Symmetry, optima and bifurcations in structural design

Péter László Várkonyi, Gábor Domokos

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)47-58
Number of pages12
JournalNonlinear Dynamics
Volume43
Issue number1-2
DOIs
Publication statusPublished - Jan 1 2006

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Keywords

  • Bifurcation
  • Catastrophe theory
  • Reflection symmetry
  • Structural optimization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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