Applied Mathematics and Mechanics

, Volume 5, Issue 6, pp 1737–1743 | Cite as

Classification of variational principles in elasticity

  • Wei-zang Chien


In this paper, variational principels in elasticity are classified according to the differences in the constraints used in these principles. It is shown in a previous paper [4] that the stress-strain relations are the constraint conditions in all these variational principles, and cannot be removed by the method of linear Lagrange multiplier. The other possible constraints are four of them: (1) equations of equilibrium, (2) strain-displacement relations, (3) boundary conditions of given external forces and (4) boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles. However, for every possible variational principle, either the strain energy density or the complementary energy density may be used. Hence, there are altogether 30 classes of functional of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.


Boundary Condition Mathematical Modeling Energy Density External Force Lagrange Multiplier 
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    Hu Hai-chang, Variational Principles in Elasticity and Their Applications, Science Press, (1981). (in Chinese)Google Scholar
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    Hu Hai-chang, Brief Introduction of Variational Principles in Elasticity, Published by Beijing Society of Mechanics, (Oct. 1982). (in Chinese)Google Scholar
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    Chien Wei-zang, Method of high-order Lagrange Multiplier and generalized variational principles of elasticity with more general forms of functionals, Applied Mathematics and Mechanics, Vol. 4 (2), (1983).Google Scholar
  4. (4).
    Chien Wei-zang, Further study of generalized variational principles in elasticity, Discussion with Mr. Hu on the problem of equivalent principle, Acta Mechanics Sinica, Vol. 15(1983), No. 4, 335–340. (in Chinese)Google Scholar

Copyright information

© HUST Press 1984

Authors and Affiliations

  • Wei-zang Chien
    • 1
  1. 1.Shanghai University of TechnologyShanghai

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