Topology optimization for synthesis of contact-aided compliant mechanisms using regularized contact modeling

Computers and Structures

Volumn 82, Issue 15-16, 2004, Pages 1267-1290

  Mankame, Nilesh D ^a   Ananthasuresh, G K ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Compliant mechanisms; Nonsmooth function generation; Regularized contact; Systematic synthesis; Topology optimization

Indexed keywords

BOUNDARY VALUE PROBLEMS; DEFLECTION (STRUCTURES); DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; FUNCTION GENERATORS; MICROELECTROMECHANICAL DEVICES; OPTIMIZATION; SENSITIVITY ANALYSIS; TOPOLOGY;

COMPLIANT MECHANISMS (CM); NONSMOOTH FUNCTION GENERATION; REGULARIZED CONTACT; SYSTEMATIC SYNTHESIS; TOPOLOGY OPTIMIZATION;

COMPUTER SCIENCE;

EID: 2542442744     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.02.024     Document Type: Article

References (47)

1. Midha A. Elastic mechanisms. Erdman A.G. Modern kinematics - the developments in the last 40 years. 1993;John Wiley & Sons. [chapter 9].
2. Ananthasuresh G.K., Kota S. Designing compliant mechanisms. Mech. Eng., ASME. 117(11):1995;93-96.
3. Howell L.L. Compliant mechanisms. 2001;Wiley Interscience Publications, John Wiley & Sons.
4. Moulton T., Ananthasuresh G.K. Design and manufacture of electro-thermal-compliant micro devices. Sens. Actuators, Phys. 90(1-2):2001;38-48.
5. Erdman A.G., Sandor G.N., Kota S. Mechanism design: analysis and synthesis. 4th ed. 2001;Prentice-Hall.
6. Mankame ND, Ananthasuresh GK. Contact aided compliant mechanisms: concept and preliminaries. CD-ROM Proceedings of the ASME DETC2002. Paper # MECH-34211, 2002.
7. Ananthasuresh GK, Frecker MI. Optimal synthesis with continuum models, in Ref. [3], 2001 [chapter 9].
8. Hilding D., Klarbring A., Petersson J. Optimization of structures in unilateral contact. Appl. Mech. Rev. 52(4):1999;139-160.
9. Mijar A.R., Arora J.S. Review of formulations for elastostatic frictional contact problems. Struct. Multidiscip. Optim. 20(3):2000;167-189.
10. Klarbring A., Rönqvist M. Nested approach to structural optimization in non-smooth mechanics. Struct. Optim. 10:1995;79-86.
11. Klarbring A., Petersson J., Rönqvist M. Truss topology optimization including unilateral contact. J. Optim. Theory Appl. 87:1995;1-31.
12. Saxena A., Ananthasuresh G.K. Topology synthesis of compliant mechanisms for nonlinear force-deflection and curved path specifications. J. Mech. Des., Trans. ASME. 123(1):2001;33-42.
13. Pedersen C.B.W., Buhl T., Sigmund O. Topology synthesis of large-displacement compliant mechanisms. Int. J. Numer. Methods Eng. 50:2001;2683-2705.
14. Mankame ND, Ananthasuresh GK. A novel compliant mechanism for converting reciprocating translation into enclosing closed paths. ASME J Mech Des, in press.
15. Kikuchi N., Oden J.T. Contact problems in elasticity: a study of variational inequalities and finite element methods. SIAM studies in applied mathematics. 1988;SIAM, Philadelphia.
16. Harker P.T., Pang J.-S. Finite dimensional variational inequalities and linear complementarity problems. Math. Programming. 48:1990;161-220.
17. Chen C., Mangasarian O.L. A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5:1996;97-138.
18. Oden J.T., Pires E.B. Nonlocal and nonlinear friction laws and variational principles contact problems in elasticity. J. Appl. Mech. 50:1983;67-76.
19. Zavarise G., Wriggers P., Schrefler B.A. A method for solving contact problems. Int. J. Numer. Methods Eng. 42:1998;473-498.
20. Wriggers P. Computational contact mechanics. 2002;John Wiley & Sons, Chichester, UK.
21. Li W., Li Q., Steven G.P., Xie Y.M. An evolutionary shape optimization procedure for contact problems in mechanical design. J. Mech. Eng. Sci., Proc. IME, Part C. 217(C4):2003;435-446.
22. Belegundu A.D., Chandrupatla T.R. Shape optimization of valve geometry with contact analysis. Saigal S., Mukjerjee S. Sensitivity analysis and optimization with numerical methods. 1990;71-78 ASME, New York.
