Surface effects on shape and topology optimization of nanostructures

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

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

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
Volume56
Issue number1
DOIs
Publication statusPublished - 2015 Jul 25

Fingerprint

Surface Effects
Topology Optimization
Shape Optimization
Shape optimization
Nanostructures
Topology
Numerical Examples
Cantilever
Process Optimization
Level Set
Aspect Ratio
Computational Methods
Least Squares
Discontinuity
Computational methods
Objective function
Potential energy
Boundary Value Problem
Boundary value problems
Boundary conditions

Keywords

  • 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

Cite this

Nanthakumar, S. S., Valizadeh, N., Park, H. S., & Rabczuk, T. (2015). Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 56(1), 97-112. https://doi.org/10.1007/s00466-015-1159-9

Surface effects on shape and topology optimization of nanostructures. / Nanthakumar, S. S.; Valizadeh, Navid; Park, Harold S.; Rabczuk, Timon.

In: Computational Mechanics, Vol. 56, No. 1, 25.07.2015, p. 97-112.

Research output: Contribution to journalArticle

Nanthakumar, SS, Valizadeh, N, Park, HS & Rabczuk, T 2015, 'Surface effects on shape and topology optimization of nanostructures', Computational Mechanics, vol. 56, no. 1, pp. 97-112. https://doi.org/10.1007/s00466-015-1159-9
Nanthakumar, S. S. ; Valizadeh, Navid ; Park, Harold S. ; Rabczuk, Timon. / Surface effects on shape and topology optimization of nanostructures. In: Computational Mechanics. 2015 ; Vol. 56, No. 1. pp. 97-112.
@article{c01d7567bc83449ab31c4c876c4ff2e2,
title = "Surface effects on shape and topology optimization of nanostructures",
abstract = "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.",
keywords = "Extended finite element method (XFEM), Level set method, Nanomaterials, Shape optimization, Surface effects",
author = "Nanthakumar, {S. S.} and Navid Valizadeh and Park, {Harold S.} and Timon Rabczuk",
year = "2015",
month = "7",
day = "25",
doi = "10.1007/s00466-015-1159-9",
language = "English",
volume = "56",
pages = "97--112",
journal = "Computational Mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "1",

}

TY - JOUR

T1 - Surface effects on shape and topology optimization of nanostructures

AU - Nanthakumar, S. S.

AU - Valizadeh, Navid

AU - Park, Harold S.

AU - Rabczuk, Timon

PY - 2015/7/25

Y1 - 2015/7/25

N2 - 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.

AB - 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.

KW - Extended finite element method (XFEM)

KW - Level set method

KW - Nanomaterials

KW - Shape optimization

KW - Surface effects

UR - http://www.scopus.com/inward/record.url?scp=84931957874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84931957874&partnerID=8YFLogxK

U2 - 10.1007/s00466-015-1159-9

DO - 10.1007/s00466-015-1159-9

M3 - Article

VL - 56

SP - 97

EP - 112

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 1

ER -