Optimal Design of Plates Loaded by Two Opposite Sets of Loads

  • F. G. Shamiev
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Optimal plastic design of plates and shells loaded by a set of unidirectional loads was considered in numerous papers (see review [1, 2]). In deriving solutions, usually the optimality condition of Drucker and Shield [3, 4] was utilized. For a plate subjected to lateral loading it requires a constant rate of dissipation per unit area of the middle surface. However, as it was shown by Mróz [5], this stationarity condition may correspond neither to local nor global minimum in the case of solid plates for which the problem of optimal design requires reformulation in order to achieve meaningful solutions [6].


Optimal Design Circular Plate Lateral Loading Sandwich Plate Stress Regime 
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  1. 1.
    Reitman, M. L, Shapiro, G. S.: Theory of Optimal Design in Structural Mechanics and the Theories of Elasticity and Plasticity (in Russian). Ac. Sci. USSR, Moscow, 1966.Google Scholar
  2. 2.
    Sheu, C. Y., Prager, W.: Recent Developments in Optimal Structural Design. Appl. Mech. Reviews 21, 10, 985–992 (1968).Google Scholar
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    Drucker, D. C., Shield, R. T.: Design for Minimum Weight, Proc. 9th Intern. Congr. Appl. Mech., Brussels, 1956.Google Scholar
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    Drucker, D. C., Shield, R. T.: Bounds on Minimum-Weight Design. Quart. Appl. Math. 15, 269–281 (1957).MATHMathSciNetGoogle Scholar
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    Mróz, Z.: On a Problem of Minimum-Weight Design. Quart. Appl. Math. 19, 127–135 (1961).MATHMathSciNetGoogle Scholar
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    Kozlowski, W., Mróz, Z.: Optimal Design of Solid Plates. Intern. J. Solids Struct. 5, 781–794 (1969).CrossRefGoogle Scholar
  7. 7.
    Onat, E. T., Schumann, W., Shield, R. T.: Design of Circular Plates for Minimum Weight. ZAMP 8, 485–499 (1957).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • F. G. Shamiev
    • 1
  1. 1.Institute of Mathematics and MechanicsBakuAzerbaijan SSR, USSR

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