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An Iterative Method for Elastic-Plastic Stress Analysis

  • T. Miyoshi
  • K. Kaminishi
  • S. Kawano
  • S. Shimizu
Conference paper

Abstract

Most numerical methods to solve incremental problems in elastic-plastic stress analysis are based on the use of so called the “elastic-plastic matrix”, which is derived from a backward or a forward finite difference approximation of constitutive equations. This kind of approximation, however, has a difficulty in satisfying some conditions which characterize the original problem, and this causes some question on the accuracy of those methods. As well known, the normality of plastic strain increments is a remarkable condition imposed on the solution of plasticity problem. Also, the conditions that stress point must move on yield surface during plastic deformation and that plastic strain increments relate to hardening parameters in a definite rule are essential in the usual formulation of plasticity problem. However, the second or the third condition is, unfortunately, not satisfied in many approximate methods. It is because those conditions are not simultaneously satisfied by a simple finite difference approximation of constitutive equations.

Keywords

Plastic Zone Yield Surface Rectangular Plate Finite Difference Approximation Plastic Strain Increment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    T. Miyoshi: Foundations of the numerical analysis of plasticity, North-Holland Mathematics studies 107, Kinokuniya/North-Holland, 1985.Google Scholar
  2. [2]
    T. Miyoshi: A new iterative method for solving quasi-static problems of plasticity (to appear).Google Scholar
  3. [3]
    Y. Yamada, N.Yoshimura, T. Sakurai: Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method, Int.J.Mech.Sci. 10 (1968) 343–354.MATHCrossRefGoogle Scholar
  4. [4]
    O. C. Zienkiewicz: The finite element method, 3rd ed., McGRAW-HILL, 1977.MATHGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • T. Miyoshi
    • 1
  • K. Kaminishi
    • 1
  • S. Kawano
    • 1
  • S. Shimizu
    • 1
  1. 1.Faculty of EngineeringYamaguchi UniversityUbe, Yamaguchi, 755Japan

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