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Variational analysis in dynamical problems of linear elasticity
Author(s) -
Kostin Georgy,
Saurin Vasily
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810301
Subject(s) - mathematics , boundary value problem , elasticity (physics) , linear elasticity , finite element method , algebraic number , mathematical analysis , variational principle , algebraic equation , prism , numerical analysis , nonlinear system , physics , quantum mechanics , thermodynamics , optics
Abstract The initial–boundary value problems in the linear theory of elasticity is considered. Based on the method of integrodifferential relations (MIDR) two dynamical variational principles is proposed and discussed. It is shown that the Hamilton principle as well as the corresponding complementary principle stated for dynamic boundary value problems follow out the variational formulations proposed. To minimize the nonnegative functional under algebraic and differential constraints a regular finite element algorithm is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. A 3D problem of lateral motions of a rectilinear elastic prism with a rectangular cross section are considered. The numerical results are presented and discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)