Design of Compliant Mechanisms with Stress Constraints Using Topology Optimization

  • Luís Renato Meneghelli
  • Eduardo Lenz CardosoEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 43)


Compliant mechanisms are mechanical devices that transform or transfer motion, force or energy through a single part. These mechanisms have important applications in micro electromechanical systems (MEMS) and other systems that require great accuracy in motion and micro scale. The compliant mechanisms design is performed by Topology Optimization Method, and the optimization problem is formulated to maximize strain-energy stored by mechanism, eliminating the appearance of hinges. The kinematic behavior of the mechanism is imposed through a set of constraints over some displacement degrees of freedom of interest. The elastic behavior of the compliant mechanisms is imposed using a global stress constraint and some important issues associated to stress parametrization are discussed in the realm of mechanism design. The characteristics and the feasibility of this proposal, as well as the influence of parameters related to the formulation, are presented with the aid of some examples.



All the post-processing images were generated using the free and general pre and post-processing program gmsh [7]. The linear programming problem was solved using the free SLATEC package dsplp [8].


  1. 1.
    Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory. Springer, New York (2003)Google Scholar
  2. 2.
    Bruggi, M.: On an alternative approach to stress constraints relaxation in topology optimization. Struct. Multidis. Optim. 36, 125–141 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cardoso, E.L., Fonseca, J.S.: Strain energy maximization approach to the design of fully compliantmechanisms using topology optimization. Latin Am. J. Solids Struct. 1, 263–275 (2004)Google Scholar
  4. 4.
    Cheng, G.D., Guo, X.: \(\epsilon \)-relaxed approach in structural topology optimization. Struct. Optim. 13, 258–266 (1997)CrossRefGoogle Scholar
  5. 5.
    Duysinx, P., Bendsøe, M.P.: Topology optimization of continuum structures with local stress constraints. Int. J. Numer. Methods Eng. 43, 1453–1478 (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Frecker, M.I., Kikuchi, N., Kota, S.: Optimal synthesis of compliant mechanisms to satisfy kinematic and structural requirements—preliminary results. In: Proceedings of the 1996 ASME Design Engineering Technical Conferences and Computers in, Engineering Conference, pp. 177–192 (1996)Google Scholar
  7. 7.
    Geuzaine, C., Remacle, J.F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Eng. 79(11), 1309–1331 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hanson, R., Hirbert, K.: A sparse linear programming subprogram. Tech. rep., Sandia National Laboratories (1981). SAND81-0297Google Scholar
  9. 9.
    Kikuchi, N., Nishiwaki, S., Fonseca, J.S.O., Silva, E.C.N.: Design optimization method for compliant mechanisms and material microstructure. Comput. Methods Appl. Mech. Eng. 151, 401–417 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Le, C., Norato, J., Bruns, T., Ha, C., Tortorelli, D.: Stress-based topology optimization for continua. Struct. Multidis. Optim. 41, 605–620 (2010)CrossRefGoogle Scholar
  11. 11.
    Pereira, J.T., Fancello, E.A., Barcellos, C.S.: Topology optimization of continuum structures with material failure constraints. Struct. Multidis. Optim. 26, 50–56 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Poulsen, T.A.: A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization. Struct. Multidis. Optim. 24, 396–399 (2002)CrossRefGoogle Scholar
  13. 13.
    Rozvany, G.I.N., Sobieszczanski-Sobieski, J.: New optimality criteria methods: forcing uniqueness of the adjoint strains by cornerrounding at constraint intersections. Struct. Multidis. Optim. 4, 244–246 (1992)CrossRefGoogle Scholar
  14. 14.
    Sigmund, O.: On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25, 495–526 (1997)CrossRefGoogle Scholar
  15. 15.
    Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidis. Optim. 43, 767–784 (2011)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Luís Renato Meneghelli
    • 1
  • Eduardo Lenz Cardoso
    • 1
    Email author
  1. 1.State University of Santa CatarinaJoinvilleBrazil

Personalised recommendations