Level set based method for design of compliant mechanisms
DOI:
https://doi.org/10.13052/REMN.17.957-968Keywords:
shape optimization, compliant mecanisms, level setAbstract
In the context of structural optimization, we propose two natural extensions of the level set method for the design of compliant mechanisms. Two new objective functions are introduced, well suited to the automatic design of compliant mechanisms, and a strategy for the design of mechanisms adapted to multiple loads is proposed. This work is illustrated with several numericals examples.
Downloads
References
Allaire G., De Gournay F., Jouve F., « Optimisation de forme de micro-mécanismes compliants
par la méthode des courbes de niveau », Actes du 7ème Colloque National en Calcul des
Structures, Hermes, Giens, p. 229-234, 2005a.
Allaire G., De Gournay F., Jouve F., Toader A., « Structural optimization using topological and
shape sensitivity via a level set method », Control and Cybernetics, vol. 34, p. 59-80, 2005b.
Allaire G., Jouve F., « A level-set method for vibration and multiple loads structural optimization
», Comput. Methods Appl. Mech. Engrg., vol. 194, p. 3269-3290, 2005c.
Allaire G., Jouve F., Toader A.-M., « A level-set method for shape optimization », C. R. Acad.
Sci., Paris, Série I, vol. 334, p. 1125-1130, 2002.
Allaire G., Jouve F., Toader A.-M., « Structural optimization using sensitivity analysis and a
level-set method », J. Comp. Phys.,, vol. 194, n° 1, p. 363-393, 2004.
Ananthasuresh G., Kota S., Gianchandani Y., « A methodical approach to design of compliant
micro-mechanisms », In Solid-State Sensor and Actuator Workshop, p. 189-192, 1994.
Céa J., « Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle
de la fonction coût », Math. Model. Num. Anal., vol. 20, n° 3, p. 371-402, 1986.
Frecker M., Ananthasuresh G., Nishiwaki S., Kikuchi N., « Topology synthesis of compliant
mechanisms using multi-criteria optimization », J. Mech. Des. Trans ASME, vol. 119, n° 2,
p. 238-245, 1997.
Howell L., Compliant mechanisms, John Wiley & Sons, New York, 2001.
Howell L., Midha A., « A method for design of compliant mechanisms with small length flexural
pivots », ASME J. Mech. Design, vol. 116, p. 280-290, 1994.
Jouve F.,Mechkour H., « Optimization assisted design of compliant mechanisms by the level set
method », In Proc. of 12th World Congress in Mechanism and Machine Science, IFToMM,
Besançon, France, June 18-21, 2007.
Murat F., Simon J., « Etudes de problèmes d’optimal design », Lectures Notes in Computer
Science 41, Springer Verlag, Berlin, p. 54-62, 1976.
Osher S., Sethian J., « Front propagating with curvature dependent speed: algorithms based on
Hamilton-Jacobi formulations », J. Comp. Phys., vol. 78, p. 12-49, 1988.
Saxena A., Ananthasuresh G., « On an optimal property of compliant topologies », Struct Multidisc
Optim., vol. 19, p. 36-49, 2000.
Sethian J., Wiegmann A., « Structural boundary design via level set and immersed interface
methods », J. Comp. Phys., vol. 163, p. 489-528, 2000.
Sigmund O., « On the design of compliant mechanisms using topology optimization », Mech.
Struct. Mach., vol. 25, p. 493-524, 1997.
Wang M., Chen S., Wang X., Mei Y., « Design of multimaterial compliant mechanisms using
level set methods », ASME J. Mech. Design, vol. 127, p. 941-955, 2005.
Wang M., Wang D., Guo A., « A level set method for structural topology optimization », Comput.
Methods Appl. Engrg., vol. 192, p. 227-246, 2003.
