Design of Piezocomposite Materials and Piezoelectric Transducers Using Topology Optimization - Part I

Archives of Computational Methods in Engineering

Volumn 6, Issue 2, 1999, Pages 117-182

  Silva, E C Nelli ^c   Fonseca, J S Ono ^d   De Espinosa, F Montero ^a   Crumm, A T ^b   Brady, G A ^b   Halloran, J W ^b   Kikuchi, N ^e  

^a Consejo Superior de Investigaciones Científicas   (Spain)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

^d FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^e NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037515311     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02736183     Document Type: Article

References (68)

1. Newnham, R. E. and G. R. Ruschau (1991), "Smart Electroceramics", Journal of the American Ceramic Society, 74 No.3, 463-480.
2. Smith, W. A. (1990), "The Application of 1-3 Piezocomposites in Acoustic Transducers", Proceedings of 7th International Symposium on Applications of Ferroelectrics, 145-152.
3. Smith, W. A. (1989), "The Role of Piezocomposites in Ultrasonic Transducers", Proceedings of IEEE Ultrasonic Symposium, 755-765.
4. Safari, A. (1994), "Development of Piezoelectric Composites for Transducers", Journal de Physique III, 4 No.7, 1129-1149.
5. Newnham, R. E., D. P. Skinner, and L. E. Cross (1978), "Connectivity and Piezoelectric-Pyroelectric Composites", Materials Research Bulletin, 13, 525-536.
6. Zhang, Q. M., J. Chen, H. Wang, J. Zhao, L. E. Cross, and M. C. Trottier (1995), "A New Transverse Piezoelectric Mode 2-2 Piezocomposites for Underwater Transducer Applications", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 42 No.4, 774-781.
7. Smith, W. A. (1993), "Modeling 1-3 Composite Piezoelectrics: Hydrostatic Response", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 40 No.1, 41-49.
8. Smith, W. A. and B. A. Auld (1991), "Modeling 1-3 Composite Piezoelectrics: Thickness-Mode Oscillations", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 38 No.1, 40-47.
9. Skinner, D. P., R. E. Newnham, and L. E. Cross (1978), "Flexible Composite Transducers", Materials Research Bulletin, 13, 599-607.
10. Haun, M. J. and R. E. Newnham (1986), "An Experimental and Theoretical Study of 1-3 and 1-3-0 Piezoelectric PZT-polymer Composites for Hydrophone Applications", Ferroelectrics, 68, 123-139.
11. Banno, H. (1994), "Theoretical Equations for Dielectric, Elastic, and Piezoelectric Constants of Diphasic Composite Changing its Connectivity from 3-0 to 0-3 via 3-3", ISAF-IEEE, 1-55.
12. Chan, H. L. W. and J. Unsworth (1989), "Simple Model for Piezoelectric Ceramic/polymer 1-3 Composites Used in Ultrasonics Transducer Applications", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 36 No.4, 434-441.
13. Hashimoto, K. Y. and M. Yamaguchi (1986), "Elastic, Piezoelectric and Dielectric Properties of Composite Materials", Proceedings of IEEE Ultrasonics Symposium, 697-702.
14. Grekov, A. A., S. O. Kramarov, and A. A. Kuprienko (1989), "Effective Properties of a Transversely Isotropic Piezoelectric Composite with Cylindrical Inclusions", Mechanics of Composite Materials, 25 No.1, 54-61.
15. Wang, B. (1992), "Three-Dimensional Analysis of an Ellipsoidal Inclusion in a Piezoelectric Material", International Journal of Solids and Structures, 29 No.3, 293-308.
16. Benveniste, Y. and G. J. Dvorak (1992), "Uniform Fields and Universal Relations in Piezoelectric Composites", Journal of the Mechanics and Physics of Solids, 40 No.6, 1295-1312.
17. Hill, R. (1965), "A Self-Consistent Mechanics of Composite Materials", Journal of the Mechanics and Physics of Solids, 13, 213-222.
18. Schulgasser, K. (1992), "Relationships Between the Effective Properties of Transversely Isotropic Piezoelectric Composites", Journal of the Mechanics and Physics of Solids, 40 No.2, 473-479.
19. Dunn, M. L. and M. Taya (1993), "Micromechanics Predictions of the Effective Electroelastic Moduli of Piezoelectric Composites", International Journal of Solids and Structures, 30 No.2, 161-175.
20. Avellaneda, M. and P. J. Swart (1994), "The Role of Matrix Porosity and Poisson's Ratio in the Design of High-Sensitivity Piezocomposite Transducers", Adaptive Structures and Composite Materials: Analysis and Application - ASME Aerospace Division AD, 45, 59-66.
21. Hayward, G. and J. Bennett (1996), "Assessing the Influence of Pillar Aspect Ratio on the Behavior of 1-3 Connectivity Composite Transducers", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43 No.1, 98-108.
22. Bennett, J. and G. Hayward (1997), "Design of 1-3 Piezocomposite Hydrophones Using Finite Element Analysis", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 44 No.3, 565-574.
23. Gómez, T. E. and F. M. de Espinosa (1997), "Piezocomposites of Complex Microstructure: Theory and Experimental Assessment of the Coupling Between Phases", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 44 No.1, 208-217.
24. Zhang, Q. M., W. Cao, J. Zhao, and L. E. Cross (1994), "Piezoelectric Performance of Piezoceramic-Polymer Composites with 2-2 Connectivity - A Combined Theoretical and Experimental Study", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 41 No.4, 556-564.
25. Sanchez, S. and F. R. M. de Espinosa (1997), "Modeling (2-2) Piezocomposites Partially Sliced in the Polymer Phase", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 44 No.2, 287-296.
26. Auld, B. A., H. A. Kunkel, Y. A. Shui, and Y. Wang (1983), "Dynamic Behavior of Periodic Piezoelectric Composites", Proceedings of IEEE Ultrasonics Symposium, 554-558.
27. Shui, Y. and Q. Xue (1997), "Dynamic Characteristics of 2-2 Piezoelectric Composite Transducers", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 44 No.5, 1110-1119.
28. Yamaguchi, M., K. Y. Hashimoto, and H. Makita (1987), "Finite Element Method Analysis of Dispersion Characteristics for 1-3 type Piezoelectric Composites", Proceedings of IEEE Ultrasonics Symposium, 657-661.
29. Hossack, J. A. and G. Hayward (1991), "Finite-Element Analysis of 1-3 Composite Transducers", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 38 No.6, 618-629.
30. Smith, W. A. (1991), "Optimizing Electromechanical Coupling in Piezocomposites Using Polymers with Negative Poisson's Ratio", Proceedings of IEEE Ultrasonic Symposium, 1, 661-666.
31. Gibiansky, L. V. and S. Torquato (1997), "On the Use of Homogenization Theory to Optimally Design Piezocomposites for Hydrophone Applications", Journal of the Mechanics and Physics of Solids, 45 No.5, 689-708.
32. Gibiansky, L. V. and S. Torquato (1997) "Optimal Design of 1-3 Composite Piezoelectrics", Structural Optimization, 13 No.1, 23-38.
33. Sigmund, O., S. Torquato, and I. A. Aksay (1997), "On the Design of 1-3 Piezocomposites Using Topology Optimization", Danish Center for Applied Mathematics and Mechanics, Report No. 542.
34. Hossack, J. A. and B. A. Auld (1992), "Improved Efficiency Piezoelectric Ceramic/Polymer CoinpositeTransducers", Proceedings of Ultrasonics Symposium, 523-526.
35. Milton, G. W. and A. V. Cherkaev (1995), "Which Elasticity Tensors are Realizable?", Journal of Engineering Materials and Technology, 117, 483-493.
36. Hashin, Z. and S. Shtrikman (1963) "A Variational Approach of the Theory of Elastic Behavior of Multiphase materials", Journal of the Mechanics and Physics of Solids, 11, 127-140.
37. Lipton, R. (1994), "Optimal Bounds on Effective Elastic Tensors for Orthotropic Composites", Proceedings of the Royal Society of London Serie A, 444 No.1921, 399-410.
38. Smith, W. A. (1992), "Limits to the Enhancement of Piezoelectric Transducers Achievable by Materials Engineering", Proceedings of IEEE Ultrasonics Symposium, 1, 697-702.
39. Gibiansky, L. V. and S. Torquato (1995), "Rigorous Link Between the Conductivity and Elastic Moduli of Fibre-reinforced Composite Materials", Philosophical Transactions of the Royal Society A, 353 No.1702 (1995), 243-278.
40. Fonseca, J. S. O. (1997), "Design of Microstructures of Periodic Composite Material", Ph.D. Dissertation, N. Kikuchi, advisor, The University of Michigan.
41. Sigmund, O. (1994), "Materials With Prescribed Constitutive Parameters: and Inverse Homogenization Problem", International Journal of Solids and Structures, 31 No.17, 2313-2329.
42. Sigmund, O. (1995), "Tailoring Materials with Prescribed Elastic Properties", Mechanics of Materials, 20, 351-368.
43. Sigmund, O. and S. Torquato (1996), "Design of Materials with Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method", Danish Center for Applied Mathematics and Mechanics, Report No.525.
44. Haslinger, J. and J. Dvorák (1995), "Optimum Composite Material Design", RAIRO Modélisation Mathématique et Analyse Numériquemm, 29 No.6, 657-686.
