Abstract
Here considered are torsioned prismatic bars with a transverse, continuous plastic nonhomo-geneity. On the basis of the Neustadt-Halkin method, the necessary conditions for such a distribution of this nonhomogeneity, which offers a maximum limiting load capacity were obtained. A straightforward graphical interpretation of these conditions is given, discussed in detail upon the example of a prismatic bar with a square cross-section. The solutions are also presented for bars with septagonal, circular and elliptical cross-sections.References
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2. H. HALKIN, L. W. NEUSTADT, General necessary conditions for optimalization problem, Proc. Nat. Acad. Sci., 4, 1966.
3. L. W. NEUSTADT, An abstract variational theory with applications to abroad class of optimalization problems. I. General theory, SJAM, J. Contral, 1, 1967.
4. K. MAKOWSKI, Współczesne metody uogólnionego rachunku wariacyjnego i regularności, Prace
Instytutu Automatyki PAN, zeszyt 72, 1968.
5. L. W. NEUSTADT, An abstract variational theory with applications to a broad class of optymalization
problem, II. Applications, SJAM, J. Contral, 1, 1967.
6. J. RYCHLEWSKI, Plastic torsion of a bar with jump nonhomogeneity, Acta Mechanica, 1, 1 (1965).
7. A. DEBSKA, A, MIODUCHOWSKI, Sprężysto-plastyczne skręcanie prętów skokowo niejednorodnych, MTT - Moskwa (w druku).
8. P.G. HODGE, Jr. Elastic-plastic torsion as a problem in non-linear programming, Int. J. Solids Structures, 3, (1967), 989 - 999.
9. H. В. Бащгаук, Упруго-пластическое кручение стержней, MTT, 1, 1967.
