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Exact analytical theory of topology optimization with some pre-existing members or elements

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Abstract

This note deals with topological optimization of structures in which some members or elements of given cross-section exist prior to design and new members are to be added to the system. Existing members are costless, but new members and additions to the cross-section of existing members have a non-zero cost. The added weight is minimized for given behavioural constraints. The proposed analytical theory is illustrated with examples of least-weight (Michell) trusses having (a) stress or compliance constraints, (b) one loading condition and (c) some pre-existing members. Different permissible stresses in tension and compression are also considered. The proposed theory is also confirmed by finite element (FE)-based numerical solutions.

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Authors and Affiliations

  1. Research Group: Computational Structural Mechanics, Hungarian Academy of Sciences and Budapest University of Technology and Economics, Müegyetem rkp. 3, Kmf. 35, 1521, Budapest, Hungary

    G. I. N. Rozvany, J. Lógó & V. Pomezanski

  2. School of Mechanical Engineering, The University of Leeds, Leeds, LS29JT, UK

    O. M. Querin

Authors
  1. G. I. N. Rozvany
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  2. O. M. Querin
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  3. J. Lógó
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  4. V. Pomezanski
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Correspondence to G. I. N. Rozvany.

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Rozvany, G.I.N., Querin, O.M., Lógó, J. et al. Exact analytical theory of topology optimization with some pre-existing members or elements. Struct Multidisc Optim 31, 373–377 (2006). https://doi.org/10.1007/s00158-005-0594-1

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  • DOI: https://doi.org/10.1007/s00158-005-0594-1

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