Abstract
The fundamentals for the correct use of the method of Lagrange multiplier are presented and illustrated by examples. Some misunderstandings of the method are clarified. Equivalent variational principles are defined. It is pointed out that for a given problem of mechanics, there may be many equivalent and unequivalent variational principles. The functional of the so called generalized variational principles of elasticity with more general forms[16] are linear combinations of the well known functionals given by Reissner and Hu-Washizu.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Courant, R.,Bulletin of the American Mathematical Society,49, 1(1943), 1.
Hlávaček, I.,Aplikace Mathematiky,12, 1(1967), 15.
Hu Hai-chang,Scientia Sinica,4, 1 (1955), 33.
Hu Hai-chang, Variational Principles of Theory of Elasticity with applications, Science Press, Beijing China. distributed by Gorden and Breach, Science Publisher, Inc., New York, (1984).
Hu Hai-chang,Acta Mechanica Sinica,15, 3(1983), 301, (in Chinese).
Hu Hai-chang,Acta Mechanica Solida Sinica, 3(1983), 462, (in Chinese).
Jin Fu-sheng,Acta Mechanica Solida Sinica, 1(1984), 111, (in Chinese).
Kuang Zhen-bang, Generalized Variational Principles and Theories of Thin Elastic Plates. Scientific and Technical Report of Xi-an Transportation University (1964), (in Chinese).
Luo En, An unpublished manuscript (1965), (in Chineses).
Tsien Ling-hi (Qian Ling-xi),Scientia Sinica,1, 2/4 (1950), 449, (in Chinese).
Qian Ling-xi, Optimal Design of Engineering Structures. (1983) (in Chinese).
Tsien Ling-hi (Qiang Ling-xi) and Tsoon Wan-shia (Zhong Wan-xie),Scientia Sinica,8, 11(1964).
Chien Wei-zang, An unpublished manuscript (1964), (in Chinese).
Chien Wei-zang,Mechanics and Practice, n. 1 and 2 (1979), (in Chinese).
Chien Wei-zang,Acta Mechanica Sinica,15, 4(1983), 325, (in Chinese).
Chien Wei-zang,Applied Mathematics and Mechanics (English edition),4, 2(1983), 137.
Chien Wei-zang,Acta Mechanica Solida Sinica, 3(1984), 461, (in Chinese).
Reissner, E.,Journal of Mathematics and Physics,29, 2(1950), 90).
Wang Chang-xing,Acta Mechanica Sinica,13, 6(1981), 629, (in Chinese).
Washizu, K., On the Variational Principles of Elasticity and Plasticity. Aeroelastic and Structures Research Laboratory, Massachusetts Institute of Technology, Technical Report 25-18 (1955).
Weinstein, A.,International Journal of Solids and Structures,4, 5(1968), 579.
Zhong Wan-xie,Acta Mechanica Sinica,15, 4(1983), 341, (in Chinese).
Zhong Wan-xie,Acta mechanica Solida Sinica, 2(1984), 157, (in Chinese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haichang, H. On the method of Lagrange multiplier and others. Acta Mech Sinica 2, 129–137 (1986). https://doi.org/10.1007/BF02485853
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02485853