The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear algebraic constraint equations that can be applied at a preprocessing stage. These algebraic constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis.

References

References
1.
Omar
,
M. A.
,
Shabana
,
A. A.
,
Mikkola
,
A.
,
Loh
,
W. Y.
, and
Basch
,
R.
,
2004
, “
Multibody System Modeling of Leaf Springs
,”
J. Vib. Control
,
10
(
11
), pp.
1601
1638
.
2.
Dunaevskii
,
B.
,
1981
, “
Calculation of Solid Beams and Flat Springs (Leaf Springs) of Varying Cross-Section
,”
Sov. Eng. Res.
,
1
(
4
), pp.
29
32
.
3.
Society of Automotive Engineers
,
1985
, “
Spring Design Manual
,” Warrendale, PA, SAE Paper No. J1123.
4.
Donoso
,
A.
,
Chacón
,
J. M.
,
Rodríguez
,
A. G.
, and
Ureña
,
F.
,
2013
, “
On an Adjustable-Stiffness Spring Composed of Two Antagonistic Pairs of Nonlinear Leaf Springs Working in Post-Buckling
,”
Mech. Mach. Theory
,
63
, pp.
1
7
.
5.
Rahman
,
M. A.
, and
Kowser
,
M. A.
,
2010
, “
Inelastic Deformations of Stainless Steel Leaf Springs Experiment and Nonlinear Analysis
,”
Meccanica
,
45
(4), pp.
503
518
.
6.
Hou
,
J. P.
,
Cherruault
,
J. Y.
,
Nairne
,
I.
,
Jeronimidis
,
G.
, and
Mayer
,
R. M.
,
2007
, “
Evolution of the Eye-End Design of a Composite Leaf Spring for Heavy Axle Loads
,”
Compos. Struct.
,
78
(
3
), pp.
351
358
.
7.
Sugiyama
,
H.
,
Shabana
,
A. A.
,
Omar
,
M. A.
, and
Loh
,
W.
,
2006
, “
Development of Nonlinear Elastic Leaf Spring Model for Multi Body Vehicle Systems
,”
Comput. Methods Appl. Mech. Eng.
,
195
(50–51), pp.
6925
6941
.
8.
Gantoi
,
F. M.
,
Brown
,
M. A.
, and
Shabana
,
A. A.
,
2013
, “
Finite Element Modeling of the Contact Geometry and Deformation in Biomechanics Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
4
), p.
041013
.
9.
Zahavi
,
E.
,
1992
, “
Analysis of a Contact Problem in Leaf Springs
,”
Mech. Res. Commun.
,
19
(
1
), pp.
21
27
.
10.
Pareek
,
J. K.
,
1995
, “
Analytical Model of a Leaf Spring Suspension for Use in Quarter and Half Vehicle Simulations
,” Ph.D. dissertation,
Pennsylvania State University
,
State College, PA
.
11.
Parisch
,
H.
, and
Lübbing
,
C.
,
1997
, “
A Formulation of Arbitrarily Shaped Surface Elements for Three-Dimensional Large Deformation Contact With Friction
,”
Int. J. Numer. Methods Eng.
,
40
(
18
), pp.
3359
3383
.
12.
Chen
,
X.
,
Nakamura
,
K.
,
Mori
,
M.
, and
Hisaida
,
T.
,
2000
, “
Finite Element Analysis for Multi-Leaf Structures With Frictional Contact and Large Deformation
,”
Comput. Assisted Mech. Eng. Sci.
,
7
, pp.
53
67
.
13.
Wang
,
Q.
,
Tian
,
Q.
, and
Hu
,
H.
,
2014
, “
Dynamic Simulation of Frictional Contact of Thin Beams During Large Overall Motions Via Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
77
(
4
), pp.
1411
1425
.
14.
Litewka
,
P.
,
2013
, “
Enhanced Multiple-Point Beam-to-Beam Frictionless Contact Finite Element
,”
Comput. Mech.
,
52
(
6
), pp.
1365
1380
.
15.
Chamekh
,
M.
,
Mani-Aouadi
,
S.
, and
Moakher
,
M.
,
2009
, “
Modeling and Numerical Treatment of Elastic Rods With Frictionless Self-Contact
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
47
), pp.
3751
3764
.
16.
Patel
,
M.
,
Orzechowski
,
G.
,
Tian
,
Q.
, and
Shabana
,
A. A.
, “
A New MBS Approach for Tire Modeling Using ANCF Finite Elements
,”
Proc. Inst. Mech. Eng., Part K
(in press).
17.
Nunney
,
M. J.
,
2007
,
Light and Heavy Vehicle Technology
,
Oxford
, UK.
18.
Heisler
,
H.
,
2002
,
Advanced Vehicle Technology
,
2nd ed.
,
Butterworth-Heinemann
,
Oxford, UK
.
19.
Shabana
,
A. A.
,
2015
, “
ANCF Tire Assembly Model for Multibody System Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
024504
.
20.
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
.
21.
Shabana
,
A. A.
,
2014
,
Dynamics of Multibody Systems
,
4th ed.
,
Cambridge University Press
, New York.
22.
Shabana
,
A. A.
,
2015
, “
ANCF Reference Node for Multibody System Analysis
,”
Proc. Inst. Mech. Eng., Part K
,
229
(
1
), pp.
109
112
.
23.
Hamed
,
A. M.
,
Jayakumar
,
P.
,
Letherwood
,
M. D.
,
Gorsich
,
D. J.
,
Recuero
,
A. M.
, and
Shabana
,
A. A.
,
2015
, “
Ideal Compliant Joints and Integration of Computer Aided Design and Analysis
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
021015
.
24.
Heisler
,
H.
,
1999
,
Vehicle and Engine Technology
,
2nd ed.
,
Society of Automotive Engineers
,
Warrendale, PA
.
You do not currently have access to this content.