This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the central processing unit (CPU) times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (nonuniform rational B-spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some multibody systems (MBS) applications, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible-link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

References

References
1.
Hamed
,
A. M.
,
2014
, “
New Finite Element Mesh for Efficient Modelling of Spatial Flexible Link Articulated Systems
,” Ph.D. dissertation, University of Illinois at Chicago, Chicago, IL.
2.
Shabana
,
A. A.
,
2014
,
Dynamics of Multibody Systems
,
4th ed.
,
Cambridge University
,
Cambridge, UK
.
3.
Korkealaakso
,
P.
,
Mikkola
,
A.
,
Rantalainen
,
T.
, and
Rouvinen
,
A.
,
2009
, “
Description of Joint Constraints in the Floating Frame of Reference Formulation
,”
Proc. Inst. Mech. Eng.
, Part K,
223
(2), pp.
133
144
.10.1243/14644193JMBD170
4.
Shabana
,
A. A.
,
Hamed
,
A. M.
,
Mohamed
,
A. A.
,
Jayakumar
,
P.
, and
Letherwood
,
M. D.
,
2012
, “
Use of B-spline in the Finite Element Analysis: Comparison With ANCF Geometry
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
4
), pp.
81
88
.10.1115/1.4004377
5.
Hamed
,
A. M.
,
Shabana
,
A. A.
,
Jayakumar
,
P.
, and
Letherwood
,
M. D.
,
2011
, “
Non-Structural Geometric Discontinuities in Finite Element/Multibody System Analysis
,”
Nonlinear Dyn.
,
66
(4), pp.
809
824
.10.1007/s11071-011-9953-1
6.
Shabana
,
A. A.
,
2010
, “
General Method for Modeling Slope Discontinuities and T-Sections Using ANCF Gradient Deficient Finite Elements
,”
ASME J. Comput. Nonlinear Dyn.
,
6
(
2
), p.
024502
.10.1115/1.4002339
7.
Shabana
,
A. A.
,
2012
,
Computational Continuum Mechanics
,
Cambridge University
,
Cambridge, UK
.
8.
Dmitrochenko
,
O. N.
, 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
9.
Abbas
,
L. K.
,
Rui
,
X.
, and
Hammoudi
,
Z. S.
,
2010
, “
Plate/Shell Element of Variable Thickness Based on the Absolute Nodal Coordinate Formulation
,”
Proc. Inst. Mech. Eng., Part K
,
224
(2), pp.
127
141
.10.1243/14644193JMBD244
10.
Dufva
,
K. E.
,
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
,
2005
, “
A Two-Dimensional Shear Deformable Beam Element Based on the Absolute Nodal Coordinate Formulation
,”
J. Sound Vib.
,
280
(3–5), pp.
719
738
.10.1016/j.jsv.2003.12.044
11.
Dufva
,
K.
,
Kerkkänen
,
K.
,
Maqueda
,
L. G.
, and
Shabana
,
A. A.
,
2007
, “
Nonlinear Dynamics of Three-Dimensional Belt Drives Using the Finite-Element Method
,”
Nonlinear Dyn.
,
48
(4), pp.
449
466
.10.1007/s11071-006-9098-9
12.
Schwab
,
A. L.
, and
Meijaard
,
J. P.
,
2010
, “
Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
5
(
1
), p. 011010.10.1115/1.4000320
13.
Shabana
,
A. A.
, and
Mikkola
,
A. M.
,
2003
, “
Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
342
350
.10.1115/1.1564569
14.
Tian
,
Q.
,
Chen
,
L. P.
,
Zhang
,
Y. Q.
, and
Yang
,
J. Z.
,
2009
, “
An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
4
(
2
), p.
021009
.10.1115/1.3079783
15.
Yakoub
,
R. Y.
, and
Shabana
,
A. A.
,
2001
, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Application
,”
ASME J. Mech. Des.
,
123
(
4
), pp.
614
621
.10.1115/1.1410099
16.
Omar
,
M. A.
, and
Shabana
,
A. A.
,
2001
, “
A Two-Dimensional Shear Deformation Beam for Large Rotation and Deformation
,”
J. Sound Vib.
,
243
(3), pp.
565
576
.10.1006/jsvi.2000.3416
17.
Gerstmayr
,
J.
, and
Shabana
,
A. A.
,
2006
, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation
,”
Nonlinear Dyn.
,
45
(1–2), pp.
109
130
.10.1007/s11071-006-1856-1
18.
Galaitsis
,
A. G.
,
1984
, “
A Model for Predicting Dynamic Track Loads in Military Vehicles
,”
ASME J. Vib. Acoust.
,
106
(
2
), pp.
286
291
.10.1115/1.3269183
19.
Bando
,
K.
,
Yoshida
,
K.
, and
Hori
,
K.
,
1991
, “
The Development of the Rubber Track for Small Size Bulldozers
,”
International Off-Highway & Powerplants Congress & Exposition
, Milwaukee, WI. 10.4271/911854
20.
Nakanishi
,
T.
, and
Shabana
,
A. A.
,
1994
, “
On the Numerical Solution of Tracked Vehicle Dynamic Equations
,”
Nonlinear Dyn.
,
6
, pp.
391
41
7.10.1007/BF0004S885
21.
