Abstract: This paper is based on the geometrical nonlinear theories of deformationpresented by Chen Zhi-da^[1], Lagrange's multiplier mothod is used to study thesymmetry elasticity problems of large deformation. The general rariational priieiplesof potential energy and coinplemenlary energy,and the general variation principle ofdynamic problem have been proved. In the meantme it is also proved that the generalvatiaton principles of potential energy and complementary energy are equivalent.

Key words: evolution equation, phenomenological description, microstructural behaviour, Zaremba’s ansatz, dynamics, large deformation, independent function, generalizedvariational principle