Ukrainian Mathematical Journal

, Volume 43, Issue 2, pp 134–137 | Cite as

Variational formulations of the static problem of elasticity theory under specified external forces

  • I. N. Molchanov
  • E. F. Galba


The initial-value problem is considered for the equations of elastic equilibrium of moving bodies when stresses are specified on the surface of the body. Two variational problems that may be solved in unique fashion over the entire space are formulated for this problem, which is known to possess a unique solution in a subspace.


Unique Solution External Force Static Problem Variational Problem Variational Formulation 
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Literature cited

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    S. G. Mikhlin, Problem of Minimizing a Quadratic Functional [in Russian], Gostekhteoretizdat, Moscow-Leningrad (1952).Google Scholar
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    S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).Google Scholar
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    G. Dewey and J.-L. Lyons, Inequalities in Mechanics and Physics [Russian translation], Nauka, Moscow (1980).Google Scholar
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    G. Fiker, Existence Theorems in the Theory of Elasticity [Russian translation], Mir, Moscow (1974).Google Scholar
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    I. N. Molchanov and E. F. Galba, “On finite element methods for the Neumann problem,” Numer. Math.,46, No. 4, 587–598 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • I. N. Molchanov
    • 1
  • E. F. Galba
    • 1
  1. 1.Cybernetics InstituteAcademy of Sciences of the Ukrainian SSRKiev

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