Acta Mechanica Sinica

, Volume 1, Issue 2, pp 138–146 | Cite as

The combined energy variational principles in linear elasticity

  • Xie Dingyi
Article
  • 7 Downloads

Abstract

In this paper, a new kind of mixed energy variational principles in linear elasticity—the combined energy variational principles is presented. First, we define the conjugate body of an elastic body, which is obtained by changing the boundary conditions of the elastic body. Next, we decompose the conjugate body into two component-states, construct functionals of potential energy and complementary energy, respectively, for the component-states and define the additional hybrid energy between the component-states. Thus the functionals of combined energy can be constructed. Three typical combined energy variational principles are demonstrated and the other forms of combined energy variational principles are given. The application of the proposed principles to the calculation of thin plates with complicated boundaries is shown.

Key Words

conjugate body of an elastic body conjugate state component-state admissible combined state variational principles elasticity 

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References

  1. [1]
    Hu, H. C., Variational Principles in Elasticity and Its Application, Science Press, Beijing, China (1981), 380–388 (in Chinese).Google Scholar
  2. [2]
    Washizu, K., Variational Methods in Elasticity and Plasticity, Pergamon Press, Sccond edition (1975), Appendix I.Google Scholar
  3. [3]
    Darkov, A., Structural Mechanics, Mir Publishers, Moscow (1983), 462–463.Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1985

Authors and Affiliations

  • Xie Dingyi
    • 1
  1. 1.Wuhan Institute of Hydraulic and Electric EngineeringWuhanChina

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