A level set approach for optimal design of smart energy harvesters

Computer Methods in Applied Mechanics and Engineering

Volumn 199, Issue 37-40, 2010, Pages 2532-2543

  Chen, Shikui ^a   Gonella, Stefano ^a   Chen, Wei ^a   Liu, Wing Kam ^a  

^a Northwestern University   (United States)

Author keywords

Design; Energy harvester; Level set method; Multi material structure; Piezoelectric materials; Topology optimization

Indexed keywords

ADJOINT VARIABLE METHODS; DESIGN PROBLEMS; ELECTRICAL ENERGY; ENERGY HARVESTER; EXISTING ENERGIES; LEVEL SET; LEVEL SET APPROACH; LEVEL SET METHOD; MATERIAL TIME DERIVATIVE; MECHANICAL ENERGIES; MICROELECTROMECHANICAL SYSTEMS; MULTI-MATERIAL STRUCTURE; MULTIPLE MATERIALS; OPTIMAL DESIGN; OPTIMAL GEOMETRY; PIEZO-ELECTRIC EFFECTS; PIEZOELECTRIC ENERGY; PIEZOELECTRIC ENERGY HARVESTING; PORTABLE ELECTRONICS; SELF-POWERED; SELF-POWERING; SHAPE AND TOPOLOGY OPTIMIZATION; SHAPE GRADIENT; TOPOLOGY OPTIMIZATION; VARIATIONAL PROBLEMS; VELOCITY FIELD; WIRELESS SENSING;

COMPUTATIONAL EFFICIENCY; CONVERSION EFFICIENCY; DESIGN; DROP BREAKUP; ENERGY CONVERSION; EVOLUTIONARY ALGORITHMS; HARVESTERS; HARVESTING; LEVEL MEASUREMENT; MATERIALS; MEMS; MICROELECTROMECHANICAL DEVICES; PIEZOELECTRIC DEVICES; PIEZOELECTRIC MATERIALS; PIEZOELECTRICITY; SHAPE OPTIMIZATION; STEEPEST DESCENT METHOD; TOPOLOGY; VIBRATIONS (MECHANICAL);

ENERGY HARVESTING;

EID: 77954757726     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.04.008     Document Type: Article

References (69)

