The objective of this paper is to introduce and demonstrate a new method for the topology optimization of compliant mechanisms. The proposed method relies on exploiting the topological derivative, and exhibits numerous desirable properties including: (1) the mechanisms are hinge-free; (2) mechanisms with different geometric and mechanical advantages (GA and MA) can be generated by varying a single control parameter; (3) a target volume fraction need not be specified, instead numerous designs, of decreasing volume fractions, are generated in a single optimization run; and (4) the underlying finite element stiffness matrices are well-conditioned. The proposed method and implementation are illustrated through numerical experiments in 2D and 3D.
Issue Section:
Design Automation
References
1.
Howell
, L. L.
, 2001
, Compliant Mechanisms
, Wiley
, New York
.2.
Ananthasuresh
, G. K.
, Kota
, S.
, and Gianchandani
, Y.
, 1994
, “A Methodical Approach to the Design of Compliant Micromechanisms
,” Solid State Sensor and Actuator Workshop
, pp. 189
–192
.3.
Kota
, S.
, Joo
, J.
, Rodgers
, S. M.
, and Sniegowski
, J.
, 2001
, “Design of Compliant Mechanisms: Applications to MEMS
,” Analog Integrated Circuits and Signal Processing
, 29
(1–2
), pp. 7
–15
.10.1023/A:10112658104714.
Kota
, S.
, Lu
, K. J.
, Kriener
, Z.
, Trease
, B.
, Arenas
, J.
, and Geiger
, J.
, 2005
, “Design and Application of Compliant Mechanisms for Surgical Tools
,” ASME J. Biomech. Eng.
, 127
(6
), pp. 981
–989
.10.1115/1.20565615.
Ma
, R.
, Slocum
, A. H.
, Sung
, E.
, Bean
, J. F.
, and Culpepper
, M. L.
, 2013
, “Torque Measurement With Compliant Mechanisms
,” ASME J. Mech. Des.
, 135
(3
), p. 034502
.10.1115/1.40233266.
Ananthasuresh
, G. K.
, and Howell
, L. L.
, 2005
, “Mechanical Design of Compliant Microsystems—A Perspective and Prospects
,” ASME J. Mech. Des.
, 127
(4
), pp. 736
–738
.10.1115/1.19001507.
Albanesi
, A. E.
, Fachinotti
, V. D.
, and Pucheta
, M. A.
, 2010
, “A Review on Design Methods for Compliant Mechanisms
,” Mec. Comput., Struct. Mech. (A)
, XXIX
(3
), pp. 59
–72
.8.
Yin
, L.
, and Ananthasuresh
, G. K.
, 2003
, “Design of Distributed Compliant Mechanisms
,” Mech. Based Des. Struct. Mach.
, 31
(2
), pp. 151
–179
.10.1081/SME-1200202899.
Cardoso
, E. L.
, and Fonseca
, J.
, 2004
, “Strain Energy Maximization Approach to the Design of Fully Compliant Mechanisms Using Topology Optimization
,” Lat. Am. J. Solids Struct.
, 1
(3
), pp. 263
–275
.10.
Saxena
, A.
, and Ananthasuresh
, G. K.
, 2000
, “On an Optimal Property of Compliant Topologies
,” Struct. Multidiscip. Optim.
, 19
(1
), pp. 36
–49
.10.1007/s00158005008411.
Frecker
, M. I.
, Ananthasuresh
, G. K.
, Nishiwaki
, S.
, Kikuchi
, N.
, and Kota
, S.
, 1997
, “Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimisation
,” ASME J. Mech. Des.
, 119
(2
), pp. 238
–245
.10.1115/1.282624212.
Sigmund
, O.
, 1997
, “On the Design of Compliant Mechanisms Using Topology Optimization
,” J. Struct. Mech.
, 25
(4
), pp. 494
–524
.10.1080/0890545970894541513.
Wang
, M. Y.
, and Shikui
, C.
, 2009
, “Compliant Mechanism Optimization: Analysis and Design With Intrinsic Characteristic Stiffness
,” Mech. Based Des. Struct. Mach.: Int. J.
, 37
(2
), pp. 183
–200
.10.1080/1539773090276193214.
Lin
, J.
, 2010
, “A New Multi-Objective Programming Scheme for Topology Optimization of Compliant Mechanisms
,” Struct. Multidiscip. Optim.
, 40
(1–6
), pp. 241
–255
.10.1007/s00158-008-0355-z15.
Rahmatalla
, S.
, and Swan
, C. C.
, 2005
, “Sparse Monolithic Compliant Mechanisms Using Continuum Structural Topology Optimization
,” Int. J. Numer. Meth. Eng.
, 62
(12
), pp. 1579
–1605
.10.1002/nme.122416.
Ansola
, R.
, Vegueria
, E.
, Maturana
, A.
, and Canales
, J.
, 2010
, “3D Compliant Mechanisms Synthesis by a Finite Element Addition Procedure
,” Finite Elem. Anal. Des.
