Loading [MathJax]/jax/output/SVG/jax.js
Search Advanced

Networks and Heterogeneous Media

2007, Volume 2, Issue 4: 761-777. doi: 10.3934/nhm.2007.2.761
Previous Article Next Article

Asymptotical compliance optimization for connected networks

  • 1.
    Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa
  • 2.
    Université Paris Dauphine, Laboratoire CEREMADE, UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16
  • Received: 01 June 2007 Revised: 01 July 2007

  • Primary: 49J45, Secondary: 49Q10,74P05.

  • We consider the problem of the optimal location of a Dirichlet region in a two-dimensional domain Ω subject to a force f in order to minimize the compliance of the configuration. The class of admissible Dirichlet regions among which we look for the optimum consists of all one-dimensional connected sets (networks) of a given length L. Then we let L tend to infinity and look for the Γ-limit of suitably rescaled functionals, in order to identify the asymptotical distribution of the optimal networks. The asymptotically optimal shapes are discussed as well and links with average distance problems are provided.

    Citation: Giuseppe Buttazzo, Filippo Santambrogio. Asymptotical compliance optimization for connected networks[J]. Networks and Heterogeneous Media, 2007, 2(4): 761-777. doi: 10.3934/nhm.2007.2.761

    Related Papers:

  • We consider the problem of the optimal location of a Dirichlet region in a two-dimensional domain Ω subject to a force f in order to minimize the compliance of the configuration. The class of admissible Dirichlet regions among which we look for the optimum consists of all one-dimensional connected sets (networks) of a given length L. Then we let L tend to infinity and look for the Γ-limit of suitably rescaled functionals, in order to identify the asymptotical distribution of the optimal networks. The asymptotically optimal shapes are discussed as well and links with average distance problems are provided.


  • This article has been cited by:

    1. Laura Abatangelo, Susanna Terracini, Harmonic functions in union of chambers, 2015, 35, 1078-0947, 5609, 10.3934/dcds.2015.35.5609
    2. Matthieu Bonnivard, Antoine Lemenant, Filippo Santambrogio, Approximation of Length Minimization Problems Among Compact Connected Sets, 2015, 47, 0036-1410, 1489, 10.1137/14096061X
    3. Davide Zucco, Dirichlet conditions in Poincaré–Sobolev inequalities: the sub-homogeneous case, 2019, 58, 0944-2669, 10.1007/s00526-019-1547-7
    4. Paolo Tilli, Compliance estimates for two-dimensional problems with Dirichlet region of prescribed length, 2012, 7, 1556-181X, 127, 10.3934/nhm.2012.7.127
    5. Al-hassem Nayam, Asymptotics of an optimal compliance-network problem, 2013, 8, 1556-181X, 573, 10.3934/nhm.2013.8.573
    6. Bohdan Bulanyi, Partial regularity for the optimal p-compliance problem with length penalization, 2022, 61, 0944-2669, 10.1007/s00526-021-02073-8
    7. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
    8. Antoine Lemenant, A selective review on Mumford–Shah minimizers, 2016, 9, 1972-6724, 69, 10.1007/s40574-016-0056-2
    9. Paolo Tilli, Davide Zucco, Where Best to Place a Dirichlet Condition in an Anisotropic Membrane?, 2015, 47, 0036-1410, 2699, 10.1137/140999402
    10. A. Lemenant, A presentation of the average distance minimizing problem, 2012, 181, 1072-3374, 820, 10.1007/s10958-012-0717-3
    11. Bohdan Bulanyi, On the importance of the connectedness assumption in the statement of the optimal p-compliance problem, 2021, 499, 0022247X, 125064, 10.1016/j.jmaa.2021.125064
    12. Laura Abatangelo, Veronica Felli, Susanna Terracini, On the sharp effect of attaching a thin handle on the spectral rate of convergence, 2014, 266, 00221236, 3632, 10.1016/j.jfa.2013.11.019
    13. Al-hassem Nayam, Constant in two-dimensional $p$-compliance-network problem, 2014, 9, 1556-181X, 161, 10.3934/nhm.2014.9.161
    14. Antonin Chambolle, Jimmy Lamboley, Antoine Lemenant, Eugene Stepanov, Regularity for the Optimal Compliance Problem with Length Penalization, 2017, 49, 0036-1410, 1166, 10.1137/16M1070578
    15. Paolo Tilli, Davide Zucco, Asymptotics of the First Laplace Eigenvalue with Dirichlet Regions of Prescribed Length, 2013, 45, 0036-1410, 3266, 10.1137/130916825
    16. Antoine Lemenant, Edoardo Mainini, On convex sets that minimize the average distance, 2012, 18, 1292-8119, 1049, 10.1051/cocv/2011190
    17. Bohdan Bulanyi, Antoine Lemenant, Regularity for the planar optimalp-compliance problem, 2021, 27, 1292-8119, 35, 10.1051/cocv/2021035
    18. Filippo Santambrogio, 2023, Chapter 6, 978-3-031-45035-8, 243, 10.1007/978-3-031-45036-5_6
    19. Filippo Santambrogio, 2023, Chapter 7, 978-3-031-45035-8, 287, 10.1007/978-3-031-45036-5_7
  • Reader Comments
  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(4599) PDF downloads(70) Cited by(19)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog