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]
Generalized Hellinger-Reissner Principle
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, September 17, 1997; final revision, January 16, 1998. Associate Technical Editor: W. K. Liu. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
He, J. (January 16, 1998). "Generalized Hellinger-Reissner Principle ." ASME. J. Appl. Mech. June 2000; 67(2): 326–331. https://doi.org/10.1115/1.1303826
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