Open AccessBimodal optimization with constraints: Critical value of the constraint and post-critical configurations
Author(s) -
Milica Atanacković,
P Alexander Seyraniany
Publication year - 2011
Publication title -
theoretical and applied mechanics/theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam1102107a
Subject(s) - constraint (computer aided design) , critical point (mathematics) , mathematics , value (mathematics) , shape optimization , mathematical optimization , pontryagin's minimum principle , mathematical analysis , geometry , physics , statistics , optimal control , finite element method , thermodynamics
By using a method based on Pontryagin’s principle, formulated in [13], and [14] we study optimal shape of an elastic column with constraints on the minimal value of the cross-sectional area. We determine the critical value of the minimal cross-sectional area separating bi from unimodal optimization. Also we study the post-critical shape of optimally shaped rod and find the preferred configuration of the bifurcating solutions from the point of view of minimal total energy