A level-set based IGA formulation for topology optimization of flexoelectric materials

Hamid Ghasemi, Harold S. Park, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

291 Citations (Scopus)


This paper presents a design methodology based on a combination of isogeometric analysis (IGA), level set and point wise density mapping techniques for topology optimization of piezoelectric/flexoelectric materials. The fourth order partial differential equations (PDEs) of flexoelectricity, which require at least C1 continuous approximations, are discretized using Non-Uniform Rational B-spline (NURBS). The point wise density mapping technique with consistent derivatives is directly used in the weak form of the governing equations. The boundary of the design domain is implicitly represented by a level set function. The accuracy of the IGA model is confirmed through numerical examples including a cantilever beam under a point load and a truncated pyramid under compression with different electrical boundary conditions. Finally, we provide numerical examples demonstrating the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization.

Original languageEnglish
Pages (from-to)239-258
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2017 Jan 1

Bibliographical note

Funding Information:
The first author gratefully acknowledges the financial support of Ernst Abbe foundation within Nachwuchsförderprogramm. Harold Park acknowledges the support of the Mechanical Engineering Department at Boston University .

Publisher Copyright:
© 2016 Elsevier B.V.


  • Flexoelectricity
  • Isogeometric analysis (IGA)
  • Level set
  • Micro-nanostructure
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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