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An approach to the optimization of the thin-walled cantilever open section
beams subjected to thå bending and to the constrained torsion is
considered. The problem is reduced to the determination of minimum mass,
i.e. minimum cross-sectional area of structural thin-walled I-beam and
channel-section beam elements for given loads, material and geometrical
characteristics. The area of the cross-section is assumed to be the
objective function. The stress constraints are introduced. Applying the
Lagrange multiplier method, the equations, whose solutions represent the
optimal values of the ratios of the parts of the chosen cross-section, are
formed. The obtained results are used for numerical calculation. |
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