In this work, an efficient topology optimization approach is proposed for a three-dimensional (3D) flexible multibody system (FMBS) undergoing both large overall motion and large deformation. The FMBS of concern is accurately modeled first via the solid element of the absolute nodal coordinate formulation (ANCF), which utilizes both nodal positions and nodal slopes as the generalized coordinates. Furthermore, the analytical formulae of the elastic force vector and the corresponding Jacobian are derived for efficient computation. To deal with the dynamics in the optimization process, the equivalent static load (ESL) method is employed to transform the topology optimization problem of dynamic response into a static one. Besides, the newly developed topology optimization method by moving morphable components (MMC) is used and reevaluated to optimize the 3D FMBS. In the MMC-based framework, a set of morphable structural components serves as the building blocks of optimization and hence greatly reduces the number of design variables. Therefore, the topology optimization approach has a potential to efficiently optimize an FMBS of large scale, especially in 3D cases. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the efficiency of the proposed optimization methodology, respectively.

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
.
2.
Olshevskiy
,
A.
,
Dmitrochenko
,
O.
,
Yang
,
H.
, and
Kim
,
C.
,
2017
, “
Absolute Nodal Coordinate Formulation of Tetrahedral Solid Element
,”
Nonlinear Dyn.
,
88
(
4
), pp.
2457
2471
.
3.
Tromme
,
E.
,
Tortorelli
,
D.
,
Brüls
,
O.
, and
Duysinx
,
P.
,
2015
, “
Structural Optimization of Multibody System Components Described Using Level Set Techniques
,”
Struct. Multidiscip. Optim.
,
52
(
5
), pp.
959
971
.
4.
Sun
,
J. L.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2017
, “
Topology Optimization Based on Level Set for a Flexible Multibody System Modeled Via ANCF
,”
Struct. Multidiscip. Optim.
,
55
, pp.
1159
1177
.
5.
Moghadasi
,
A.
,
Held
,
A.
, and
Seifried
,
R.
,
2016
, “
Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
1
), p.
011015
.
6.
Wang
,
Q. T.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2014
, “
Dynamic Simulation of Frictional Contacts of Thin Beams During Large Overall Motions Via Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
77
(
4
), pp.
1411
1425
.
7.
Shabana
,
A. A.
,
1996
, “An Absolute Nodal Coordinates Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,” University of Illinois at Chicago, Chicago, IL, Report No. MBS96-1-UIC.
8.
Tian
,
Q.
,
Zhang
,
Y. Q.
,
Chen
,
L. P.
, and
Yang
,
J. Z.
,
2010
, “
Simulation of Planar Flexible Multibody Systems With Clearance and Lubricated Revolute Joints
,”
Nonlinear Dyn.
,
60
(
4
), pp.
489
511
.
9.
Tian
,
Q.
,
Lou
,
J.
, and
Mikkola
,
A.
,
2017
, “
A New Elastohydrodynamic Lubricated Spherical Joint Model for Rigid-Flexible Multibody Dynamics
,”
Mech. Mach. Theory
,
107
, pp.
210
228
.
10.
Tian
,
Q.
,
Sun
,
Y. L.
,
Liu
,
C.
,
Hu
,
H. Y.
, and
Flores
,
P.
,
2013
, “
Elastohydrodynamic Lubricated Cylindrical Joints for Rigid-Flexible Multibody Dynamics
,”
Comput. Struct.
,
114–115
, pp.
106
120
.
11.
Shabana
,
A. A.
, and
Yakoub
,
R. Y.
,
2001
, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
,”
ASME J. Mech. Des.
,
123
(
4
), p.
606–613
.
12.
Zhao
,
J.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2011
, “
Modal Analysis of a Rotating Thin Plate Via Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
6
(
4
), p.
041013
.
13.
Liu
,
C.
,
Tian
,
Q.
,
Yan
,
D.
, and
Hu
,
H. Y.
,
2013
, “
Dynamic Analysis of Membrane Systems Undergoing Overall Motions, Large Deformations and Wrinkles Via Thin Shell Elements of ANCF
,”
Comput. Methods Appl. Mech. Eng.
,
258
, pp.
81
95
.
14.
Olshevskiy
,
A.
,
Dmitrochenko
,
O.
, and
Kim
,
C.
,
2013
, “
Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(2), p.
021001
.
15.
Brüls
,
O.
,
Lemaire
,
E.
,
Duysinx
,
P.
, and
Eberhard
,
P.
,
2011
, “
Optimization of Multibody Systems and Their Structural Components
,”
Multibody Dyn.: Comput. Methods Appl.
,
23
, pp.
49
68
.
16.
Tromme
,
E.
,
Brüls
,
O.
, and
Duysinx
,
P.
,
2016
, “
Weakly and Fully Coupled Methods for Structural Optimization of Flexible Mechanisms
,”
Multibody Syst. Dyn.
,
38
(
4
), pp.
391
417
.
17.
Hong
,
E. P.
,
You
,
B. J.
,
Kim
,
C. H.
, and
Park
,
G. J.
,
2010
, “
Optimization of Flexible Components of Multibody Systems Via Equivalent Static Loads
,”
Struct. Multidiscip. Optim.
