Structural and Multidisciplinary Optimization

, Volume 43, Issue 3, pp 405–417 | Cite as

On the effect of self-penalization of piezoelectric composites in topology optimization

  • Fabian WeinEmail author
  • Manfred Kaltenbacher
  • Barbara Kaltenbacher
  • Günter Leugering
  • Eberhard Bänsch
  • Fabian Schury
Research Paper


We investigate the occurrence of self-penalization in topology optimization problems for piezoceramic-mechanical composites. Our main goal is to give physical interpretations for this phenomenon, i.e., to study the question why for various problems intermediate material values are not optimal in the absence of explicit penalization of the pseudo densities. In order to investigate this effect numerical experiments for several static and/or dynamic actuator and sensor objective functions are performed and their respective results are compared. The objective functions are mean transduction, displacement, sound power, electric potential, electric energy, energy conversion and electric power.


SIMP Topology optimization Piezoelectricity Self-penalization 



The authors gratefully acknowledge the funding of the German Research Council (DFG) by the DFG Priority Program 1253 ‘Optimization with Partial Differential Equations’ through grants DFG06-381 and partially support within the framework of its ‘Excellence Initiative’ for the Cluster of Excellence ‘Engineering of Advanced Materials’ at the University of Erlangen-Nuremberg.

The authors would like to thank the anonymous reviewers for the helpful comments.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Fabian Wein
    • 1
    Email author
  • Manfred Kaltenbacher
    • 2
  • Barbara Kaltenbacher
    • 3
  • Günter Leugering
    • 1
  • Eberhard Bänsch
    • 1
  • Fabian Schury
    • 1
  1. 1.Department of MathematicsUniversity of Erlangen-NurembergErlangenGermany
  2. 2.Department of Applied MechatronicsAlps-Adriatic University KlagenfurtKlagenfurtAustria
  3. 3.Institute of Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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