452
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Hierarchical optimization for topology design of multi-material compliant mechanisms

, &
Pages 2013-2035 | Received 10 Nov 2015, Accepted 16 Dec 2016, Published online: 26 Jan 2017

References

  • Aguirre, M. E, G. R. Hayes, R. A. Meirom, M. I. Frecker, C. L. Muhlstein, and J. H. Adair. 2011. “Optimal Design and Fabrication of Narrow-Gauge Compliant Forceps.” Journal of Mechanical Design 133 (8): Article No. 081005. doi: 10.1115/1.4004539.
  • Alonso, C., R. Ansola, and O. M. Querin. 2014. “Topology Synthesis of Multi-Material Compliant Mechanisms with a Sequential Element Rejection and Admission Method.” Finite Elements in Analysis and Design 85: 11–19. doi: 10.1016/j.finel.2013.11.006.
  • Anandalingam, G., and T. L. Friesz. 1992. “Hierarchical Optimization: An Introduction.” Annals of Operations Research 34 (1): 1–11. doi: 10.1007/BF02098169
  • Ansola, R., E. Veguería, J. Canales, and J. Tárrago. 2007. “A Simple Evolutionary Topology Optimization Procedure for Compliant Mechanism Design.” Finite Elements in Analysis and Design 44 (1): 53–62. doi: 10.1016/j.finel.2007.09.002
  • Bard, J. F. 1983. “Coordination of a Multidivisional Organization Through Two Levels of Management.” Omega 11 (5): 457–468. doi: 10.1016/0305-0483(83)90038-5
  • Bejgerowski, W., J. W. Gerdes, S. K. Gupta, and H. A. Bruck. 2011. “Design and Fabrication of Miniature Compliant Hinges for Multi-Material Compliant Mechanisms.” The International Journal of Advanced Manufacturing Technology 57 (5-8): 437–452. doi: 10.1007/s00170-011-3301-y
  • Bendsøe, Martin Philip. 1989. “Optimal Shape Design as a Material Distribution Problem.” Structural Optimization 1 (4): 193–202. doi: 10.1007/BF01650949
  • Bendsøe, Martin Philip., and X. OleSigmund. 2003. Topology Optimization: Theory, Methods and Applications. Berlin: Springer. doi: 10.1007/978-3-662-05086-6.
  • Bruns, T. E. 2005. “A Reevaluation of the SIMP Method with Filtering and an Alternative Formulation for Solid–Void Topology Optimization.” Structural and Multidisciplinary Optimization 30 (6): 428–436. doi: 10.1007/s00158-005-0537-x
  • Bruns, T. E., O. Sigmund, Daniel A. Tortorelli. 2002. “Numerical Methods for the Topology Optimization of Structures That Exhibit Snap-Through.” International Journal for Numerical Methods in Engineering 55 (10): 1215–1237. doi: 10.1002/nme.544
  • Dempe, Stephan, and Joydeep Dutta. 2012. “Is Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?.” Mathematical Programming 131 (12): 37–48. doi: 10.1007/s10107-010-0342-1
  • DiBiasio, C.M., M. L. Culpepper, R. Panas, L. L. Howell, and S. P. Magleby. 2008. “Comparison of Molecular Simulation and Pseudo-Rigid-Body Model Predictions for a Carbon Nanotube-Based Compliant Parallel-Guiding Mechanism.” Journal of Mechanical Design 130 (4): Article No. 042308. doi: 10.1115/1.2885192.
  • Garcia-Ruiz, M. J., Grant P. Steven. 1999. “Fixed Grid Finite Elements in Elasticity Problems.” Engineering Computations 16 (2): 145–164. doi: 10.1108/02644409910257430
  • Gaynor, Andrew T., NicholasA. Meisel, Christopher B. Williams, and James K. Guest. 2014. “Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing.” Journal of Manufacturing Science and Engineering 136 (6): Article No. 061015. doi: 10.1115/1.4028439.
  • Guo, X., W. Bai, Weisheng Zhang, and Xixin Gao. 2009. “Confidence Structural Robust Design and Optimization Under Stiffness and Load Uncertainties.” Computer Methods in Applied Mechanics and Engineering 198 (41): 3378–3399. doi: 10.1016/j.cma.2009.06.018.