45. Swan, C. C. and J. S. Arora (1997), "Topology Design of Material Layout in Structured Composites of High Stiffness and Strength", Structural Optimization, 13, 45-59.
46. Silva, E. C. N., J. S. O. Fonseca, and N. Kikuchi (1997), "Optimal Design of Piezoelectric Microstructures", Computational Mechanics, 19 No.5, 397-410.
47. Silva, E. C. N., J. S. O. Fonseca, and N. Kikuchi (1997), "Optimal Design of Periodic Piezocomposites", Computer Methods in Applied Mechanics and Engineering.
48. ANSI/IEEE Std 176-1978 (1984), "IEEE Standard on Piezoelectricity, Special Issue of Transactions on Sonics and Ultrasonics", SU-31 No.2.
49. Sanchez-Palencia, E. (1980), Non-Homogeneous Media and Vibration Theory, Lectures Notes in Physics 127, Springer, Berlin.
50. Guedes, J. M. and N. Kikuchi (1990), "Preprocessing and Postprocessing for Materials Based on the Homogenization Method with Adaptive Finite Element Methods", Computer Methods in Applied Mechanics and Engineering, 83, 143-198.
51. Telega, J. J. (1990), "Piezoelectricity and Homogenization: Application to Biomechanics", Continuum Models and Discrete Systems, 2 in: G.A. Maugin, ed., Longman, London, 220-230.
52. Galka, A., J.J. Telega, and R. Wojnar (1992), "Homogenization and Thermopiezoelectricity", Mechanics Research Communications, 19 No.4, 315-324.
53. Turbé, N. and G. A. Maugin (1991), "On the Linear Piezoelectricity of Composite Materials", Mathematical Methods in the Applied Sciences, 14 No.6, 403-412.
54. Otero, J. A., J. B. Castillero, and R. R. Ramos (1997), "Homogenization of Heterogeneous Piezoelectric Medium", Mechanics Research Communications, 24 No.1, 75-84.
55. Allik, H. and T.J.R. Hughes (1970), "Finite Element Method for Piezoelectric Vibration", International Journal of Numerical Methods in Engineering, 2, 151-157.
56. Bathe, K. J. (1996), Finite Element Procedures, Englewood Cliffs, N.J., Prentice-Hall.
57. Kikuchi, N., S. Hollister, and J. Yoo (1997), "A Concept of Image-Based Integrated CAE for Production Engineering", Proceedings of International Symposium on Optimization and Innovative Design, Japan, 75-90.
58. Bendsøe, M. P. and N. Kikuchi (1988), "Generating Optimal Topologies in Structural Design Using a Homogenization Method", Computer Methods in Applied Mechanics and Engineering, 71, 197-224.
59. Vanderplaatz, G. N. (1984), Numerical Optimization Techniques for Engineering Design: with Applications, McGraw-Hill, NY.
60. Hanson, R. and K. Hiebert (1981), "A Sparse Linear Programming Subprogram", Sandia National Laboratories, Technical Report SAND81-0297.
61. Ting, R. Y., A. A. Shaulov, and W. A. Smith (1990), "Piezoelectric Properties of 1-3 composites of a Calcium-Modified Lead Titanate in Epoxy Resins", Proceedings of IEEE Ultrasonic Symposium, 707-710.
62. Gururaja, T. R., W. A. Schulze, L. E. Cross, R. E. Newnham, B. A. Auld, and Y. J. Wang (1985), "Piezoelectric Composite Materials for Ultrasonic Transducer Applications. Part I: Resonant Modes of Vibration of PZT Rod-Polymer Composites", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, SU-32 No.4, 481-498.
63. Gururaja, T. R., W. A. Schulze, L. E. Cross, and R. E. Newnham (1985), "Piezoelectric Composite Materials for Ultrasonic Transducer Applications. Part II: Evaluation of Ultrasonic Medical Applications", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, SU-32 No.4, 499-513.
64. Bendsøe, M. P. (1989), "Optimal Shape Design as a Material Distribution Problem", Structural Optimization, 1, 192-202.
65. Eyraud, L., C. Richard, and D. Guyomar (1994), "Power Ceramic Materials for Piezocomposite Hydrophone", Proceedings of IEEE Ultrasonics Symposium, 2, 929-934.
66. Crumm, A. T. and J. W. Halloran (1997), "Fabrication of Micro-Configured Multicomponent Ceramics", Submitted to Journal of the American Ceramic Society.
67. Jacobs, P. F. (1996), Stereolithography and Other RP&M Technologies from Rapid Prototyping to Rapid Tooling, Society of Manufacturing Engineers in Cooperation with the Rapid Prototyping Association of SME, ASME Press, New York.
68. Safari, A., G. S. Gong, J. Giniewicz, and R. E. Newnham (1986), "Composite Piezoelectric Sensors", Proceedings of the Twenty-First University Conference on Ceramic Science, Plenum New York NY, 445-454.