Abstract
We study an inverse elastoplastic problem of determining the residual stresses, the plasticity zone, and the external loads for a plate for known residual deflections which occur after removal of these loads and elastic unloading. Assuming that the deformation theory of plasticity is valid at the active stage of deformation, we prove the theorem of unique solution. An iterative method of solution is proposed and a variational formulation of the problem is given. Some simple examples are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Yu. Tsvelodub,Stability Postulate and Its Applications to the Theory of Creep of Metallic Materials [in Russian], Lavrent’ev Institute of Hydrodynamics, Novosibirsk (1991).
I. Yu. Tsvelodub, “Inverse problems of variation in the shape of inelastic plates,”Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 96–106 (1996).
I. A. Banshchikova and I. Yu. Tsvelodub, “One class of inverse problems of variation in shape of viscoelastic plates,”Prikl. Mekh. Tekh. Fiz.,37, No. 6, 122–131 (1996).
V. V. Sokolovskii,Theory of Plasticity [in Russian], Vysshaya Shkola, Moscow (1969).
E. Beckenbach and R. Bellman,Inequalities, Springer-Verlag, Berlin (1971).
Additional information
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 186–194, July–August, 1999.
Rights and permissions
About this article
Cite this article
Tsvelodub, I.Y. An inverse elastoplastic problem for plates. J Appl Mech Tech Phys 40, 719–726 (1999). https://doi.org/10.1007/BF02468449
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02468449