H.A. Mang, G. Hofstetter, R.H. Gallagher:

"On the Elimination of Lagrange Multipliers in Multifield Finite Element Methods";

in: "Proceedings of the Symposium on Hybrid and Mixed Finite Element Methods - 1985 ASME Winter Annual Meeting", R. Spilker, K.W. Reed (ed.); ASME, 1985, 77 - 90.

The purpose of this paper is to report on the consequences of eliminating Lagrange multipliers in Principles of Stationarity of Generalized Potential Energy (PSGPE) by means of the Euler equations for the multipliers. Such variational principles serve as the basis for the development of multifield finite element methods. Through elimination of Lagrange multipliers the number of fields of independent variables is reduced, resulting in a reduction of unknowns.The paper covers elastic solids and Kirchhoff plates. For solids treated first as mechanical systems with infinitely many degrees of freedom it is shown that the Euler equations of a typical PSGPE do not hold unconditionally for the corresponding Simplified Variational Principle (SVP) following from elimination of Lagrange multipliers. It is also demonstrated that the characteristics of SVP-based (as opposed to PSGPE-based) finite element methods for solids and Kirchhoff plates, respectively, are problem-dependent. The results of the theoretical investigation are verified numerically.

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