Polymer Mechanics

, Volume 1, Issue 3, pp 98–103 | Cite as

A successive approximations method of designing viscoplastic film structures

  • O. F. Shlenskii


The solution of problems in which plasticity and creep have to be taken into account necessitates the formulation of cumber some nonlinear differential equations. Finding a solution (analytical or numerical) of these equations is a complex mathematical problem. In some cases, when more detailed data on the mechanical properties of the material in a complex stress state are available, the solution of such problems can be simplified by making use of the aging theory associated with the Tresca-St. Venant conditions of creep. A numerical solution is obtained in this case with the aid of geometrical conditions and equilibrium equations; the accuracy of the solution is determined by the number of approximations.


Mechanical Property Differential Equation Stress State Approximation Method Equilibrium Equation 
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    S. D. Ponomarev, et al., Strength Calculations in Mechanical Engineering [in Russian], 2, Moscow, 1958.Google Scholar
  2. 2.
    O. F. Shlenskii and L. M. Dubin, Mekh. polim. [Polymer Mechanics], 2, 146, 1965.Google Scholar
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    L. E. Andreeva, Elastic Elements in Instruments [in Russian], Moscow, 1962.Google Scholar
  4. 4.
    S. Timoshenko and S. Woinowsky, Theory of Plates and Shells [Russian translation], Moscow, 1963.Google Scholar

Copyright information

© The Faraday Press, Inc 1966

Authors and Affiliations

  • O. F. Shlenskii
    • 1
  1. 1.Moscow

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