0
Technical Brief

An Evolutionary Soft-Add Topology Optimization Method for Synthesis of Compliant Mechanisms With Maximum Output Displacement

[+] Author and Article Information
Chih-Hsing Liu

Department of Mechanical Engineering,
National Cheng Kung University,
Tainan 701, Taiwan
e-mail: chliu@mail.ncku.edu.tw

Guo-Feng Huang, Ta-Lun Chen

Department of Mechanical Engineering,
National Cheng Kung University,
Tainan 701, Taiwan

Manuscript received November 5, 2016; final manuscript received April 29, 2017; published online June 22, 2017. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 9(5), 054502 (Jun 22, 2017) (12 pages) Paper No: JMR-16-1343; doi: 10.1115/1.4037000 History: Received November 05, 2016; Revised April 29, 2017

This paper presents an evolutionary soft-add topology optimization method for synthesis of compliant mechanisms. Unlike the traditional hard-kill or soft-kill approaches, a soft-add scheme is proposed in this study where the elements are equivalent to be numerically added into the analysis domain through the proposed approach. The objective function in this study is to maximize the output displacement of the analyzed compliant mechanism. Three numerical examples are provided to demonstrate the effectiveness of the proposed method. The results show that the optimal topologies of the analyzed compliant mechanisms are in good agreement with previous studies. In addition, the computational time can be greatly reduced by using the proposed soft-add method in the analysis cases. As the target volume fraction in topology optimization for the analyzed compliant mechanism is usually below 30% of the design domain, the traditional methods which remove unnecessary elements from 100% turn into inefficient. The effect of spring stiffness on the optimized topology has also been investigated. It shows that higher stiffness values of the springs can obtain a clearer layout and minimize the one-node hinge problem for two-dimensional cases. The effect of spring stiffness is not significant for the three-dimensional case.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Shuib, S. , Ridzwan, M. I. Z. , and Kadarman, A. H. , 2007, “ Methodology of Compliant Mechanisms and Its Current Developments in Applications: A Review,” Am. J. Appl. Sci., 4(3), pp. 160–167. [CrossRef]
Howell, L. L. , Magleby, S. P. , and Olsen, B. M. , 2013, Handbook of Compliant Mechanisms, Wiley, West Sussex, UK.
Howell, L. L. , Midha, A. , and Norton, T. W. , 1996, “ Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms,” ASME J. Mech. Des., 118(1), pp. 126–131. [CrossRef]
Midha, A. , Howell, L. L. , and Norton, T. W. , 2000, “ Limit Positions of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept,” Mech. Mach. Theory, 35(1), pp. 99–115. [CrossRef]
Boyle, C. , Howell, L. L. , Magleby, S. P. , and Evans, M. S. , 2003, “ Dynamic Modeling of Compliant Constant-Force Compression Mechanisms,” Mech. Mach. Theory, 38(12), pp. 1469–1487. [CrossRef]
Wang, W. , and Yu, Y. , 2010, “ New Approach to the Dynamic Modeling of Compliant Mechanisms,” ASME J. Mech. Rob., 2(2), p. 021003. [CrossRef]
Hassani, B. , and Hinton, E. , 1998, “ A Review of Homogenization and Topology Optimization III—Topology Optimization Using Optimality Criteria,” Comput. Struct., 69(6), pp. 739–756. [CrossRef]
Eschenauer, H. A. , and Olhoff, N. , 2001, “ Topology Optimization of Continuum Structures: A Review,” ASME Appl. Mech. Rev., 54(4), pp. 331–390. [CrossRef]
Rozvany, G. I. N. , 2009, “ A Critical Review of Established Methods of Structural Topology Optimization,” Struct. Multidiscip. Optim., 37(3), pp. 217–237. [CrossRef]
Sigmund, O. , and Maute, K. , 2013, “ Topology Optimization Approaches,” Struct. Multidiscip. Optim., 48(6), pp. 1031–1055. [CrossRef]
van Dijk, N. P. , Maute, K. , Langelaar, M. , and van Keulen, F. , 2013, “ Level-Set Methods for Structural Topology Optimization: A Review,” Struct. Multidiscip. Optim., 48(3), pp. 437–472. [CrossRef]
Deaton, J. D. , and Grandhi, R. V. , 2014, “ A Survey of Structural and Multidisciplinary Continuum Topology Optimization: Post 2000,” Struct. Multidiscip. Optim., 49(1), pp. 1–38. [CrossRef]
Xie, Y. M. , and Steven, G. P. , 1993, “ A Simple Evolutionary Procedure for Structural Optimization,” Comput. Struct., 49(5), pp. 885–896. [CrossRef]
Xie, Y. M. , and Steven, G. P. , 1997, Evolutionary Structural Optimization, Springer, London.
Querin, O. M. , Steven, G. P. , and Xie, Y. M. , 2000, “ Evolutionary Structural Optimisation Using an Additive Algorithm,” Finite Elem. Anal. Des., 34(3–4), pp. 291–308. [CrossRef]
Ansola, R. , Veguería, E. , Canales, J. , and Tárrago, J. A. , 2007, “ A Simple Evolutionary Topology Optimization Procedure for Compliant Mechanism Design,” Finite Elem. Anal. Des., 44(1–2), pp. 53–62. [CrossRef]
Ansola, R. , Veguería, 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. [CrossRef]
Huang, X. , and Xie, Y. M. , 2007, “ Convergent and Mesh-Independent Solutions for the Bidirectional Evolutionary Structural Optimization Method,” Finite Elem. Anal. Des., 43(14), pp. 1039–1049. [CrossRef]
Huang, X. , and Xie, Y. M. , 2009, “ Bi-Directional Evolutionary Topology Optimization of Continuum Structures With One or Multiple Materials,” Comput. Mech., 43(3), pp. 393–401. [CrossRef]
Huang, X. , and Xie, Y. M. , 2010, “ A Further Review of ESO Type Methods for Topology Optimization,” Struct. Multidiscip. Optim., 41(5), pp. 671–683. [CrossRef]
Huang, X. , and Xie, Y. M. , 2010, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, Wiley, West Sussex, UK.
Li, Y. , Huang, X. , Xie, Y. M. , and Zhou, S. , 2013, “ Bi-Directional Evolutionary Structural Optimization for Design of Compliant Mechanisms,” Key Eng. Mater., 535–536, pp. 373–376. [CrossRef]
Huang, X. , Li, Y. , Zhou, S. W. , and Xie, Y. M. , 2014, “ Topology Optimization of Compliant Mechanisms With Desired Structural Stiffness,” Eng. Struct., 79, pp. 13–21. [CrossRef]
