Bilevel Approach of a Decomposed Topology Optimization Problem

A. Makrizi; B. Radi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 128-131
  • ISSN: 0973-5348

Abstract

top
In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed on non-overlapping sub-domains. In this paper, we consider the resulting problem as multilevel one and show that it can be written as one level problem

How to cite

top

Makrizi, A., and Radi, B.. Taik, A., ed. "Bilevel Approach of a Decomposed Topology Optimization Problem." Mathematical Modelling of Natural Phenomena 5.7 (2010): 128-131. <http://eudml.org/doc/197713>.

@article{Makrizi2010,
abstract = {In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed on non-overlapping sub-domains. In this paper, we consider the resulting problem as multilevel one and show that it can be written as one level problem},
author = {Makrizi, A., Radi, B.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {topology optimization; domain decomposition method; compliance; multilevel optimization},
language = {eng},
month = {8},
number = {7},
pages = {128-131},
publisher = {EDP Sciences},
title = {Bilevel Approach of a Decomposed Topology Optimization Problem},
url = {http://eudml.org/doc/197713},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Makrizi, A.
AU - Radi, B.
AU - Taik, A.
TI - Bilevel Approach of a Decomposed Topology Optimization Problem
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 128
EP - 131
AB - In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed on non-overlapping sub-domains. In this paper, we consider the resulting problem as multilevel one and show that it can be written as one level problem
LA - eng
KW - topology optimization; domain decomposition method; compliance; multilevel optimization
UR - http://eudml.org/doc/197713
ER -

References

top
  1. A. Makrizi, B. Radi, A. E. Hami. Solution of the topology optimization problem based subdomains method. Applied Mathematical Sciences, 2 (2008), No. 41, 2029–2045. 
  2. A. Makrizi, B. Radi and A. El Hami. Approche multiniveaux pour la résolution de l’optimisation topologique décomposée. Proceedings du premier congrès de la société marocaine de mathématiques appliquées, ENIM, Rabat, 06-08 Février 2008.  
  3. J.F. Bard. Practical bilevel optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht, 1998.  
  4. M.P. Bendsøe, O. Sigmund. Topology optimization, theory, methods and applications. Springer Verlag, 2003.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.