E. Haugeneder, H.A. Mang:
"On an Improper Modification of a Variational Principle for Finite Element Analysis";
ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 59 (1979), 637 - 640.
In finite element analysis of thin plates subjected to bending application of principles of stationary value of modified potential energy (MOPPE) enables satisfaction of originally violated geometric boundary and interelement continuity conditions. This is achieved by means of algebraic constraint conditions for the components of the vector of nodal displacements. In this way, nonconforming finite elements can be utilized, yielding a significant reduction of degrees of freedom (d. o. f.).
A disadvantage of such finite element methods (FEM) is the appearance if a set if additional unknown parameters, Lagrangian multipliers employed for the derivation of the aforementioned algebraic constraint conditions.
More recently, some researchers hace advocated simplifications of FEM based on MOPPE, aimed at further reducing the number of d.o.f. In this note, simplifications of MOPPE will be abbreviated as SMOPPE. These simplifications are characterized by a priori eliminating the Lagrangian multipliers from the functional subject to variation. MANG and GALLAGHER have published a critical assessment of such a technique. In this method, the Lagrangian multipliers are replaced by somewhat arbitrary chosen linear functions, expressed solely in terms of certain nodal displacements.
Thise note deals with a different state of affairs. Its purpose is to analyze the consequence of employing the EULER equations for the Lagrangian multipliers to eliminate the latter a priori from the functional subject to variation.