Abstract
Optimal design of rigid-plastic beams is considered taking account of the post-yield behaviour. The analysis is carried out for the beams loaded by a transverse pressure and axial tension. A problem of optimal design is set up in the parametrical form. The parameters subjected to variation are certain constant quantities, which could specify the optimal distribution of the external loading as well as the cross sectional area of the beam. An unknown constant can serve as the position coordinate of an additional support. Necessary optimality conditions are derived by means of the variational methods of the optimal control theory. An illustrative example is given.
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