, 46
(9
), pp. 760
–769
.10.1016/j.finel.2010.04.00617.
Luo
, Z.
, 2005
, “Compliant Mechanism Design Using Multi-Objective Topology Optimization Scheme of Continuum Structures
,” Struct. Multidiscip. Optim.
, 30
(2
), pp. 142
–154
.10.1007/s00158-004-0512-y18.
Bruns
, T. E.
, and Tortorelli
, D. A.
, 2001
, “Topology Optimization of Non-Linear Elastic Structures and Compliant Mechanisms
,” Comput. Meth. Appl. Mech. Eng.
, 190
(26–27
), pp. 3443
–3459
.10.1016/S0045-7825(00)00278-419.
Krishnan
, G.
, Kim
, C.
, and Kota
, S.
, 2013
, “A Metric to Evaluate and Synthesize Distributed Compliant Mechanisms
,” ASME J. Mech. Des.
, 135
(1
), p. 011004
.10.1115/1.400792620.
Mehta
, V.
, Frecker
, M.
, and Lesieutre
, G. A.
, 2012
, “Two-Step Design of Multicontact-Aided Cellular Compliant Mechanisms for Stress Relief
,” ASME J. Mech. Des.
, 134
(12
), p. 121001
.10.1115/1.400769421.
Deepak
, S.
, Dinesh
, M.
, Sahu
, D.
, and Ananthasuresh
, G. K.
, 2009
, “A Comparative Study of the Formulations and Benchmark Problems for Topology Optimization of Compliant Mechanisms
,” ASME J. Mech. Rob.
, 1
(1
), p. 011003
.10.1115/1.295909422.
Bendsoe
, M. P.
, and Sigmund
, O.
, 2003
, Topology Optimization: Theory, Methods and Application
, 2nd ed., Springer, Berlin, Heidelberg, Germany
.23.
Rozvany
, G. I. N.
, 2009
, “A Critical Review of Established Methods of Structural Topology Optimization
,” Struct. Multidiscip. Optim.
, 37
(3
), pp. 217
–237
.10.1007/s00158-007-0217-024.
Sethian
, J. A.
, 1999
, Level Set Methods and Fast Marching Methods
, Cambridge University Press, Cambridge, UK
.25.
Wang
, M. Y.
, Chen
, S. K.
, Wang
, X. M.
, and Mei
, Y. L.
, 2005
, “Design of Multi-Material Compliant Mechanisms Using Level Set Methods
,” ASME J. Mech. Des.
, 127
(5
), pp. 941
–956
.10.1115/1.190920626.
Yamada
, T.
, Izui
, K.
, Nishiwaki
, S.
, and Takezawa
, A.
, 2010
, “A Topology Optimization Method Based on the Level Set Method Incorporating a Fictitious Interface Energy
,” Comput. Meth. Appl. Mech. Eng.
, 199
(45–48
), pp. 2876
–2891
.10.1016/j.cma.2010.05.01327.
Ansola
, R.
, Vegueria
, E.
, Canales
, J.
, and Tarrago
, J. A.
, 2007
, “A Simple Evolutionary Topology Optimization Procedure for Compliant Mechanism Design
,” Finite Elem. Anal. Des.
, 44
(1–2
), pp. 53
–62
.10.1016/j.finel.2007.09.00228.
Frecker
, M. I.
, Kikuchi
, N.
, and Kota
, S.
, 1999
, “Topology Optimization of Compliant Mechanisms With Multiple Outputs
,” Struct. Multidiscip. Optim.
, 17
(4
), pp. 269
–278
.10.1007/BF0120700329.
Poulsen
, T. A.
, 2002
, “A New Scheme for Imposing a Minimum Length Scale in Topology Optimization
,” Int. J. Numer. Meth.
, 53
(3
), pp. 567
–582
.10.1002/nme.28530.
Shield
, R. T.
, and Prager
, W.
, 1970
, “Optimal Structural Design for Given Deflection
,” J. Appl. Math. Phys.
, ZAMP21
, pp. 513
–523
.10.1007/BF0158768131.
Eschenauer
, H. A.
, Kobelev
, V. V.
, and Schumacher
, A.
, 1994
, “Bubble Method for Topology and Shape Optimization of Structures
,” Struct. Optim.
, 8
(1
), pp. 42
–51
.10.1007/BF0174293332.
Novotny
, A. A.
, Feijóo
, R. A.
, Padra
, C.
, and Taroco
, E.
, 2005
, “Topological Derivative for Linear Elastic Plate Bending Problems
,” Control Cybern.
, 34
(1
), pp. 339
–361
.33.
Novotny
, A. A.
, Feijoo
, R. A.
, and Taroco
, E.
, 2007
, “Topological Sensitivity Analysis for Three-Dimensional Linear Elasticity Problem
,” Comput. Meth. Appl. Mech. Eng.
, 196
(41–44
), pp. 4354
–4364
.10.1016/j.cma.2007.05.00634.
