, Report No. NASA TN D-2737.
9.
Ranganathan
,
R.
,
Rakheja
,
S.
, and
Sankar
,
S.
,
1989
, “
Steady Turning Stability of Partially Filled Tank Vehicles With Arbitrary Tank Geometry
,”
ASME J. Dyn. Syst. Meas. Control
,
111
(
3
), pp.
481
489
.10.1115/1.3153078
10.
Aliabadi
,
S.
,
Johnson
,
A.
, and
Abedi
,
J.
,
2003
, “
Comparison of Finite Element and Pendulum Models for Simulation of Sloshing
,”
Comput. Fluids
,
32
(
4
), pp.
535
545
.10.1016/S0045-7930(02)00006-3
11.
Versteeg
,
H. K.
, and
Malalasekera
,
W.
,
2007
,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
, 2nd ed.,
Pearson/Prentice Hall
,
Upper Saddle River, NJ
.
12.
Reddy
,
J. N.
, and
Gartling
,
D. K.
,
2001
,
The Finite Element Method in Heat Transfer and Fluid Dynamics
, 2nd ed.,
CRC Press
,
Boca Raton, FL
.
13.
Zienkiewicz
,
O. C.
,
Nithiarasu
,
P.
, and
Taylor
,
R. L.
,
2005
,
The Finite Element Method for Fluid Dynamics
, 6th ed.,
Elsevier Butterworth-Heinemann
,
Amsterdam
.
14.
Anderson
,
J. D.
,
1995
,
Computational Fluid Dynamics: The Basics With Applications
,
McGraw-Hill
,
New York
.
15.
Zikanov
,
O.
,
2010
,
Essential Computational Fluid Dynamics
,
Wiley
,
Hoboken, NJ
.
16.
Gingold
,
R. A.
, and
Monaghan
,
J. J.
,
1977
, “
Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars
,”
Mon. Not. R. Astrono. Soc.
,
181
(
3
), pp.
375
389
.10.1093/mnras/181.3.375
17.
Liu
,
M. B.
, and
Liu
,
G. R.
,
2010
, “
Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments
,”
Arch. Comput. Methods Eng.
,
17
(
1
), pp.
25
76
.10.1007/s11831-010-9040-7
18.
Monaghan
,
J. J.
,
1988
, “
An Introduction to SPH
,”
Comput. Phys. Commun.
,
48
(
1
), pp.
89
96
.10.1016/0010-4655(88)90026-4
19.
Monaghan
,
J. J.
,
1992
, “
Smoothed Particle Hydrodynamics
,”
Annu. Rev. Astron. Astrophys.
,
30
(
1
), pp.
543
574
.10.1146/annurev.aa.30.090192.002551
20.
Monaghan
,
J. J.
,
1994
, “
Simulating Free Surface Flows With SPH
,”
J. Comput. Phys.
,
110
(
2
), pp.
399
406
.10.1006/jcph.1994.1034
21.
Wang
,
L.
,
Octavio
,
J. R. J.
,
Wei
,
C.
, and
Shabana
,
A. A.
,
2015
, “
Low Order Continuum-Based Liquid Sloshing Formulation for Vehicle System Dynamics
,”
ASME J. Comput. Nonlinear Dyn.
,
10
, p.
021022
.10.1115/1.4027836
22.
Hirt
,
C. W.
,
Amsden
,
A. A.
, and
Cook
,
J. L.
,
1997
, “
An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds
,”
J. Comput. Phys.
,
135
(
2
), pp.
203
216
.10.1006/jcph.1997.5702
23.
Hughes
,
T. J.
,
Liu
,
W. K.
, and
Zimmermann
,
T. K.
,
1981
, “
Lagrangian-Eulerian Finite Element Formulation for Incompressible Viscous Flows
,”
Comput. Methods Appl. Mech. Eng.
,
29
(
3
), pp.
329
349
.10.1016/0045-7825(81)90049-9
24.
Navti
,
S. E.
,
Ravindran
,
K.
,
Taylor
,
C.
, and
Lewis
,
R. W.
,
1997
, “
Finite Element Modelling of Surface Tension Effects Using a Lagrangian-Eulerian Kinematic Description
,”
Comput. Methods Appl. Mech. Eng.
,
147
(
1–2
), pp.
41
60
.10.1016/S0045-7825(97)00017-0
25.
Onate
,
E.
, and
Garcia
,
J.
,
2001
, “
A Finite Element Method for Fluid–Structure Interaction With Surface Waves Using a Finite Calculus Formulation
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
6–7
), pp.
635
660
.10.1016/S0045-7825(01)00306-1
26.
Soulaimani
,
A.
, and
Saad
,
Y.
,
1998
, “
An Arbitrary Lagrangian-Eulerian Finite Element Method for Solving Three-Dimensional Free Surface Flows
,”
Comput. Methods Appl. Mech. Eng.
,
162
(
1–4
), pp.
79
106
.10.1016/S0045-7825(97)00330-7
27.
Belytschko
,
T.
,
Liu
,
W. K.
,
Moran
,
B.
, and
Elkhodary
,
K.
,
2013
,
Nonlinear Finite Elements for Continua and Structures
,
Wiley
,
New York
.
28.
Wei
,
C.
,
Wang
,
L.
, and
Shabana
,
A. A.
,
2015
, “
A Total Lagrangian ANCF Liquid Sloshing Approach for Multibody System Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
5
), p.
