In using the Lagrange multiplier method to eliminate constraints of Hellinger-Reissner principle, the multipliers may vanish during the process of variation.

The variational crises (such as, some of the Lagrangemultipliers vanish completely) are of its inherent character of Lagrange multiplier method.

In using the Lagrange multiplier method to eliminate the constraints imposed on conditional variational principles, the multipliers might vanish during the process of variation ( λ =0, where λ is a Lagange multiplier).

In this method,without depending upon small parameter,a trial function with possible unknowns is used as initial approximation,then a correction functional is constructed by means of a general Lagrange multiplier,which can be identified via variational theory.

A concept of splitting factor (an arbitrary parameter) is introduced into Lagrange multiplier,enabling it to do what the traditional Lagrange multiplier could not do.

In EFGM, in order to get a numerical solution for a partial differential equation, shape function is constructed by Moving Least Square (MLS), control equation is produced from the weak form of variational equation and Lagrange multipliers are used to satisfy essential boundary conditions.

The traditional approach(Lagrange multiplier method)might fail due to the variational crisis occurring during the derivation of generalized variational principles.

To overcome this crisis, Chien suggested a method called the high order Lagrange multiplier method.

The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.

The constraint conditions of variation are eliminated by the method of identified Lagrangian multipliers and a generalized variational principle is estab-lished.

Two patterns of constrained conditions --initialconditions and end conditions,peculiar to dynamical problems,may berelaxed by using the method of bimixed Lagrange multipliers presentedin this paper.