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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 58143, 18 pages

Monotonicity of nonlinear boundary value problems related to deformation theory of plasticity

Applied Mathematical Sciences Research Center and Department of Mathematics, Kocaeli University, Ataturk Bulvari, Izmit, Kocaeli 41300, Turkey

Received 1 March 2005; Accepted 20 June 2005

Copyright © 2006 Alemdar Hasanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study nonlinear boundary value problems arising in the deformation theory of plasticity. These problems include 3D mixed problems related to nonlinear Lame system, elastoplastic bending of an incompressible hardening plate, and elastoplastic torsion of a bar. For all these different problems, we present a general variational approach based on monotone potential operator theory and prove solvability and monotonicity of potentials. The obtained results are illustrated on numerical examples.