International Applied Mechanics

, Volume 43, Issue 5, pp 519–525 | Cite as

Mixed variational principle in elasticity theory and canonical systems of equations

  • N. P. Semenyuk
  • V. M. Trach
  • N. B. Zhukova


The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko theory of plates


variational principle theory of elasticity stationarity condition canonical system of equations Timoshenko theory of plates 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • N. P. Semenyuk
    • 1
  • V. M. Trach
    • 1
  • N. B. Zhukova
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyiv

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