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 r...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.展开更多
In this paper, based on the mathematical theory of classical mechanics and Chen's theorem, the variational method was used in the study of large deformation symmetrical elasticity problems. The generalized variati...In this paper, based on the mathematical theory of classical mechanics and Chen's theorem, the variational method was used in the study of large deformation symmetrical elasticity problems. The generalized variational principles of potential energy and complementary energy based on the instantaneous configuration were obtained, and the equivalence between the two principles was proved. Besides, the generalized variational principles of dynamical problems based on the instantaneous configuration were also given.展开更多
文摘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.
文摘In this paper, based on the mathematical theory of classical mechanics and Chen's theorem, the variational method was used in the study of large deformation symmetrical elasticity problems. The generalized variational principles of potential energy and complementary energy based on the instantaneous configuration were obtained, and the equivalence between the two principles was proved. Besides, the generalized variational principles of dynamical problems based on the instantaneous configuration were also given.