Multi-actuated functionally graded piezoelectric micro-tools design: A multiphysics topology optimization approach

Ronny C. Carbonari, Emílio C.N. Silva, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


Micro-tools offer significant promise in a wide range of applications such as cell manipulation, microsurgery, and micro/nanotechnology processes. Such special micro-tools consist of multi-flexible structures actuated by two or more piezoceramic devices that must generate output displacements and forces at different specified points of the domain and at different directions. The micro-tool structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics output displacements. The design of these micro-tools involves minimization of the coupling among movements generated by various piezoceramics. To obtain enhanced micro-tool performance, the concept of multifunctional and functionally graded materials is extended by tailoring elastic and piezoelectric properties of the piezoceramics while simultaneously optimizing the multi-flexible structural configuration using multiphysics topology optimization. The design process considers the influence of piezoceramic property gradation and also its polarization sign. The method is implemented considering continuum material distribution with special interpolation of fictitious densities in the design domain. As examples, designs of a single piezoactuator, an XY nano-positioner actuated by two graded piezoceramics, and a micro-gripper actuated by three graded piezoceramics are considered. The results show that material gradation plays an important role to improve actuator performance, which may also lead to optimal displacements and coupling ratios with reduced amount of piezoelectric material. The present examples are limited to two-dimensional models because many of the applications for such micro-tools are planar devices.

Original languageEnglish (US)
Pages (from-to)301-336
Number of pages36
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
StatePublished - Jan 15 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Functionally graded material (FGM)
  • Micro-electro-mechanical systems (MEMs)
  • Multiphysics
  • Nano-positioners
  • Piezoelectric actuators
  • Topology optimization


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