Microbeam pull-in voltage topology optimization including material deposition constraint

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 45-48, 2008, Pages 4040-4050

  Lemaire, E ^a   Rochus, V ^a   Golinval, J C ^a   Duysinx, P ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Electromechanical coupling; Manufacturing constraint; Pull in; Topology optimization

Indexed keywords

ARSENIC; CONSTRAINED OPTIMIZATION; FINITE ELEMENT METHOD; PORTABLE EQUIPMENT; PROCESS ENGINEERING; REINFORCEMENT; SENSITIVITY ANALYSIS; STIFFNESS MATRIX; STRUCTURAL OPTIMIZATION; TOPOLOGY;

DEPOSITION PROCESSING; DRIVING VOLTAGES; EIGEN MODES; ELECTRICAL PHENOMENA; ELECTROMECHANICAL COUPLING; FINITE ELEMENT FORMULATION; HOMOTOPY METHODS; MANUFACTURING CONSTRAINT; MANUFACTURING CONSTRAINTS; MATERIAL DEPOSITION; MICRO-BEAMS; MICRO-DEVICES; NON-LINEAR PROBLEMS; NORMAL FLOWS; OPTIMIZ ATION PROBLEMS; PULL-IN; PULL-IN EFFECT; PULL-IN VOLTAGES; STRONG COUPLINGS; TANGENT STIFFNESS MATRIX; TOPOLOGY DESIGN; TOPOLOGY OPTIMIZATION; UNSTABLE BEHAVIOR;

OPTIMIZATION;

EID: 50049125803     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.03.024     Document Type: Article

References (37)

1. Bendsøe M., and Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engrg. 71 2 (1988) 197-224
2. Bendsøe M. Optimal shape design as a material distribution problem. Struct. Opt. 1 (1989) 193-202
3. Sigmund O., and Petersson J. Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Opt. 16 1 (1998) 68-75
4. M. Bendsøe, O. Sigmund, Topology Optimization: Theory, Methods, and Applications, Springer-Verlag.
5. Wang S., and Kang J. Topology optimization of nonlinear magnetostatics. IEEE Trans. Magnet. 38 (2002) 1029-1032
6. Sigmund O. Design of multiphysic actuators using topology optimization - Part I: One material structures - Part II: Two-material structures. Comput. Methods Appl. Mech. Engrg. 190 49-50 (2001) 6577-6627
7. Yin L., and Ananthasuresh G. A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisms. Sensor Act. 97-98 (2002) 599-609
8. Raulli M., and Maute K. Topology optimization of electrostatically actuated microsystems. Struct. Multidiscip. Opt. 30 5 (2005) 342-359
9. Liu Z., Korvink J., and Reed M. Multiphysics for structural topology optimization. Sensor Lett. 4 (2006) 191-199
10. G. Yoon, O. Sigmund, Topology optimization for electrostatic system, in: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, 2007, pp. 1686-1693.
11. Abdalla M., Reddy C., Faris W., and Gurdal Z. Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage. Comput. Struct. 83 (2005) 1320-1329
12. E. Lemaire, P. Duysinx, V. Rochus, J.-C. Golinval, Improvement of pull-in voltage of electromechanical microbeams using topology optimization, in: III European Conference on Computational Mechanics, 2006.
13. Klapka I., Cardona A., and Géradin M. An object-oriented implementation of the finite element method for coupled problems. Revue Européenne des Elements Finis 7 5 (1998) 469-504
14. Neves M., Rodrigues H., and Guedes J. Generalized topology design of structures with a buckling load criterion. Struct. Opt. 10 (1995) 71-78
15. Buhl T., Pedersen C., and Sigmund O. Stiffness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Opt. 19 (2000) 93-104
16. Rahmatalla S., and Swan C. Continuum structural topology optimization of buckling-sensitive structures. AIAA 41 6 (2003) 1180-1189
17. Kemmler R., Lipka A., and Ramm E. Large deformation and stability in topology optimization. Struct. Multidiscip. Opt. 30 (2005) 459-476
18. M. Agrawal, G. Ananthasuresh, On including manufacturing constraints in the topology optimization of surface-micromachined structures, in: 7th World Congress on Structural and Multidisciplinary Optimization, 2007, pp. 2256-2265.
19. Reitz J., Milford F., and Christy R. Foundations of Electromagnetic Theory. 3rd ed. (1979), Addison-Wesley
20. Merlijn van Spengen W., Puers R., and De Wolf I. A physical model to predict stiction in MEMS. J. Micromech. Microengng. 12 (2002) 702-713
21. Rochus V., Rixen D.J., and Golinval J.-C. Monolithic modelling of electro-mechanical coupling in micro-structures. Int. J. Numer. Methods Engrg. 65 4 (2006) 461-493
22. Géradin M., and Rixen D. Mechanical Vibrations: Theory and Application to Structural Dynamics. 2nd ed. (1997), John Wiley & Sons Ltd.
23. Ragon S., Gurdal Z., and Watson L. A comparison of three algorithms for tracing nonlinear equilibrium paths of structural systems. Int. J. Solids Struct. 39 (2002) 689-698
24. Crisfield M. Non-linear Finite Element Analysis of Solids and Structures (1991), Wiley, New York
25. Seyranian A., Lund E., and Olhof N. Multiple eigenvalues in structural optimization problems. Struct. Opt. 8 (1994) 207-227
26. Eschenauer H.A., and Olhoff N. Topology optimization of continuum structures: a review. Appl. Mech. Rev. 54 4 (2001) 331-390
27. Sigmund O. On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25 4 (1997) 493-526
28. C. Fleury, Mathematical programming methods for constrained optimization: dual methods, in: Progress in astronautics and aeronautics, vol. 150, AIAA, 1993, pp. 123-150 (chapter 7).
29. Svanberg K. The method of moving asymptotes-a new method for structural optimization. Int. J. Numer. Methods Engrg. 24 2 (1987) 359-373
30. Fleury C. Conlin: an efficient dual optimizer based on convex approximation concepts. Struct. Multidiscip. Opt. 1 2 (1989) 81-89
31. M. Zhou, R. Fleury, Y. Shyy, H. Thomas, J. Brennan, Progress in topology optimization with manufacturing constraints, in: 9th AIAA/ISSMO Symposium on Mutlidisciplinary Analysis and Optimization, AIAA, Atlanta, Georgia, 2002.
32. M. Zhou, Y. Shyy, H. Thomas, Topology optimization with manufacturing constraints, in: 4th World Congress of Structural and Multidisciplinary Optimization, Dalian, China, 2001.
33. Sigmund O. Materials with prescribed constitutive parameters: an inverse homogenization problem. Int. J. Solids Struct. 31 (1994) 2313-2329
34. Seyranian A., and Privalova O. The lagrange problem on an optimal column: old and new results. Struct. Opt. 25 (2003) 393-410
35. J. Carter, A. Cowen, B. Hardy, R. Mahadevan, M. Stonefield, S. Wilcenski, PolyMUMPs Design Hanbook, MEMSCAP, 11th ed., 2005.
36. Senturia S. Microsystem Design (2001), Kluwer Academic Publisher
37. Duysinx P., and Bendsøe M. Topology optimization of continuum structures with local stress constraints. Int. J. Numer. Methods Engrg. 43 (1998) 1453-1478