Bendsøe, M. P. , 1989, “ Optimal Shape Design as a Material Distribution Problem,” Struct. Optim., 1(4), pp. 193–202. [CrossRef]
Bendsøe, M. P. , and Sigmund, O. , 1999, “ Material Interpolation Schemes in Topology Optimization,” Arch. Appl. Mech., 69(9), pp. 635–654. [CrossRef]
Bendsøe, M. P. , and Sigmund, O. , 2003, Topology Optimization: Theory, Method and Application, Springer, Berlin.
Rietz, A. , 2001, “ Sufficiency of a Finite Exponent in SIMP (Power Law) Methods,” Struct. Multidiscip. Optim., 21(2), pp. 159–163. [CrossRef]
Rahmatalla, S. , and Swan, C. C. , 2005, “ Sparse Monolithic Compliant Mechanisms Using Continuum Structural Topology Optimization,” Int. J. Numer. Methods Eng., 62(12), pp. 1579–1605. [CrossRef]
Alonso, C. , Querin, O. M. , and Ansola, R. , 2013, “ A Sequential Element Rejection and Admission (SERA) Method for Compliant Mechanisms Design,” Struct. Multidiscip. Optim., 47(6), pp. 795–807. [CrossRef]
Luo, Z. , Chen, L. , Yang, J. , Zhang, Y. , and Abdel-Malek, K. , 2005, “ Compliant Mechanism Design Using Multi-Objective Topology Optimization Scheme of Continuum Structures,” Struct. Multidiscip. Optim., 30(2), pp. 142–154. [CrossRef]
Zhu, B. , Zhang, X. , and Fatikow, S. , 2014, “ Level Set-Based Topology Optimization of Hinge-Free Compliant Mechanisms Using a Two-Step Elastic Modeling Method,” ASME J. Mech. Des., 136(3), p. 031007. [CrossRef]
Cao, L. , Dolovich, A. T. , and Zhang, W. , 2015, “ Hybrid Compliant Mechanism Design Using a Mixed Mesh of Flexure Hinge Elements and Beam Elements Through Topology Optimization,” ASME J. Mech. Des., 137(9), p. 092303. [CrossRef]
Pedersen, C. B. W. , Buhl, T. , and Sigmund, O. , 2001, “ Topology Synthesis of Large-Displacement Compliant Mechanisms,” Int. J. Numer. Methods Eng., 50(12), pp. 2683–2705. [CrossRef]
Zhou, H. , and Killekar, P. P. , 2011, “ The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms,” ASME J. Mech. Des., 133(11), p. 111007. [CrossRef]
Zhou, H. , 2010, “ Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model,” ASME J. Mech. Des., 132(11), p. 111003. [CrossRef]
Hull, P. V. , and Canfield, S. , 2005, “ Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA,” ASME J. Mech. Des., 128(2), pp. 337–348. [CrossRef]
Liu, C.-H. , and Huang, G.-F. , 2016, “ A Topology Optimization Method With Constant Volume Fraction During Iterations for Design of Compliant Mechanisms,” ASME J. Mech. Rob., 8(4), p. 044505. [CrossRef]
Liu, C.-H. , Huang, G.-F. , and Chiu, C.-H. , 2015, “ An Evolutionary Topology Optimization Method for Design of Compliant Mechanisms With Two-Dimensional Loading,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Busan, South Korea, July 7–11, pp. 1340–1345.
Sigmund, O. , and Petersson, J. , 1998, “ Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima,” Struct. Optim., 16(1), pp. 68–75. [CrossRef]
Sigmund, O. , 2007, “ Morphology-Based Black and White Filters for Topology Optimization,” Struct. Multidiscip. Optim., 33(4), pp. 401–424. [CrossRef]
Poulsen, T. A. , 2002, “ A Simple Scheme to Prevent Checkerboard Patterns and One-Node Connected Hinges in Topology Optimization,” Struct. Multidiscip. Optim., 24(5), pp. 396–399. [CrossRef]
Zhou, M. , Shyy, Y. K. , and Thomas, H. L. , 2001, “ Checkerboard and Minimum Member Size Control in Topology Optimization,” Struct. Multidiscip. Optim., 21(2), pp. 152–158. [CrossRef]
Jang, G.-W. , Jeong, J. H. , Kim, Y. Y. , Sheen, D. , Park, C. , and Kim, M.-N. , 2003, “ Checkerboard-Free Topology Optimization Using Non-Conforming Finite Elements,” Int. J. Numer. Methods Eng., 57(12), pp. 1717–1735. [CrossRef]
Saxena, A. , and Ananthasuresh, G. K. , 1999, “ Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications,” ASME J. Mech. Des., 123(1), pp. 33–42. [CrossRef]
Wang, N. F. , and Tai, K. , 2008, “ Design of Grip-and-Move Manipulators Using Symmetric Path Generating Compliant Mechanisms,” ASME J. Mech. Des., 130(11), p. 112305. [CrossRef]
Mankame, N. D. , and Ananthasuresh, G. K. , 2004, “ Topology Optimization for Synthesis of Contact-Aided Compliant Mechanisms Using Regularized Contact Modeling,” Comput. Struct., 82(15–16), pp. 1267–1290. [CrossRef]
Tummala, Y. , Wissa, A. , Frecker, M. , and Hubbard, J. E. , 2014, “ Design and Optimization of a Contact-Aided Compliant Mechanism for Passive Bending,” ASME J. Mech. Rob., 6(3), p. 031013. [CrossRef]
Pedersen, C. B. W. , Fleck, N. A. , and Ananthasuresh, G. K. , 2006, “ Design of a Compliant Mechanism to Modify an Actuator Characteristic to Deliver a Constant Output Force,” ASME J. Mech. Des., 128(5), pp. 1101–1112. [CrossRef]
Chen, Y.-H. , and Lan, C.-C. , 2012, “ An Adjustable Constant-Force Mechanism for Adaptive End-Effector Operations,” ASME J. Mech. Des., 134(3), p. 031005. [CrossRef]
Tolman, K. A. , Merriam, E. G. , and Howell, L. L. , 2016, “ Compliant Constant-Force Linear-Motion Mechanism,” Mech. Mach. Theory, 106, pp. 68–79. [CrossRef]
Delimont, I. L. , Magleby, S. P. , and Howell, L. L. , 2015, “ Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms,” ASME J. Mech. Rob., 7(1), p. 011009. [CrossRef]
Sigmund, O. , 2001, “ A 99 Line Topology Optimization Code Written in Matlab,” Struct. Multidiscip. Optim., 21(2), pp. 120–127. [CrossRef]
Andreassen, E. , Clausen, A. , Schevenels, M. , Lazarov, B. S. , and Sigmund, O. , 2011, “ Efficient Topology Optimization in MATLAB Using 88 Lines of Code,” Struct. Multidiscip. Optim., 43(1), pp. 1–16. [CrossRef]
Liu, K. , and Tovar, A. , 2014, “ An Efficient 3D Topology Optimization Code Written in Matlab,” Struct. Multidiscip. Optim., 50(6), pp. 1175–1196. [CrossRef]
Sigmund, O. , 1997, “ On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach., 25(4), pp. 493–524. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Load scheme and its equivalent load cases