,
40
(
1–6
), pp.
549
562
.
18.
Kang
,
B. S.
,
Park
,
G. J.
, and
Arora
,
J. S.
,
2005
, “
Optimization of Flexible Multibody Dynamic Systems Using the Equivalent Static Load Method
,”
AIAA J.
,
43
(
4
), pp.
846
852
.
19.
Lee
,
H. A.
, and
Park
,
G. J.
,
2015
, “
Nonlinear Dynamic Response Topology Optimization Using the Equivalent Static Loads Method
,”
Comput. Methods Appl. Mech. Eng.
,
283
, pp.
956
970
.
20.
Tromme
,
E.
,
Sonneville
,
V.
,
Brüls
,
O.
, and
Duysinx
,
P.
,
2016
, “
On the Equivalent Static Load Method for Flexible Multibody Systems Described With a Nonlinear Finite Element Formalism
,”
Int. J. Numer. Methods Eng.
,
108
(
6
), pp.
646
664
.
21.
Yang
,
Z. J.
,
Chen
,
X.
, and
Kelly
,
R.
,
2012
, “
A Topological Optimization Approach for Structural Design of a High-Speed Low-Load Mechanism Using the Equivalent Static Loads Method
,”
Int. J. Numer. Methods Eng.
,
89
(
5
), pp.
584
598
.
22.
Zhang
,
W. S.
,
Li
,
D.
,
Yuan
,
J.
,
Song
,
J. F.
, and
Guo
,
X.
,
2017
, “
A New Three-Dimensional Topology Optimization Method Based on Moving Morphable Components (MMCs)
,”
Comput. Mech.
,
59
(
4
), pp.
647
665
.
23.
Moghadasi
,
A.
,
Held
,
A.
, and
Seifried
,
R.
,
2014
, “
Topology Optimization of Flexible Multibody Systems Using Equivalent Static Loads and Displacement Fields
,”
Proc. Appl. Math. Mech.
,
14
(
1
), pp.
35
36
.
24.
Ghandriz
,
T.
,
Führer
,
C.
, and
Elmqvist
,
H.
,
2017
, “
Structural Topology Optimization of Multibody Systems
,”
Multibody Syst. Dyn.
,
39
(
1–2
), pp.
135
148
.
25.
Xia
,
Q.
, and
Shi
,
T.
,
2016
, “
Topology Optimization of Compliant Mechanism and Its Support Through a Level Set Method
,”
Comput. Methods Appl. Mech. Eng.
,
305
, pp.
359
375
.
26.
Guo
,
X.
,
Zhang
,
W. S.
, and
Zhong
,
W. L.
,
2014
, “
Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework
,”
ASME J. Appl. Mech.
,
81
(
8
), p.
081009
.
27.
Zhang
,
W. S.
,
Yuan
,
J.
,
Zhang
,
J.
, and
Guo
,
X.
,
2016
, “
A New Topology Optimization Approach Based on Moving Morphable Components (MMC) and the Ersatz Material Model
,”
Struct. Multidiscip. Optim.
,
53
(
6
), pp.
1243
1260
.
28.
Guo
,
X.
,
Zhang
,
W. S.
,
Zhang
,
J.
, and
Yuan
,
J.
,
2016
, “
Explicit Structural Topology Optimization Based on Moving Morphable Components (MMC) With Curved Skeletons
,”
Comput. Methods Appl. Mech. Eng.
,
310
, pp.
711
748
.
29.
Zhang
,
W. S.
,
Li
,
D.
,
Zhang
,
J.
, and
Guo
,
X.
,
2016
, “
Minimum Length Scale Control in Structural Topology Optimization Based on the Moving Morphable Components (MMC) Approach
,”
Comput. Methods Appl. Mech. Eng.
,
311
, pp.
327
355
.
30.
Hoang
,
V.
, and
Jang
,
G.
,
2017
, “
Topology Optimization Using Moving Morphable Bars for Versatile Thickness Control
,”
Comput. Methods Appl. Mech. Eng.
,
317
, pp.
153
173
.
31.
Garcia-Vallejo
,
D.
,
Mayo
,
J.
, and
Escalona
,
J. L.
,
2004
, “
Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
,
35
(
4
), pp.
313
329
.
32.
Arnold
,
M.
, and
Brüls
,
O.
,
2007
, “
Convergence of the Generalized-α Scheme for Constrained Mechanical Systems
,”
Multibody Syst. Dyn.
,
18
(2), pp.
185
202
.
33.
Sun
,
J. L.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2016
, “
Structural Optimization of Flexible Components in a Flexible Multibody System Modeled Via ANCF
,”
Mech. Mach. Theory
,
104
, pp.
59
80
.
34.
Luo
,
Z.
,
Chen
,
L. P.
,
Yang
,
J. Z.
, and
Zhang
,
Y. Q.
,
2006
, “
Multiple Stiffness Topology Optimizations of Continuum Structures
,”
Int. J. Adv. Manuf. Technol.
,
30
(
3–4
), pp.
203
214
.
35.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
.
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