Abstract

This paper presents a configuration and sizing design optimization method for large deformation planar compliant mechanisms, using a continuum-based adjoint design sensitivity analysis (DSA) approach for built-up structures. Under the total Lagrangian formulation, the Jaumann strain formulation using the discretization of the global displacement field is employed to account for the finite deformation of arbitrarily curved Kirchhoff beams. In multipatch models, a rotational junction continuity condition is imposed using penalty and Lagrange multiplier methods. The developed adjoint DSA method can handle nonconservative loading conditions, which lead to asymmetry of tangent operator. Performance measures are displacements and rotation angles, and neutral axis configuration and cross-sectional thickness are considered as design variables. Also, analytical design sensitivity expressions for the rotation continuity condition are derived. Various compliant mechanisms including path-generators and an angular rotator are synthesized to demonstrate the applicability of the proposed method.

References

References
1.
McCarthy
,
J. M.
,
2011
, “
21st Century Kinematics: Synthesis, Compliance, and Tensegrity
,”
ASME J. Mech. Rob.
,
3
(
2
), p.
020201
. 10.1115/1.4003181
2.
Sigmund
,
O.
,
1997
, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
J. Struct. Mech.
,
25
(
4
), pp.
493
524
.10.1080/08905459708945415
3.
Pedersen
,
C. B.
,
Buhl
,
T.
, and
Sigmund
,
O.
,
2001
, “
Topology Synthesis of Large-Displacement Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
50
(
12
), pp.
2683
2705
. 10.1002/(ISSN)1097-0207
4.
Zhao
,
K.
, and
Schmiedeler
,
J. P.
,
2016
, “
Using Rigid-Body Mechanism Topologies to Design Path Generating Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
8
(
1
), p.
014506
. 10.1115/1.4030623
5.
Saxena
,
A.
,
2005
, “
Synthesis of Compliant Mechanisms for Path Generation Using Genetic Algorithm
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
745
752
. 10.1115/1.1899178
6.
Rai
,
A. K.
,
Saxena
,
A.
, and
Mankame
,
N. D.
,
2007
, “
Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements
,”
ASME J. Mech. Des.
,
129
(
10
), pp.
1056
1063
. 10.1115/1.2757191
7.
Hughes
,
T. J.
,
Cottrell
,
J. A.
, and
Bazilevs
,
Y.
,
2005
, “
Isogeometric Analysis: Cad, Finite Elements, Nurbs, Exact Geometry and Mesh Refinement
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
39
), pp.
4135
4195
. 10.1016/j.cma.2004.10.008
8.
Kiendl
,
J.
,
Bletzinger
,
K.-U.
,
Linhard
,
J.
, and
Wüchner
,
R.
,
2009
, “
Isogeometric Shell Analysis With Kirchhoff–Love Elements
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
49
), pp.
3902
3914
. 10.1016/j.cma.2009.08.013
9.
Choi
,
M.-J.
,
Yoon
,
M.
, and
Cho
,
S.
,
2016
, “
Isogeometric Configuration Design Sensitivity Analysis of Finite Deformation Curved Beam Structures Using Jaumann Strain Formulation
,”
Comput. Methods Appl. Mech. Eng.
309
, pp.
41
73
. 10.1016/j.cma.2016.05.040
10.
Duong
,
T. X.
,
Roohbakhshan
,
F.
, and
Sauer
,
R. A.
,
2017
, “
A New Rotation-Free Isogeometric Thin Shell Formulation and a Corresponding Continuity Constraint for Patch Boundaries
,”
Comput. Methods Appl. Mech. Eng.
316
, pp.
43
83
. 10.1016/j.cma.2016.04.008
11.
Cho
,
S.
, and
Ha
,
S.-H.
,
2009
, “
Isogeometric Shape Design Optimization: Exact Geometry and Enhanced Sensitivity
,”
Struct. Multidiscip. Optim.
,
38
(
1
), pp.
53
70
. 10.1007/s00158-008-0266-z
12.
Nagy
,
A. P.
,
Abdalla
,
M. M.
, and
Gürdal
,
Z.
,
2010
, “
Isogeometric Sizing and Shape Optimisation of Beam Structures
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
17
), pp.
1216
1230
. 10.1016/j.cma.2009.12.010
13.
Choi
,
M.-J.
, and
Cho
,
S.
,
2018
, “
Isogeometric Configuration Design Optimization of Shape Memory Polymer Curved Beam Structures for Extremal Negative Poisson’s Ratio
,”
Struct. Multidiscip. Optim.
,
58
(
5
), pp.
1861
1883
. 10.1007/s00158-018-2088-y
14.
Vu-Bac
,
N.
,
Duong
,
T.
,
Lahmer
,
T.
,
Zhuang
,
X.
,
Sauer
,
R.
,
Park
,
H.
, and
Rabczuk
,
T.
,
2018
, “
A Nurbs-Based Inverse Analysis for Reconstruction of Nonlinear Deformations of Thin Shell Structures
,”
Comput. Methods Appl. Mech. Eng.
331
, pp.
427
455
. 10.1016/j.cma.2017.09.034
15.
Radaelli
,
G.
, and
Herder
,
J. L.
,
2016
, “
Shape Optimization and Sensitivity of Compliant Beams for Prescribed Load–Displacement Response
,”
Mech. Sci.
,
7
(
2
), pp.
219
232
. 10.5194/ms-7-219-2016
16.
Crisfield
,
M. A.
, and
Jelenić
,
G.
,
1999
, “
Objectivity of Strain Measures in the Geometrically Exact Three-Dimensional Beam Theory and Its Finite-Element Implementation
,”
Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci.
,
455
(
1983
), pp.
1125
1147
. 10.1098/rspa.1999.0352
17.
Pai
,
P. F.
,
Anderson
,
T. J.
, and
Wheater
,
E. A.
,
2000
, “
Large-Deformation Tests and Total-Lagrangian Finite-Element Analyses of Flexible Beams
,”
Int. J. Solids Struct.
,
37
(
21
), pp.
2951
2980
. 10.1016/S0020-7683(99)00115-8
18.
Armero
,
F.
, and
Valverde
,
J.
,
2012
, “
Invariant Hermitian Finite Elements for Thin Kirchhoff Rods. I: The Linear Plane Case
,”
Comput. Methods Appl. Mech. Eng.
213
, pp.
427
457
. 10.1016/j.cma.2011.05.009
19.
Choi
,
M.-J.
, and
Cho
,
S.
,
2016
, “
Elimination of Self-Straining in Isogeometric Formulations of Curved Timoshenko Beams in Curvilinear Coordinates
,”
Comput. Methods Appl. Mech. Eng.
309
, pp.
680
692
. 10.1016/j.cma.2016.07.019
20.
Lin
,
C.
, and
Shih
,
C.
,
2002
, “
Topological Optimum Design of a Compliant Mechanism for Planar Optical Modulator
,”
J. Appl. Sci. Eng.
,
5
(
3
), pp.
151
158
.
You do not currently have access to this content.