Grahic Jump Location
Fig. 2

Analysis domain of the 2D force–displacement inverter mechanism

Grahic Jump Location
Fig. 3

Objective function ratio and volume fraction versus iteration number for the 2D inverter mechanism

Grahic Jump Location
Fig. 4

Optimized topologies at specific iterations for the 2D inverter mechanism

Grahic Jump Location
Fig. 5

The effect of spring stiffness on optimized topology for the 2D inverter mechanism

Grahic Jump Location
Fig. 6

Analysis domain of the 2D crunching mechanism

Grahic Jump Location
Fig. 7

Objective function ratio and volume fraction versus iterations for the 2D crunching mechanism

Grahic Jump Location
Fig. 8

Optimized topologies at specific iterations for the 2D crunching mechanism

Grahic Jump Location
Fig. 9

The effect of spring stiffness on optimized topology for the 2D crunching mechanism

Grahic Jump Location
Fig. 10

Analysis domain of the 3D inverter mechanism

Grahic Jump Location
Fig. 11

Objective function ratio and volume fraction versus iterations for the 3D inverter mechanism

Grahic Jump Location
Fig. 12

Optimized topologies at specific iterations for the 3D inverter mechanism

Grahic Jump Location
Fig. 13

The effect of spring stiffness on optimized topology for the 3D inverter mechanism: (a) input = output = 105 N/m, (b) input = output = 107 N/m, and (c) input = output = 1012 N/m

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In