Structural and Multidisciplinary Optimization

, Volume 59, Issue 4, pp 1125–1141 | Cite as

An optimality criteria-based method for the simultaneous optimization of the structural design and placement of piezoelectric actuators

  • Alexandre MolterEmail author
  • Lucas dos Santos Fernandez
  • Jonathan Brum Lauz
Research Paper


This work provides an optimality criteria-based method for the simultaneous optimization of the structural design and optimal placement of piezoelectric actuators for statically loaded structures. The goal of the topology optimization is to find the optimal distribution of the structural and piezoelectric materials in the compliance minimization context with a volume constraint for each material. All expressions used in the implementation of the resulting algorithm are developed in detail. Some numerical complications inherent to the type of problem we are dealing with are discussed and a numerical procedure is proposed for each one. Results are shown for two-dimensional beams through four numerical examples.


Topology optimization Actuator placement Piezoelectric material Statically loaded structures Optimality criteria-based method 



The authors are grateful to Fabrício Bandeira Cabral and Leslie Darien Pérez Fernández for their contributions to the improvement of this work.

Funding information

The second and third authors received financial support from the CNPq (Brazilian Research Council) and CAPES (Brazilian Higher Education Staff Training Agency), respectively.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexandre Molter
    • 1
    Email author
  • Lucas dos Santos Fernandez
    • 2
  • Jonathan Brum Lauz
    • 3
  1. 1.Department of Mathematics and StatisticsFederal University of PelotasPelotasBrazil
  2. 2.National Laboratory for Scientific ComputingLNCC/MCTICPetrópolisBrazil
  3. 3.Federal University of PelotasPelotasBrazil

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