1. Huang Y., Loewke K., Schaaf K., Nemat-Nasser S. Localized SHM with Embedded Sensor Network. Structural Health Monitoring 2005: Advancements and Challenges for Implementation 2005, DEStech Publications, Inc. F.-K. Chang (Ed.).
2. Yuan S., Wang L., Shi L. Active monitoring for on-line damage detection in composite structures. Journal of Vibration and Acoustics 2003, 125(2):178-186.
3. Starner T. Human-powered wearable computing. IBM Systems Journal 1996, 35(3&4):618-629.
4. Masri S.F., Ghanem R., Govindan R., Nayeri R. A decentralized procedure for structural health monitoring of uncertain nonlinear systems provided with dense active sensor arrays. Smart Materials and Structures 2008, 17:045024. (045015pp.).
5. Priya S., Inman D.J. Energy Harvesting Technologies 2009, Springer.
6. Dutoit N.E., Wardle B.L., Kim S.-G. Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. Integrated Ferroelectrics 2005, 71(1):121-160.
7. Gonella S., To A.C., Liu W.K. Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting. Journal of the Mechanics and Physics of Solids 2009, 57(3):621-633.
8. Koh S.J.A., Zhao X., Suo Z. Maximal energy that can be converted by a dielectric elastomer generator. Applied Physics Letters 2009, 94:262902.
9. Roundy S., Leland E., Baker J., Carleton E., Reilly E., Lai E., Otis B., Rabaey J., Sundararajan V., Wright P.K. Improving power output for vibration-based energy scavengers. IEEE Pervasive Computing Journal on Mobile and Ubiquitous Computing 2005, 4(1):28-36.
10. Y. Liao, and H.A. Sodano, 2009, "Structural Effects and Energy Conversion Efficiency of Power Harvesting," Intelligent Material Systems and Structures, OnlineFirst.
11. Liao Y., Sodano H.A. Model of a single mode energy harvester and properties for optimal power generation. Smart Materials and Structures 2008, 17:065026. (065014pp.).
12. Silva E.C.N., Kikuchi N. Design of piezocomposite materials and piezoelectric transducers using topology optimization-part III. Archives of Computational Methods in Engineering 1999, 6(4):305-329.
13. Naillon M., Coursant R.H., Besnier F. Analysis of piezoelectric structures by a finite element method. Acta Electronica 1983, 25(4):341-362.
14. Silva E.C.N., Kikuchi N. Design of piezoelectric transducers using topology optimization. Smart Materials and Structures 1999, 8:350-364.
15. Bendsøe M. Optimal shape design as a material distribution problem. Structural and Multidisciplinary Optimization 1989, 1:193-202.
16. Rozvany G.I.N., Zhou M., Birker T. Generalized shape optimization without homogenization. Strutural Optimization 1992, 4:250-254.
17. Nakasone P.H., Silva E.C.N. Design of piezoelectric energy harvesting devices and laminate structures by applying topology optimization. Modeling, Signal Processing, and Control for Smart Structures 2009, Proc. of SPIE 2009, pp. 728603-728601-728611.
18. F. Wein, M. Kaltenbacher, B. Kaltenbacher, G.u. Leugering, E. B ansch, F. Schury, Topology optimization of piezoelectric layers using the SIMP method, Structural and Multidisciplinary Optimization, (submitted for publication).
19. F. Wein, B. Kaltenbacher, G. Leugering, E. Bansch F. Schury, Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation, International Journal of Applied Electromagnetics and Mechanics 30 (3-4) (2009) 201-221.
20. Zheng B., Chang C.-J., Gea H.C. Topology optimization of energy harvesting devices using piezoelectric materials. Structural and Multidisciplinary Optimization 2009, 38(1):17-23.
21. Rupp C.J., Evgrafov A., Maute K., Dunn M.L. Design of Piezoelectric Energy Harvesting Systems: a Topology Optimization Approach Based on Multilayer Plates and Shells. Journal of Intelligent Material Systems and Structures 2009, 20(16):1923-1939.
22. Sigmund O., Peterson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural and Multidisciplinary Optimization 1998, 16(1):68-75.
23. A.R. Diaz, O. Sigmund, A topology optimization method for design of negative permeability metamaterials, Structural and Multidisciplinary Optimization 41 (2) (2010) 163-177.
24. Sigmund O. Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 2007, 33(4-5):401-424.
25. Wang M., Wang X.M., Guo D.M. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering 2003, 192:227-246.
26. Allaire G., Jouve F., Toader A.M. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics 2004, 194:363-393.
27. Xia Q., Wang M.Y. Topology optimization of thermoelastic structures using level set method. Computational Mechanics 2008, 42(6):837-857.
28. Luo Z., Tong L., Ma H. Shape and topology optimization for electrothermomechanical microactuators using level set methods. Journal of Computational Physics 2009, 228(9):3173-3181.
29. Persson P.-O., Strang G. A simple mesh generator in MATLAB. SIAM Review 2004, 46(2):329-345.
30. Fayolle P.-A., Pasko A., Schmitt B. SARDF: signed approximate real distance functions in heterogeneous objects modeling. Heterogeneous Objects Modelling and Applications 2008, 118-141. Springer Berlin, Heidelberg.
31. Carbonari R.C., Silva E.C.N., Paulino G.H. Topology optimization design of functionally graded bimorph-type piezoelectric actuators. Smart Materials and Structures 2007, 16:2605-2620.
32. V. Piefort, 2001, Finite Element Modelling of Piezoelectric Active Structures, Ph.D. Thesis, Universit'e Libre de Bruxelles, Belgium.
33. Biegler L.T., Ghattas O., Heinkenschloss M., Waanders B.v.B. Large-Scale PDE-Constrained Optimization 2003, Springer.
34. Osher S., Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988, 79:12-49.
