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Modelling and numerical approach to a class of metal‐forming problems—Quasi‐steady case
Author(s) -
Angelov T. A.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1441
Subject(s) - uniqueness , mathematics , variational inequality , finite element method , nonlinear system , convergence (economics) , mathematical analysis , compressibility , rate of convergence , stiffness , mechanics , key (lock) , structural engineering , physics , computer science , engineering , computer security , quantum mechanics , economics , economic growth
A class of quasi‐steady metal‐forming problems, with rigid‐plastic, incompressible, strain and strain‐rate dependent material model and with unilateral frictionless and nonlinear, nonlocal Coulomb's frictional contact conditions is considered. A coupled variational formulation, constituted of a variational inequality, with nonlinear and nondifferentiable terms, and a strain evolution equation, is derived and under a restriction on the material characteristics and using a variable stiffness parameters method with time retardation, existence, uniqueness and convergence results are obtained and presented. An algorithm, combining this method and the finite element method, is proposed and applied for solving an example strip drawing problem. Copyright © 2011 John Wiley & Sons, Ltd.