Variational Approach to Static and Dynamic Elasticity Problems

  • Georgy V. Kostin
  • Vasily V. Saurin
Chapter

Abstract

The integrodifferential approach incorporated in variational technique for static and dynamic problems of the linear theory of elasticity is considered. A families of statical and dynamical variational principles, in which displacement, stress, and momentum fields are varied, is proposed. It is shown that the Hamilton principle and its complementary principle for the dynamical problems of linear elasticity follow out the variational formulation proposed. A regular numerical algorithm of constrained minimization for the initial-boundary value problem is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. As an example, a problem of lateral controlled motions of a 3D rectilinear elastic prism with a rectangular cross section is investigated.

Keywords

Linear Elasticity Elastic Foundation Complementary Energy Hamilton Principle Elastic Modulus Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • Georgy V. Kostin
    • 1
  • Vasily V. Saurin
    • 1
  1. 1.Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia

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