Surface effects on shape and topology optimization of nanostructures

S. S. Nanthakumar, Navid Valizadeh, Harold S. Park, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


We present a computational method for the optimization of nanostructures, where our specific interest is in capturing and elucidating surface stress and surface elastic effects on the optimal nanodesign. XFEM is used to solve the nanomechanical boundary value problem, which involves a discontinuity in the strain field and the presence of surface effects along the interface. The boundary of the nano-structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. We present results of optimal topologies of a nanobeam subject to cantilever and fixed boundary conditions. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams.

Original languageEnglish
Pages (from-to)97-112
Number of pages16
JournalComputational Mechanics
Issue number1
Publication statusPublished - 2015 Jul 25


  • Extended finite element method (XFEM)
  • Level set method
  • Nanomaterials
  • Shape optimization
  • Surface effects

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mathematics


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