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Symmetry, Optima and Bifurcations in Structural Design

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Abstract

Motivated by optimization problems in structural engineering, we study the critical points of symmetric, ‘reflected', one-parameter family of potentials U(p, x) = max (f(p,x), f(p, −x)), yielding modest generalizations of classical bifurcations, predicted by elementary catastrophe theory. One such generalization is the ‘five-branch pitchfork’, where the symmetric optimum persists beyond the critical parameter value. Our theory may help to explain why symmetrical structures are often optimal.

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Authors and Affiliations

  1. Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Müegyeten RKP. 3, K242 H-1111, Budapest, Hungary

    Péter László Várkonyi & Gábor Domokos

  2. Computer and Automation Research Institute of the Hungarian Academy of Sciences, Kende u. 13-17, H-1111, Budapest, Hungary

    Péter László Várkonyi

  3. Center for Applied Mathematics and Computational Physics, Budapest University of Technology and Economics, Budapest, Hungary

    Gábor Domokos

Authors
  1. Péter László Várkonyi
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  2. Gábor Domokos
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Correspondence to Gábor Domokos.

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Várkonyi, P.L., Domokos, G. Symmetry, Optima and Bifurcations in Structural Design. Nonlinear Dyn 43, 47–58 (2006). https://doi.org/10.1007/s11071-006-0749-7

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  • DOI: https://doi.org/10.1007/s11071-006-0749-7

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