  • Guo, X., W. Zhang, J. Zhang, and J. Yuan. 2016. “Explicit Structural Topology Optimization Based on Moving Morphable Components (MMC) with Curved Skeletons.” Computer Methods in Applied Mechanics and Engineering 310: 711–748. doi: 10.1016/j.cma.2016.07.018
  • Guo, Xu, Weisheng Zhang, and Wenliang Zhong. 2014a. “Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework.” Journal of Applied Mechanics 81 (8): Article No. 081009. doi: 10.1115/1.4027609.
  • Guo, Xu., Weisheng. Zhang, and Wenliang. Zhong. 2014b. “Stress-Related Topology Optimization of Continuum Structures Involving Multi-Phase Materials.” Computer Methods in Applied Mechanics and Engineering 268: 632–655. doi: 10.1016/j.cma.2013.10.003.
  • Hao, G. 2013. “Towards the Design of Monolithic Decoupled XYZ Compliant Parallel Mechanisms for Multi-Function Applications.” Mechanical Sciences 4: 291–302. doi: 10.5194/ms-4-291-2013
  • Hiller, J., and H. Lipson. 2012. “Automatic Design and Manufacture of Soft Robots.” IEEE Transactions on Robotics 28 (2): 457–466. doi: 10.1109/TRO.2011.2172702
  • Howell, Larry L. 2001. Compliant Mechanisms. New York: Wiley.
  • Huang, Xiaodong, and Y. Mike Xie. 2010. Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. Chichester, UK: Wiley.
  • Kim, N. H., and Y. M. Chang. 2005. “Eulerian Shape Design Sensitivity Analysis and Optimization with a Fixed Grid.” Computer Methods in Applied Mechanics and Engineering 194 (3033): 3291–3314. doi: 10.1016/j.cma.2004.12.019
  • Lai, Y. J. 1996. “Hierarchical Optimization: A Satisfactory Solution.” Fuzzy Sets and Systems 77 (3): 321–335. doi: 10.1016/0165-0114(95)00086-0
  • Lobontiu, Nicolae. 2010. Compliant Mechanisms: Design of Flexure Hinges. Boca Raton, FL: CRC Press.
  • Mei, Y., and X. Wang. 2004. “A Level Set Method for Structural Topology Optimization and Its Applications.” Advances in Engineering Software 35 (7): 415–441. doi: 10.1016/j.advengsoft.2004.06.004
  • Nishiwaki, S., M. I. Frecker, S. Min, and N. Kikuchi. 1998. “Topology Optimization of Compliant Mechanisms Using the Homogenization Method.” International Journal of Numerical Methods in Engineering 42 (3): 535–559. doi: 10.1002/(SICI)1097-0207(19980615)42:3<535::AID-NME372>3.0.CO;2-J
  • Parsons, R., and S. L. Canfield. 2002. “Developing Genetic Programming Techniques for the Design of Compliant Mechanisms.” Structural and Multidisciplinary Optimization 24 (1): 78–86. doi: 10.1007/s00158-002-0216-0
  • Pedersen, Claus B. W., Thomas Buhl, and Ole. Sigmund. 2001. “Topology Synthesis of Large-Displacement Compliant Mechanisms.” International Journal for Numerical Methods in Engineering 50 (12): 2683–2705. doi: 10.1002/nme.148
  • Ramrakhyani, D. S., M. I. Frecker, and G. A. Lesieutre. 2009. “Hinged Beam Elements for the Topology Design of Compliant Mechanisms Using the Ground Structure Approach.” Structural and Multidisciplinary Optimization 37 (6): 557–567. doi: 10.1007/s00158-008-0262-3
  • Rozvany, G. I. N. 2009. “A Critical Review of Established Methods of Structural Topology Optimization.” Structural and Multidisciplinary Optimization 37 (3): 217–237. doi: 10.1007/s00158-007-0217-0
  • Saxena, A. 2005. “Topology Design of Large Displacement Compliant Mechanisms with Multiple Materials and Multiple Output Ports.” Structural and Multidisciplinary Optimization 30 (6): 477–490. doi: 10.1007/s00158-005-0535-z
  • Schalkoff, Robert J. 1989. Digital Image Processing and Computer Vision: An Introduction to Theory and Implementations. New York: Wiley.
  • Sigmund, Ole. 1997. “On the Design of Compliant Mechanisms Using Topology Optimization.” Journal of Structural Mechanics 25 (4): 493–524.
  • Sigmund, Ole. 2001. “A 99 Line Topology Optimization Code Written in Matlab.” Structural and Multidisciplinary Optimization 21 (2): 120–127. doi: 10.1007/s001580050176
  • Sigmund, Ole. 2001a. “Design of Multiphysics Actuators Using Topology Optimization—Part I: One-Material Structures.” Computer Methods in Applied Mechanics and Engineering 190 (4950): 6577–6604. doi: 10.1016/S0045-7825(01)00251-1
  • Sigmund, Ole. 2001b. “Design of Multiphysics Actuators Using Topology Optimization—Part II: Two-Material Structures.” Computer Methods in Applied Mechanics and Engineering 190 (4950): 6605–6627. doi: 10.1016/S0045-7825(01)00252-3
  • Sigmund, Ole. 2009. “Manufacturing Tolerant Topology Optimization.” Acta Mechanica Sinica 25 (2): 227–239. doi: 10.1007/s10409-009-0240-z.
  • Stoilova, Krasimira, and Todor. Stoilov. 2012. “Hierarchical Optimization for Fast Resource Allocation.” Chap. 2 in Time Management, edited by Todor Stoilov, 31–46. http://idl.isead.edu.es:8080/jspui/bitstream/10954/1767/1/9789535103356.pdf#page=39.
  • Takezawa, A., and M. Kitamura. 2012. “Topology Optimization of Compliant Circular Path Mechanisms Based on an Aggregated Linear System and Singular Value Decomposition.” International Journal for Numerical Methods in Engineering 89 (6): 706–725. doi: 10.1002/nme.3259
  • Tavakoli, R., and S. M. Mohseni. 2014. “Alternating Active-Phase Algorithm for Multimaterial Topology Optimization Problems: A 115-Line MATLAB Implementation.” Structural and Multidisciplinary Optimization 49 (4): 621–642. doi: 10.1007/s00158-013-0999-1
  • Tcherniak, D. 2002. “Topology Optimization of Resonating Structures Using SIMP Method.” International Journal for Numerical Methods in Engineering 54 (11): 1605–1622. doi: 10.1002/nme.484
  • Vaezi, M., S. Chianrabutra, B. Mellor, and S. Yang. 2013. “Multiple Material Additive Manufacturing—Part 1: A Review.” Virtual and Physical Prototyping 8 (1): 19–50. doi: 10.1080/17452759.2013.778175
  • Vicente, Luis N, Paul H. Calamai. 1994. “Bilevel and Multilevel Programming: A Bibliography Review.” Journal of Global Optimization 5 (3): 291–306. doi: 10.1007/BF01096458.
  • Wang, M. Y., X. Wang, and D. Guo. 2003. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 192 (1): 227–246. doi: 10.1016/S0045-7825(02)00559-5
  • Yin, L., and G. K. Ananthasuresh. 2001. “Topology Optimization of Compliant Mechanisms with Multiple Materials Using a Peak Function Material Interpolation Scheme.” Structural and Multidisciplinary Optimization 23 (1): 49–62. doi: 10.1007/s00158-001-0165-z
  • Yoon, Gil Ho. 2011. “Topology Optimization for Nonlinear Dynamic Problem with Multiple Materials and Material-Dependent Boundary Condition.” Finite Elements in Analysis and Design 47 (7): 753–763. doi: 10.1016/j.finel.2011.02.006
  • Zhan, Jinqing, and Xianmin Zhang. 2010. “Topology Optimization of Multiple Inputs and Multiple Outputs Compliant Mechanisms Using the Ground Structure Approach.” In Proceedings of the 2nd IEEE International Conference on Industrial Mechatronics and Automation (ICIMA2010), 30–31 May 2010, Wuhan, PR China, 20–24. doi: 10.1109/ICINDMA.2010.5538111.
  • Zhang, Weisheng, Wanying Yang, Jianhua Zhou, Dong Li, and Xu Guo. 2017. “Structural Topology Optimization Through Explicit Boundary Evolution.” Journal of Applied Mechanics 84 (1): Article No. 011011. doi: 10.1115/1.4034972.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.