Topology optimization applied to the design of functionally graded piezoelectric bimorph

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Functionally Graded Materials (FGMs) possess continuously graded material properties and are characterized by spatially varying microstructures. The smooth variation of properties may offer advantages such as reduction of stress concentration and increased bonding strength. Recently, this concept has been explored in piezoelectric materials to improve properties and to increase the lifetime of bimorph piezoelectric actuators. Usually, elastic, piezoelectric, and dielectric properties are graded along the thickness of a piezoceramic FGM. Thus the gradation law of piezoceramic properties can influence the performance of piezoactuators. In this work, topology optimization has been applied to find the optimum gradation variation in piezoceramic FGMs to improve actuator performance measured in terms of output displacements. A bimorph type actuator design is considered. Accordingly, the optimization problem is posed as finding the optimized gradation variation of piezoelectric properties that maximizes output displacement or output force in the tip of bimorph actuator. The optimization algorithm combines the finite element method with sequential linear programming (SLP). The finite element method applied is based on the graded finite element concept where the properties change smoothly inside the element. This approach provides a continuum approximation of material distribution (CAMD), which is appropriate to model FGMs. The alternative FGM modelling using traditional FEM formulation and discretizing the FGM into layers gives a discontinuous stress distribution, which is not compatible with FGM behavior. The present results consider gradation between two different piezoceramic properties and consider two-dimensional models with plane stress assumption.

Original languageEnglish (US)
Title of host publicationMultiscale and Functionally Graded Materials - Proceedings of the International Conference, FGM IX
Number of pages6
StatePublished - 2008
Externally publishedYes
Event9th International Conference on Multiscale and Functionally Graded Materials, FGM IX - Oahu Island, HI, United States
Duration: Oct 15 2006Oct 18 2006

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference9th International Conference on Multiscale and Functionally Graded Materials, FGM IX
Country/TerritoryUnited States
CityOahu Island, HI

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • FGM
  • Micromachines
  • Nanopositioners
  • Piezoelectric actuators
  • Topology optimization


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