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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2003, Volume 44, Issue 3, Pages 124–135
(Mi pmtf2505)
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This article is cited in 5 scientific papers (total in 5 papers)
Formulation and solution of dynamic problems of elastic rod systems subjected to boundary conditions described by multivalued relations
I. N. Vasserman, I. N. Shardakov Institute of Mechanics of Continuous Media, Ural Division, Russian Academy of Sciences, Perm', 614013
Abstract:
The dynamic behavior of rod systems under the action of external force factors described by multivalued (subdifferential) relations is studied. The mathematical formulation of the problem is given in the form of a dynamic quasivariational inequality. With the use of the Newmark difference scheme, successive approximations, and finite-element discretization, the problem is reduced to minimization of a convex nonsmooth finite-dimensional functional with respect to velocities at each time step. Introduction of auxiliary variables by the method of a modified Lagrangian reduces the problem of minimization of this functional to a sequence of smooth problems of nonlinear programming. The algorithm is verified using the numerical solution for a problem with one degree of freedom. The algorithm proposed is used to calculate the rods of deep-well pumps.
Keywords:
dynamic problems, rod systems, finite-element discretization.
Received: 30.01.2002 Accepted: 18.11.2002
Citation:
I. N. Vasserman, I. N. Shardakov, “Formulation and solution of dynamic problems of elastic rod systems subjected to boundary conditions described by multivalued relations”, Prikl. Mekh. Tekh. Fiz., 44:3 (2003), 124–135; J. Appl. Mech. Tech. Phys., 44:3 (2003), 406–414
Linking options:
https://www.mathnet.ru/eng/pmtf2505 https://www.mathnet.ru/eng/pmtf/v44/i3/p124
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