By the semi-inverse method of establishing variational principles, the Hellinger-Reissner principle can be obtained straightforwardly from energy trial-functionals without using Lagrange multipliers, and a family of generalized Hellinger-Reissner principles with an arbitrary constant are also obtained, some of which are unknown to us at the present time. The present theory provides a straightforward tool to search for various variational principles directly from governing equations and boundary conditions. [S0021-8936(00)00702-9]
Issue Section:Technical Papers
Keywords:inverse problems, elasticity
Generalized Variational Principle in Elasticity,”
Eng. Mech. Civil Eng.,
Washizu, K., 1982, Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford.
He, J. H., 1997, Involutory Transformation Without Using Lagrange Multipliers and Its Applications to Establishing Variational Principles With Multi-Variables in Thin Plate Bending Problems, Modern Mechanics and Advances in Science and Technology, F. G. Zhuang, ed., Qinghua University Press, Beijing, pp. 1417–1418 (in Chinese).
Liu, G. L., 1990, “A System Approach to the Search and Transformation for Variational Principles in Fluid Mechanics With Emphasis on Inverse and Hybrid Problems,” Proc. 1st Int. Symp. Aerotheromdynamics of Internal Flow, pp. 128–135.
Semi-inverse Method of Establishing Generalized Variational Principles for Fluid Mechanics With Emphasis on Turbomachinery Aerodynamics,”
Int. J. Turbo Jet Eng.,
Semi-Inverse Method: A New Approach to Establishing Variational Principles in Fluid Mechanics,”
J. Eng. Thermophys.,
Equivalent Theorem of Hellinger-Reissner and Hu-Washizu Principles,”
J. Shanghai University,
He, J. H., 1997, “On C. C. Lin’s Constraints,” Modern Mechanics and Advances in Science and Technology, F. G. Zhuang, ed., Qinghua University Press, Beijing, pp. 603–604.
Method of High-Order Lagrange Multiplier and Generalized Variational Principles of Elasticity With More General Forms of Functionals,”
Appl. Math. Mech. (in Chinese),
He, J. H., 1997, “Modified Lagrange Multiplier Method and Generalized Variational Principles in Fluid Mechanics,” J. Shanghai University, 1, No. 2 (English edition).
Goldstein H., 1981, Classical Mechanics, 2nd Ed; Addision-Wesley, Reading PA.
Parametrized Multifield Variational Principles in Elasticity,”
Commun. Appl. Num. Eng.,
A Survey of Parametrized Variational Analysis and Applications to Computational Mechanics,”
Comput. Methods Appl. Mech. Eng.,
Recent Developments in Parametrized Variational Principles for Mechanics,”
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