Choi
,
J. H.
,
Lee
,
H. C.
, and
Shabana
,
A. A.
,
1998
, “
Spatial Dynamics of Multibody Tracked Vehicles, Part I: Contact Forces and Simulation Results
,”
Veh. Syst. Dyn.
,
29
(1), pp.
27
49
.10.1080/00423119808969365
22.
Choi
,
J. H.
,
Lee
,
H. C.
, and
Shabana
,
A. A.
,
1998
, “
Spatial Dynamics of Multibody Tracked Vehicles, Part II: Contact Forces and Simulation Results
,”
Veh. Syst. Dyn.
,
29
(2), pp.
113
137
.10.1080/00423119808969369
23.
Maqueda
,
L. G.
,
Mohamed
,
A. A.
, and
Shabana
,
A. A.
,
2010
, “
Use of General Nonlinear Material Models in Beam Problems: Application to Belts and Rubber Chains
,”
ASME J. Comput. Nonlinear Dyn.
,
5
(
2
), pp.
849
859
.10.1115/1.4000795
24.
Sugiyama
,
H.
,
Escalona
,
J. L.
, and
Shabana
,
A. A
,
2003
, “
Formulation of Three-Dimensional Joint Constraints Using the Absolute Nodal Coordinates
,”
Nonlinear Dyn.
,
31
(2), pp.
167
195
.10.1023/A:1022082826627
25.
Vallejo
,
D. G.
,
Escalona
,
J. L.
,
Mayo
,
J.
, and
Dominguez
,
J.
,
2003
, “
Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates
,”
Nonlinear Dyn.
,
34
(1–2), pp.
75
94
.10.1023/B:NODY.0000014553.98731.8d
26.
Hughes
,
T. J. R.
,
Cottrell
,
J. A.
, and
Bazilevs
,
Y.
,
2005
, “
Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement
,”
Comput. Methods Appl. Mech. Eng.
,
197
(49–50), pp.
4104
4412
.10.1016/j.cma.2008.04.006
27.
Piegl
,
L.
, and
Tiller
,
W.
,
1997
,
The NURBS Book
,
2nd ed.
,
Springer
,
New York
.
28.
Lan
,
P.
, and
Shabana
,
A. A.
,
2010
, “
Integration of B-spline Geometry and ANCF Finite Element Analysis
,”
Nonlinear Dyn.
,
61
(1–2), pp.
193
206
.10.1007/s11071-009-9641-6
29.
Mikkola
,
A.
,
Shabana
,
A. A.
,
Rebollo
,
C. S.
, and
Octavio
,
J. R. J.
,
2013
, “
Comparison Between ANCF and B-spline Surfaces
,”
Multibody Syst. Dyn.
,
30
(
2
), pp.
119
138
.10.1007/s11044-013-9353-z
30.
Berzeri
,
M.
,
Campanelli
,
M.
, and
Shabana
,
A. A.
,
2001
, “
Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation
,”
Multibody Syst. Dyn.
,
5
(1), pp.
21
54
.10.1023/A:1026465001946
31.
Gerstmayr
,
J.
, and
Irschik
,
H.
,
2008
, “
On the Correct Representation of Bending and Axial Deformation in the Absolute Nodal Coordinate Formulation with an Elastic Line Approach
,”
J. Sound Vib.
,
318
(3), pp.
461
487
.10.1016/j.jsv.2008.04.019
32.
Mohamed
,
A. A.
, and
Shabana
,
A. A.
,
2011
, “
Nonlinear Visco-Elastic Constitutive Model for Large Rotation Finite Element Formulation
,”
Multibody Syst. Dyn.
,
26
(1), pp.
57
79
.10.1007/s11044-011-9244-0
33.
Vallejo
,
D. G.
,
Valverde
,
J.
, and
Domínguez
,
J.
,
2005
, “
An Internal Damping Model for the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
42
(4), pp.
347
369
.10.1007/s11071-005-6445-1
34.
Mohamed
,
A. A.
,
2011
,
Visco-Elastic Nonlinear Constitutive Model for the Large Displacement Analysis of Multibody Systems
,
University of Illinois at Chicago
,
Chicago, IL
.
35.
Hussein
,
B.
,
Negrut
,
D.
, and
Shabana
,
A. A
,
2008
, “
Implicit and Explicit Integration in the Solution of the Absolute Nodal Coordinate Differential/Algebraic Equations
,”
Nonlinear Dyn.
,
54
(4), pp.
283
296
.10.1007/s11071-007-9328-9
36.
Hilber
,
H. M.
,
Hughes
,
T. J. R.
, and
Taylor
,
R. L
,
1977
, “
Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics
,”
Earthquake Eng. Struct. Dyn.
,
5
(3), pp.
283
292
.10.1002/eqe.4290050306
37.
Aboubak
,
A. K.
, and
Shabana
,
A. A.
,
2014
, “
Efficient Implementation of the TLISMNI Method
,” Technical Report No. MBS 2014-10-UIC, Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL.
38.
Maqueda
,
L. G.
, and
Shabana
,
A. A.
,
2007
, “
Poisson Modes and General Nonlinear Constitutive Models in the Large Displacement Analysis of Beams
,”
J. Multibody Syst. Dyn.
,
18
(
3
), pp.
375
396
.10.1007/s11044-007-9077-z
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