23. Hilding D., Torstenfelt B., Klarbring A. A computational methodology for shape optimization of structures in frictionless contact. Comput. Methods Appl. Mech. Eng. 190:2001;4043-4060.
24. Zabaras N., Bao Y., Srikanth A., Frazier W.G. A continuum sensitivity analysis for metal forming processes with application to die design problems. Int. J. Numer. Methods Eng. 48:2000;679-720.
25. Frecker M.I., Ananthasuresh G.K., Nishiwaki S., Kikuchi N., Kota S. Topological synthesis of compliant mechanisms using multi-criteria optimization. J. Mech. Des., Trans. ASME. 119(2):1997;238-245.
26. Benedict R.L., Taylor J.E. Optimal design for elastic bodies in contact. Haug E.J., Cea J. Optimization of distributed parameter structures. 2:1981;1553-1599 Sijthoff and Noordhoff Publishers, Holland.
27. Klarbring A. On the problem of optimizing contact force distributions. J. Optim. Theory Appl. 74:1992;131-150.
28. Hilding D. A heuristic smoothing procedure for avoiding local optima in optimization of structures subject to unilateral constraints. Struct. Multidiscip. Optim. 20:2000;29-36.
29. Park J., Anderson W.J. Geometric optimization in the presence of contact singularities. AIAA J. 33:1995;1503-1509.
30. Petersson J., Patriksson M. Topology optimization of sheets in contact by a subgradient method. Int. J. Numer. Methods Eng. 40:1997;1295-1321.
31. Stavroulakis G.E. Optical prestress of cracked unilateral structures: finite element analysis of an optimal control problem for variational inequalities. Comput. Methods Appl. Mech. Eng. 123:1995;231-246.
32. Outrata J., Zowe J. Numerical approach to optimization problems with variational inequality constraints. Math. Programming. 68:1995;105-130.
33. Tin-Loi F. On the numerical solution of a class of unilateral contact structural optimization problems. Struct. Multidiscip. Optim. 17:1999;155-161.
34. Facchinei F., Jiang H., Qi L. A smoothing method for mathematical programs with equilibrium constraints. Math. Programming. 85:1999;107-134.
35. Kim N.H., Park Y.H., Choi K.K. Optimization of a hyper-elastic structure with optimization multibody contact using continuum-based shape design sensitivity analysis. Struct. Multidiscip. Optim. 21:2001;196-208.
36. Saxena A., Ananthasuresh G.K. On an optimal property of compliant topologies. Struct. Multidiscip. Optim. 19:2000;36-49.
37. Bendsøe M.P., Sigmund O. Topology optimization: theory, methods and applications. 2003;Springer, New York.
38. Belegundu A.D., Chandrupatla T.R. Introduction to finite elements in engineering. 2nd ed. 1997;Prentice-Hall, Upper Saddle River, NJ, USA.
39. Ortega J.M., Rheinboldt W.C. Iterative solution of nonlinear equations in several variables. 1970;Academic Press, New York.
40. Bendsøe M.P., Olhoff N., Sokolowski J. Sensitivity analysis of problems of elasticity with unilateral constraints. J. Struct. Mech. 13(2):1985;201-222.
41. Crisfield M.A. Nonlinear finite element analysis of solids and structures. vol. 1:1991;John Wiley & Sons.
42. Bergstrom PL, Tamagawa T, Polla DL. Design and fabrication of micromechanical logic elements. In: Proceedings of the 1990 IEEE Micro Electro Mechanical Systems conference, Napa Valley, CA, 1990. p. 15-20.
43. Sigmund O. On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25(4):1997;493-524.
44. Mankame ND, Ananthasuresh GK. Topology synthesis of electrothermal compliant (ETC) mechanisms using line elements. In: Proceedings of the 2001 ASME Design Engineering Technical Conferences, Pittsburgh, 2001, Paper no. DETC2001/DAC-21019.
45. Bruns T.E., Tortorelli D.A. Topology optimization for nonlinear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190(26-27):2001;3443-3459.
46. Dzeidzic R, Frecker MI. Design of multifunctional compliant mechanisms for minimally invasive surgery - preliminary results. In: Proceedings of the 2001 ASME Design Engineering Technical Conferences, Symposium on Mechanisms and Devices for Medical Applications, Pittsburgh, 2001, Paper no. DETC2001/DAC-21055.
47. Ullah I., Kota S. Optimal synthesis of mechanisms for path generation using fourier descriptors and global search methods. ASME J. Mech. Des. 119:1997;504-510.