Plane boundary value problems are formulated in terms of an elastic-plastic stress function and the plastic strains. The governing relation is a non-homogeneous biharmonic equation. It is applicable to the total or deformation theories and to the incremental theories. Sample problems illustrate the practicality of the method.
Get full access to this article
View all access options for this article.
References
1.
MendelsonA.MansonS. S.‘Practical solution of plastic deformation problems in the elastic-plastic range’, NACA TN-4088, also NASA TR-28, Sept. 1957.
2.
DavisE. A.‘Extension of iteration method for determining strain distributions to the uniformly stressed plate with a hole’, J. appl. Mech., 30, Trans. Am. Soc. mech. Engrs 1963 85 (Series E), 210.
3.
PlatusD. L.‘The plane-stress problem for a doubly connected region in which the medium undergoes elastic and creep deformation’, J. appl. Mech., 31, Trans. Am. Soc. mech. Engrs 1964 86 (Series E), 54.
4.
TubaI. S.‘Elastic-plastic stress and strain concentration’, Ph.D. Dissertation, University of Pittsburgh, Spring 1964.
5.
RobertsE.MendelsonA.‘Analysis of plastic thermal stresses and strains in finite thin plate of strain-hardening material’, NASA TN-D-2206, Oct. 1964.
6.
SouthwellR. V.Relaxation methods in theoretical physics1956 (Clarendon Press, Oxford).
7.
GriffinD. S.VargaR. S.‘Numerical solution of plane elasticity problems’, J. Soc. Ind. Appl. Maths, 196311, 1046.
