Structural Design of Piezoelectric Actuator Considering Polarization Direction and Continuous Approximation of Material Distribution

분극방향과 재료분포의 연속적 근사방법을 고려한 압전형 액추에이터의 구조설계

  • 임영석 (한양대학교 대학원 기계설계학과) ;
  • 유정훈 (연세대학교 기계공학부) ;
  • 민승재 (한양대학교 기계공학부)
  • Published : 2006.09.01


In this paper, the polarization of piezoelectric materials is considered to improve actuation since the piezoelectric polarization has influences on the performance of the actuator. The topology design of compliant mechanism can be formulated as an optimization problem of material distribution in a fixed design domain and continuous approximation of material distribution (CAMD) method has demonstrated its effectiveness to prevent the numerical instabilities in topology optimization. The optimization problem is formulated to maximize the mean transduction ratio subject to the total volume constraints and solved using a sequential linear programming algorithm. The effect of CAMD and the performance improvement of actuator are confirmed through Moonie actuator and PZT suspension design.


Topology Optimization;Piezoelectric Actuator;Polarization Direction;Homogenization Design Method;Simple Isotropic Material with Penalization;Continuous Approximation of Material Distribution


  1. Sun, C. T. and Zhang, X. D., 1995, 'Use of Thickness-shear Mode in Adaptive Sandwich Structures,' Smart Materials and Structures, Vol. 4, pp. 202-206
  2. Benjeddou, A., Trindade, M. A. and Ohayon, R., 1997, 'A Unified-Beam Finite Element Model for Extension and Shear Piezoelectric Actuation,' Journal of Intelligent Material Systems and Strnctures, Vol. 8, pp. 1012-1025
  3. Silva, E. C. N. and Kikuchi, N., 1998, 'Optimization Methods Applied to Material and Flextensional Actuator Design Using the Homogenization Method,' Computer Methods in Applied Mechanics and Engineering, Vol. 159, pp.49-77
  4. Silva, E. C. N., Nishiwaki, S. and Kikuchi, N., 2000, 'Topology Optimization of Flextensional Actuators,' IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 47, pp. 657-671
  5. Chae, J. and Min, S, 2004, 'Structural Design of Piezoelectric Microactuator Using Topology Optimization,' Transactions of the KSME, A, Vo. 28, No.2, pp. 206-213
  6. Bendsoe, M. P. and Kikuchi, N., 1988, 'Generating Optimal Topologies in Structural Design Using a Homogenization Method,' Computer Methods in Applied Mechanics and Engineering, Vol. 71, pp. 197-224
  7. Gibert, J. M. and Austin, E. M., 2004, 'Inclusion of Piezoelectric Polarization in the Design of a Flextensional Actuator,' Smart Materials and Structures, Vol. 5383, pp. 183-193
  8. Huber, J. E. and Fleck, N. A., 2001, 'Multi-Axial Electrical Switching of a Ferroelectric: Theory Versus Experiment,' Journal of the Mechanics and Physics of Solids, Vol. 49, pp. 785-811
  9. Sigmund, O. and Petersson, J., 1998, 'Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing with Checkerboards, MeshDependencies and Local Minima,' Structural Optimization, Vol. 16, pp. 68-75
  10. Diaz, A. R. and Sigmund, O., 1995, 'Checkerboard Patterns in Layout Optimization,' Structural Optimization, Vol. 10, pp. 40-45
  11. Sigmund, O., 1994, 'Design of Material Structures Using Topology Optimization,' Ph.D. thesis, Department of solid Mechanics, Technical University of Denmark
  12. Bourdin, B., 2001, 'Filters in Topology Optimization,' International Journal for Numerical Methods in Engineering, Vol. 50, pp. 2143-2158
  13. Nishiwaki, S., Frecker, M., I., Min, S. and Kikuchi, N., 1998, 'Topology Optimization of Compliant Mechanisms Using the Homogenization Method,' International Journal for Numerical Methods in Engineering, Vol. 42, pp.535-559<535::AID-NME372>3.0.CO;2-J
  14. Nishiwaki, S., Min, S., Yoo, J. and Kikuchi, N., 2001, 'Optimal Structural Considering Flexibility,' Computer Methods in Applied Mechanics and Engineering, Vol. 190, pp. 4457-4504
  15. Matsui, K. and Terada, K., 2004, 'Continuous Approximation of Material Distribution for Topology Optimization,' International Journal for Numerical Methods in Engineering, Vol. 59, pp. 1925-1944
  16. Lim, Y. S., Min, S., Yoo, J., Terada, K. and Nishiwaki, S., 2006, 'Comparative Studies on Topology Optimization Using Continuous Approximation of Material Distribution,' Transactions of the KSME, A, Vo. 30, No.2. pp. 164-170
  17. Naillon, M., Coursant, R. H. and Besnier, F, 1983, 'Analysis of Piezoelectric Structures by a Finite Element Method,' Acta Electronica, Vol.25, pp. 341-362
  18. Bendsee, M. P., 1989, 'Optimal Shape Design as a Material Distribution Problem,' Structural Optimization, Vol. 17, pp. 193-202