Symmetry, Optima and Bifurcations in Structural Design |
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| Authors: | Péter László Várkonyi Gábor Domokos |
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| Affiliation: | (1) Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Müegyeten RKP. 3, K242 H-1111 Budapest, Hungary;(2) Computer and Automation Research Institute of the Hungarian Academy of Sciences, Kende u. 13-17, H-1111 Budapest, Hungary;(3) Center for Applied Mathematics and Computational Physics, Budapest University of Technology and Economics, Budapest, Hungary |
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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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| Keywords: | bifurcation catastrophe theory reflection symmetry structural optimization |
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