Novotny
, A. A.
, 2006
, “Topological-Shape Sensitivity Method: Theory and Applications
,” Solid Mech. Appl.
, 137
, pp. 469
–478
.10.1007/1-4020-4752-5_4535.
Sokolowski
, J.
, and Zochowski
, A.
, 1999
, “On Topological Derivative in Shape Optimization
,” SIAM J. Control Optim.
, 37
(4
), pp. 1251
–1272
.10.1137/S036301299732323036.
Céa
, J.
, Garreau
, S.
, Guillaume
, P.
, and Masmoudi
, M.
, 2000
, “The Shape and Topological Optimization Connection
,” Comput. Meth. Appl. Mech. Eng.
, 188
(4
), pp. 713
–726
.10.1016/S0045-7825(99)00357-637.
Turevsky
, I.
, Gopalakrishnan
, S. H.
, and Suresh
, K.
, 2009
, “An Efficient Numerical Method for Computing the Topological Sensitivity of Arbitrary Shaped Features in Plate Bending
,” Int. J. Numer. Meth. Eng.
, 79
(13
), pp. 1683
–1702
.10.1002/nme.263738.
Turevsky
, I.
, and Suresh
, K.
, 2007
, “Generalization of Topological Sensitivity and its Application to Defeaturing
,” ASME
Paper No. DETC2007-35353. 10.1115/DETC2007-3535339.
Gopalakrishnan
, S. H.
, and Suresh
, K.
, 2008
, “Feature Sensitivity: A Generalization of Topological Sensitivity
,” Finite Elem. Anal. Des.
, 44
(11
), pp. 696
–704
.10.1016/j.finel.2008.03.00640.
Novotny
, A. A.
, Feijoo
, R. A.
, Taroco
, E.
, and Padra
, C.
, 2003
, “Topological Sensitivity Analysis
,” Comput. Meth. Appl. Mech. Eng.
, 192
(7–8
), pp. 803
–829
.10.1016/S0045-7825(02)00599-641.
Choi
, K. K.
, and Kim
, N. H.
, 2005
, Structural Sensitivity Analysis and Optimization I: Linear Systems
, Springer
, New York
.42.
Tortorelli
, D. A.
, and Zixian
, W.
, 1993
, “A Systematic Approach to Shape Sensitivity Analysis
,” Int. J. Solids Struct.
, 30
(9
), pp. 1181
–1212
.10.1016/0020-7683(93)90012-V43.
Feijoo
, R. A.
, Novotny
, A. A.
, Taroco
, E.
, and Padra
, C.
, 2005
, “The Topological-Shape Sensitivity Method in Two-Dimensional Linear Elasticity Topology Design
,” Applications of Computational Mechanics in Structures and Fluids
, CIMNE, Rio de Janeiro, Brazil
.44.
Norato
, J. A.
, Bendsoe
, M. P.
, Haber
, R. B.
, and Tortorelli
, D. A.
, 2007
, “A Topological Derivative Method for Topology Optimization
,” Struct. Multidiscip. Optim.
, 33
(4–5
), pp. 375
–386
.10.1007/s00158-007-0094-645.
Suresh
, K.
, 2013
, “Efficient Generation of Large-Scale Pareto-Optimal Topologies
,” Struct. Multidiscip. Optim.
, 47
(1
), pp. 49
–61
.10.1007/s00158-012-0807-346.
Suresh
, K.
, and Takalloozadeh
, M.
, 2013
, “Stress-Constrained Topology Optimization: A Topological Level-Set Approach
,” Struct. Multidiscip. Optim.
, 48
(2
), pp. 295
–309
.10.1007/s00158-013-0899-447.
Zienkiewicz
, O. C.
, and Taylor
, R. L.
, 2005
, The Finite Element Method for Solid and Structural Mechanics
, Elsevier, Oxford
.48.
Wang
, S.
, Sturler
, E. D.
, and Paulino
, G.
, 2007
, “Large-Scale Topology Optimization Using Preconditioned Krylov Subspace Methods With Recycling
,” Int. J. Numer. Meth. Eng.
, 69
(12
), pp. 2441
–2468
.10.1002/nme.179849.
Augarde
, C. E.
, Ramage
, A.
, and Staudacher
, J.
, 2006
, “An Element-Based Displacement Preconditioner for Linear Elasticity Problems
,” Comput. Struct.
, 84
(31–32
), pp. 2306
–2315
.10.1016/j.compstruc.2006.08.05750.
Saad
, Y.
, 2003
, Iterative Methods for Sparse Linear Systems
, SIAM, Philadelphia, PA
.10.1137/1.978089871800351.
Stanford
, B.
, and Beran
, P.
, 2012
, “Optimal Compliant Flapping Mechanism Topologies With Multiple Load Cases
,” ASME J. Mech. Des.
, 134
(5
), p. 051007
.10.1115/1.4006438Copyright © 2015 by ASME
You do not currently have access to this content.