051014
.10.1115/1.4028720
29.
Grossi
,
E.
, and
Shabana
,
A. A.
,
2017
, “
Validation of a Total Lagrangian ANCF Solution Procedure for Fluid–Structure Interaction Problems
,”
ASME J. Verif. Valid. Uncertainty Quantif.
,
2
(
4
), p.
041001
.10.1115/1.4038904
30.
Atif
,
M.
,
Chi
,
S. W.
,
Grossi
,
E.
, and
Shabana
,
A. A.
,
2019
, “
Evaluation of Breaking Wave Effects in Liquid Sloshing Problems: ANCF/SPH Comparative Study
,”
Nonlinear Dyn.
,
97
(
1
), pp.
45
62
.10.1007/s11071-019-04927-5
31.
Shi
,
H.
,
Wang
,
L.
,
Nicolsen
,
B.
, and
Shabana
,
A. A.
,
2017
, “
Integration of Geometry and Analysis for the Study of Liquid Sloshing in Railroad Vehicle Dynamics
,”
Proc. Inst. Mech. Eng., Part K: J. Multi-Body Dyn.
,
231
(
4
), pp.
608
629
.10.1177/1464419317696418
32.
Nicolsen
,
B.
,
Wang
,
L.
, and
Shabana
,
A.
,
2017
, “
Nonlinear Finite Element Analysis of Liquid Sloshing in Complex Vehicle Motion Scenarios
,”
J. Sound Vib.
,
405
, pp.
208
233
.10.1016/j.jsv.2017.05.021
33.
Grossi
,
E.
, and
Shabana
,
A. A.
,
2018
, “
ANCF Analysis of the Crude Oil Sloshing in Railroad Vehicle Systems
,”
J. Sound Vib.
,
433
, pp.
493
516
.10.1016/j.jsv.2018.06.035
34.
Gonzalez
,
J. A.
,
Lee
,
Y. S.
, and
Park
,
K. C.
,
2017
, “
Stabilized Mixed Displacement–Pressure Finite Element Formulation for Linear Hydrodynamic Problems With Free Surfaces
,”
Comput. Methods Appl. Mech. Eng.
,
319
, pp.
314
337
.10.1016/j.cma.2017.03.004
35.
Bonet
,
J.
, and
Wood
,
R. D.
,
1997
,
Nonlinear Continuum Mechanics for Finite Element Analysis
,
Cambridge University Press
,
Cambridge, UK
.
36.
Shabana
,
A. A.
,
2018
,
Computational Continuum Mechanics
, 3rd ed.,
Cambridge University Press
,
Cambridge, UK
37.
Pappalardo
,
C. M.
,
Wang
,
T.
, and
Shabana
,
A. A.
,
2017
, “
Development of ANCF Tetrahedral Finite Elements for the Nonlinear Dynamics of Flexible Structures
,”
Nonlinear Dyn.
,
89
(
4
), pp.
2905
2932
.10.1007/s11071-017-3635-6
38.
Ma
,
C.
,
Wang
,
R.
,
Wei
,
C.
, and
Zhao
,
Y.
,
2016
, “
A New Absolute Nodal Coordinate Formulation of Solid Element With Continuity Condition and Viscosity Model
,”
Int. J. Simul.: Syst., Sci. Technol.
,
17
(
21
), pp.
10.1
10.6
.https://ijssst.info/Vol-17/No-21/paper10.pdf
39.
Shabana
,
A. A.
, and
Zhang
,
D. Y.
,
2020
, “
ANCF Curvature Continuity: Application to Soft and Fluid Materials
,”
Nonlinear Dyn.
,
100
(
2
), pp.
1497
1517
.10.1007/s11071-020-05550-5
40.
Spencer
,
A. J. M.
,
1980
,
Continuum Mechanics
,
Longman
,
London, UK
.
41.
Ogden
,
R. W.
,
1984
,
Non-Linear Elastic Deformations
,
Dovers Publications
,
Mineola, NY
.
42.
Olshevskiy
,
A.
,
Dmitrochenko
,
O.
, and
Kim
,
C. W.
,
2014
, “
Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
2
), pp.
1
10
.10.1115/1.4024910
43.
Grüneisen
,
E.
,
1912
, “
Theorie Des Festen Zustandes Einatomiger Elemente
,”
Ann. Phys.
,
344
(
12
), pp.
257
306
.10.1002/andp.19123441202
44.
LS-DYNA,
2018
, “
LS-DYNA keyword user's manual
,”
LSTC
,
Livermore, CA
.
45.
Shabana
,
A. A.
,
Tobaa
,
M.
,
Sugiyama
,
H.
, and
Zaazaa
,
K.
,
2005
, “
On the Computer Formulations of the Wheel/Rail Contact Problem
,”
Nonlinear Dyn.
,
40
(
2
), pp.
169
193
.10.1007/s11071-005-5200-y
46.
Berzeri
,
M.
,
Sany
,
J. R.
, and
Shabana
,
A. A.
,
2000
, “
Curved Track Modeling Using the Absolute Nodal Coordinate Formulation
,”
University of Illinois
,
Chicago, IL
, Report No. MBS00-4-UIC.
47.
Shabana
,
A. A.
,
Zaazaa
,
K. E.
, and
Sugiyama
,
H.
,
2008
,
Railroad Vehicle Dynamics: A Computational Approach
,
Taylor & Francis/CRC
,
Boca Raton, FL
.
You do not currently have access to this content.