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Journal of Intelligent Material Systems and Structures
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Topology Optimization of Smart Structures Using a Homogenization Approach

Markus J. Buehler

Department of Mechanical Engineering — Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA

Bernhard Bettig

Department of Mechanical Engineering — Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA, bettig{at}mtu.edu

Gordon G. Parker

Department of Mechanical Engineering — Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA

Engineers are often required to design mechanical structures to meet specific loading conditions. Topology optimization automates the process of finding an optimal structural design, allowing for size, shape, and topology variations. For a given set of boundary conditions and design specifications, an optimal structure is computed, based on a formulated cost function. In this paper, the optimization considers not only the distribution of conventional material, but also simultaneously the distribution of active piezoelectric material within the domain. In the formulation of the topology optimization problem, a microstructure consisting of smart as well as conventional material is used. Instances of the microstructure occur in a rectangular grid and cover the design domain. Since the microstructure is defined parametrically, the density of each material can be controlled individually at each point. This enables us to formulate the problem of finding an optimal material distribution as a parameter optimization problem. A homogenization approach is used to find and use effective material properties for the limiting case of an infinitely small microstructure. Several numerical examples are provided to demonstrate the application of the method to find structures that maximize the deflection at a point when the piezoelectric material is activated.

Key Words: topology optimization • smart structures • piezoelectric material • structural optimization • finite element method • extended unit cell

References

  • Bathe, K.-J. 1982. Finite Element Procedures in Engineering Analysis. Prentice-Hall, Inc.
  • Bendsøe, M. 1989. "Optimal Shape Design as a Material Distribution Problem," Structural Optimization, 1: 193-202 .[CrossRef]
  • Bensoussan, A., Lions, J. and Papanicolao, G. 1978. Asymptotic Analysis for Periodic Structures. ISBN 0-444-85172-0. North Holland Publishing Company, Amsterdam .
  • Buehler, M., Bettig, B. and Parker, G. 2003. "Numerical Homogenization of Active Material Finite-element Cells," Commun. Numer. Meth. Engng, 19: 977-989 .[CrossRef]
  • Chattopadhyay, A., Seeley, C. and Jha, R. 1999. "Aeroelastic Tailoring using Piezoelectric Actuation and Hybrid Optimization," Smart Materials and Structures, 190: 6605-6627 .
  • Chen, B., Silva, E. and Kikuchi, N. 2001. "Advances in Computational Design and Optimization with Application to Mems," International Journal for Numerical Methods in Engineering, 52: 23-62 .
  • Chen, W., Buehler, M., Kiilluunen, C., Parker, G. and Bettig, B. 2003. "Robust Control of Piezoelectric Laminate Beams using Simultaneous Optimization Method," Accepted for publication in IEEE Transactions on Control Systems Technology .
  • Collet, July 2001. "Shape Optimization of Piezoelectric Sensors Dealing with Spill-over Instability," IEEE Transactions on Control Systems Technology, 9(4): 654-662 .[CrossRef]
  • Dosch, J., Inman, D. and Garcia, E. 1992. "A Self-sensing Piezolectric Actuator for Collocated Control," Journal of Intell. Material Systems and Struct., 3: 166-185 .[Abstract]
  • Francu, J. 1982. "Homogenization of Linear Elasticity Equations," Aplikace Matematiky, Oslo, 27: 96-117 .
  • Frecker, M. 2002. "A Review of Current Research Activities in Optimization of Smart Structures and Actuators, Smart Structures and Materials 2002: Modeling, Signal Processing and Control," In: Rao, Vittal S. (ed.), Proceedings of the SPIE 4693, pp. 112-123 .
  • Frecker, M., Kikuchi, N. and Kota, S. 1999. "Topology Optimization of Compliant Mechanisms with Multiple Outputs," Structural Optimization, 17: 269-278 .[CrossRef]
  • Fujii, D., Chen, B. and Kikuchi, N. 2001. "Composite Material Design of Two-dimensional Structures using the Homogenization Design Method," International Journal for Numerical Methods in Engineering, 50: 2031-2051 .[CrossRef]
  • Gabbert, U. and Weber, C.-T. 1999. "Optimization of Piezoelectric Material Distribution in Smart Structures," In: Proceedings, SPIE Conference on Mathematics and Control in Smart Structures, 3667: 13-22 .
  • Kikuchi, N. and Bendsøe, M. 1988. "Generating Optimal Topologies in Structural Design using a Homogenization Method," Computer Methods Appl. Mech. Engng, 71(2): 197-224 .[CrossRef]
  • Maugin, G. and Turbe, N. 1991. "Homogenization of Piezoelectric Composites via Bloch Expansions," International Journal of Applied Electromagnetics in Materials, 14(2): 135-140 .
  • Mleijnek, H. and Schirrmacher, R. 1993. "An Engineer’s Approach to Optimal Material Distribution and Shape Finding," Comp. Meth. in Appl. Mech. and Engng, 106: 1-26 .
  • Nishiwaki, S., Frecker, M., Min, S. and Kikuchi, N. 1998. "Topology Optimization of Compliant Mechanisms using the Homogenization Method," Int. J. for Numerical Methods in Engng, 42: 535-559 .[CrossRef]
  • Padula, S. and Kincaid, R. 1999. Optimization strategies for sensor and actuator placement. Natl. Aeronautics and Space Administration Langley Res. Center, Langley, Virgina, 23681 , pp. 1-12.
  • Sigmund, O. 1997. "On the Design of Compliant Mechanisms using Topology Optimization," Mechanics of Structures and Machines, 25(4): 495-526 .
  • Sigmund, O. 2000. "A 99 Line Topology Optimization Code Written in Matlab," Struct. Multidiscpl. Optimization, 21(2): 120-127 .
  • Sigmund, O. 2001. "Design of Multiphysics Actuators using Topology Optimization — Part II: Two Material Structures," Computer Methods in Applied Mechanics and Engineering, 190: 6605-6627 .[CrossRef]
  • Sigmund, O. and Torquato, S. 1997. "Design of Materials with Extreme Thermal Expansion using a Three-phase Topology Optimization Method," J. Mech. Phys. Solids, 46(6): 1037-1067 .
  • Sigmund, O. and Torquato, S. 1999. "Design of Smart Composite Materials using Topology Optimization," Smart Material Structures, 8: 365-379 .[CrossRef]
  • Silva, E. and Kukuchi, N. 1999. "Design of Piezoelectric Transducers using Topology Optimization," Smart Materials and Structures, 8: 350-365 .[CrossRef]
  • Silva, E., Fonseca, J., de Espinosa, F., Crumm, A., G.A.Brady, J.H. and Kikuchi, N. 1999. "Design of Piezocomposite Materials and Piezoelectric Transducers using Topology Optimization — Part I," Archives of Computational Methods in Engng, 6: 117-182 .
  • Silva, E.C.N., Nishiwaki, S. and Kukuchi, N. 2000. "Topology Optimization Design of Flextensional Actuators," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47(3): 657-671 .[CrossRef]
  • Weber, C., Gabbert, U. and Enzmann, M. March 1988. "Simultaneuos Optimization of Actuator Position and Control Parameter for Adaptive Mechanical Structures," In: SPIE Conference on Mathematics and Control in Smart Structures.

Journal of Intelligent Material Systems and Structures, Vol. 15, No. 8, 655-667 (2004)
DOI: 10.1177/1045389X04043944
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J. Drenckhan, A. Lumsdaine, and M. Parsons
Topology Optimization of a Piezoelectric Actuator on an Elastic Beam
Journal of Intelligent Material Systems and Structures, April 1, 2008; 19(4): 445 - 455.
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