35. Sethian J.A. Level Set Methods and Fast Marching Methods 1999, Cambridge University Press.
36. Osher S., Fedkiw R. Level Sets Methods and Dynamic Implicit Surfaces 2003, Springer.
37. Sethian J., Wiengmann A. Structural boundary design via level set and immersed interface methods. Journal of Computational Physics 2000, 163:489-528.
38. Osher S.J., Santosa F. Level set methods for optimization problems involving geometry and constraints. I. Frequencies of a two-density inhomogeneous drum. Journal of Computational Physics 2001, 171:272-288.
39. Allaire G., Jouve F., Toader A.-M. A level-set method for shape optimization. Comptes Rendus Mathematique 2002, 334(12):1125-1130.
40. Wang M.Y., Wang X.M. PDE-driven level sets, shape sensitivity, and curvature flow for structural topology optimization. Computer Modeling in Engineering & Sciences 2004, 6:373-395.
41. Haber E. A multilevel, level-set method for optimizing eigenvalues in shape design problems. Journal of Computational Physics 2004, 198:518-534.
42. Belytschko T., Xiao S.P., Parimi C. Topology optimization with implicitly function and regularization. International Journal of Numerical Method for Engineering 2003, 57:1177-1196.
43. Wang S., Wang M.Y. Radial basis functions and level set method for structural topology optimization. Interational Journal of Numerical Method for Engineering 2006, 65:2060-2090.
44. Wang S., Wang M.Y. Structural shape and topology optimization using implicit free boundary parameterization method. Computer Modeling in Engineering & Sciences 2006, 13(2):119-147.
45. Wang S., Lim K., Khoo B., Wang M. An extended level set method for shape and topology optimization. Journal of Computational Physics 2007, 221:395-421.
46. Luo Z., Wang M.Y., Tong L., Wang S. Shape and topology optimization of compliant mechanisms using a parameterization level set method. Journal of Computational Physics 2007, 227(1):680-705.
47. Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987, 24(2):359-373.
48. Wang M.Y., Wang X.M. 'Color' level sets: a multi-phase level set method for structural topology optimization with multiple materials. Computer Methods in Applied Mechanics and Engineering 2004, 193:469-496.
49. Wang M.Y., Chen S.K., Wang X., Mei Y. Design of multi-material compliant mechanisms using level set methods. ASME Journal of Mechanical Design 2005, 127(5):941-956.
50. Wang M.Y., Wang X. A level-set based variational method for design and optimization of heterogeneous objects. Computer-Aided Design 2005, 37(3):321-337.
51. Li H.W., Tai X.C. Piecewise constant level set methods for multiphase motion. No. Technical Report 06-17 2006, University of California at Los Angeles, Los Angeles.
52. Lie J., Lysaker M., Tai X.C. A variant of the level set method and applications to image segmentation. Mathematics of Computation 2006, 75:1151-1174.
53. Wei P., Wang M.Y. Piecewise constant level set method for structural topology optimization. International Journal for Numerical Methods in Engineering 2009, 78(4):379-402.
54. Luo Z., Tong L., Luo J., Wei P., Wang M.Y. Design of piezoelectric actuators using a multiphase level set method of piecewise constants. Journal of Computational Physics 2009, 228(7):2643-2659.
55. Merriman B., Bence J.K., Osher S. Motion of multiple junctions: a level set approach. Journal of Computational Physics 1994, 112(2):334-363.
56. Zhang X., Chen J.-S., Osher S. A multiple level set method for modeling grain boundary evolution of polycrystalline materials. Interaction and Multiscale Mechanics 2008, 1(2):178-191.
57. Bloomfield M.O., Richards D.F., Cale T.S. A computational framework for modelling grain-structure evolution in three dimensions. Philosophical Magazine 2003, 83(31):3549-3568.
58. Wang M.Y., Zhou S.W. Phase field: a variational method for structural topology optimization. CMES: Computer Modeling in Engineering & Sciences 2004, 6(6):547-566.
59. Roman S., Martin B. Phase-field relaxation of topology optimization with local stress constraints. SIAM Journal on Control and Optimization 2006, 45(4):1447-1466.
60. Pironneau O. Optimal Shape Design for Elliptic Systems 1984, Springer, New York.
61. Haug E.J., Choi K.K., Komkov V. Design sensitivity analysis of structural systems 1986, Academic Press, Orlando.
62. Choi K.K., Kim N.H. Structural Sensitivity Analysis and Optimization 1: Linear Systems 2005, Springer.
63. Belytschko T., Liu W.K., Moran B. Nonlinear Finite Elements for Continua and Structures 2000, John Wiley & Sons Ltd., New York.
64. Bonet J., Wood R.D. Nonlinear Continuum Mechanics for Finite Element Analysis 1997, Cambridge University Press, Cambridge.
65. Roundy S., Wright P.K., Rabaey J. A study of low level vibrations as a power source for wireless sensor nodes. Computer Communications 2002, 26(11):1131-1144.
66. Anton S.R., Sodano H.A. A review of power harvesting using piezoelectric materials (2003-2006). Smart Materials and Structures 2007, 16:R1-R21.
67. Allik H., Hughes T.J.R. Finite element method for piezoelectric vibration. International Journal for Numerical Methods in Engineering 1970, 2:151-157.
68. Sokolowski J., Zolesio J.P. Introduction to Shape Optimization: Shape Sensitivity Analysis 1992, Springer.
69. I. Stoianov, L. Nachman, S. Madden, T. Tokmouline, Pipenet: a wireless sensor network for pipeline monitoring, Proceedings of the 6th international conference on Information processing in sensor networks, 2007, Cambridge, Massachusetts, U.S.A., pp. 264-273.