Applying functional principal components to structural topology optimization

Applying functional principal components to structural topology optimization Structural topology optimization aims to enhance the mechanical performance of a structure while satisfying some functional constraints. Nearly all approaches proposed in the literature are iterative, and the optimal solution is found by repeatedly solving a finite element analysis (FEA). It is thus clear that the bottleneck is the high computational effort, as these approaches require solving the FEA a large number of times. In this work, we address the need for reducing the computational time by proposing a reduced basis method that relies on functional principal component analysis (FPCA). The methodology has been validated considering a simulated annealing approach for compliance minimization in 2 classical variable thickness problems. Results show the capability of FPCA to provide good results while reducing the computational times, ie, the computational time for an FEA is about one order of magnitude lower in the reduced FPCA space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

Applying functional principal components to structural topology optimization

20 pages
Read Article

Loading next page...
 
/lp/wiley/applying-functional-principal-components-to-structural-topology-ZZ9id8jIzo
Publisher
Wiley
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/nme.5801
Publisher site
See Article on Publisher Site

Abstract

Structural topology optimization aims to enhance the mechanical performance of a structure while satisfying some functional constraints. Nearly all approaches proposed in the literature are iterative, and the optimal solution is found by repeatedly solving a finite element analysis (FEA). It is thus clear that the bottleneck is the high computational effort, as these approaches require solving the FEA a large number of times. In this work, we address the need for reducing the computational time by proposing a reduced basis method that relies on functional principal component analysis (FPCA). The methodology has been validated considering a simulated annealing approach for compliance minimization in 2 classical variable thickness problems. Results show the capability of FPCA to provide good results while reducing the computational times, ie, the computational time for an FEA is about one order of magnitude lower in the reduced FPCA space.

Journal

International Journal for Numerical Methods in Engineering – Wiley

Published: Jan 13, 2018

Keywords: ; ;

References

  • Topology Optimization: Theory, Methods, and Applications
    Bendsøe, M; Sigmund, O
  • Level‐set methods for structural topology optimization: a review
    Dijk, NP; Maute, K; Langelaar, M; Keulen, F
  • Homogenization and Structural Topology Optimization: Theory, Practice and Software
    Hassani, B; Hinton, E
  • A further review of ESO type methods for topology optimization
    Huang, X; Xie, YM
  • Topology Optimization in Structural and Continuum Mechanics
    Rozvany, GIN; Lewiński, T
  • Shape and Layout Optimization of Structural Systems and Optimality Criteria Methods
    Rozvany, GIN
  • Topology optimization approaches
    Sigmund, O; Maute, K
  • Large‐scale topology optimization in 3D using parallel computing
    Borrvall, T; Petersson, J
  • On the usefulness of non‐gradient approaches in topology optimization
    Sigmund, O
  • Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components
    Bianchini, I; Argiento, R; Auricchio, F; Lanzarone, E
  • A critical review of established methods of structural topology optimization
    Rozvany, GIN
  • Bridging topology optimization and additive manufacturing
    Zegard, T; Paulino, GH
  • Optimal shape design as a material distribution problem
    Bendsøe, MP
  • Morphology‐based black and white filters for topology optimization
    Sigmund, O
  • The COC algorithm, Part II: topological, geometrical and generalized shape optimization
    Zhou, M; Rozvany, GIN
  • A finite element analysis of optimal variable thickness sheets
    Petersson, J
  • An optimal design problem with perimeter penalization
    Ambrosio, L; Buttazzo, G
  • Generating optimal topologies in structural design using a homogenization method
    Bendsøe, MP; Kikuchi, N
  • Filters in topology optimization
    Bourdin, B
  • Topology optimization of non‐linear elastic structures and compliant mechanisms
    Bruns, TE; Tortorelli, DA
  • A new approach to variable‐topology shape design using a constraint on perimeter
    Haber, R; Jog, C; Bendsøe, MP
  • On the design of compliant mechanisms using topology optimization
    Sigmund, O
  • Volume preserving nonlinear density filter based on heaviside functions
    Xu, S; Cai, Y; Cheng, G
  • Stochastic Finite Elements: A Spectral Approach
    Ghanem, RG; Spanos, PD
  • A short review on model order reduction based on proper generalized decomposition
    Chinesta, F; Ladeveze, P; Cueto, E
  • Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems
    Nouy, A
  • A non‐intrusive proper generalized decomposition scheme with application in biomechanics
    Zou, X; Conti, M; Diez, P; Auricchio, F
  • The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer
    Chinesta, F; Keunings, R; Leygue, A
  • On the capabilities of the polynomial chaos expansion method within SFE analysis – an overview
    Panayirci, H; Schuëller, GI
  • A polynomial chaos expansion based reliability method for linear random structures
    Yu, H; Gillot, F; Ichchou, M
  • Polynomial chaos expansion for subsurface flows with uncertain soil parameters
    Sochala, P; Le Maître, O
  • Material uncertainty effect on vibration control of smart composite plate using polynomial chaos expansion
    Umesh, K; Ganguli, R
  • Applied Multivariate Statistical Analysis
    Johnson, RA; Wichern, DW
  • Functional Data Analysis
    Ramsay, J; Silverman, BW
  • The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
    Kerschen, G; Golinval, JC; Vakakis, AF; Bergman, LA
  • Turbulence and the dynamics of coherent structures. Part 2: symmetries and transformations
    Sirovich, L
  • A model reduction approach for real‐time part deformation with nonlinear mechanical behavior
    Dulong, JL; Druesne, F; Villon, P
  • Proper orthogonal decomposition for model reduction of a vibroimpact system
    Ritto, T; Buezas, F; Sampaio, R
  • Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
    Florentin, E; Díez, P
  • Inference for Functional Data with Applications
    Horváth, L; Kokoszka, P
  • Handbook of Metaheuristics
    Henderson, D; Jacobson, SH; Johnson, AW
  • The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
    Hughes, TJ
  • The Finite Element Method: Its Basis and Fundamentals
    Zienkiewicz, O; Taylor, Z; Zhu, J
  • A 99 line topology optimization code written in Matlab
    Sigmund, O

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial