| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
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