Improvement of Classical Shell Theory and Its Application to Numerical Analysis of Stability for Shells

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It can be confirmed in the general theory of nonlinear elasticity of solid that the lost of stability can take place only in the form of static instability and the dynamic instability by no means take place, if the external forces have a potential. This means that the linearized equation for the stability of shell is self-adjoint mathematically. As the basic theory is originally in the form of solid, the stability equation for the shell obtained from any kinds of methodology should be self - adjoint definitely. But some equations of theories for stability of shells, eg. Vlassoy type equations, have inconsistency with a self-adjointness.It is important to compose the basic equations consistent with the theory mentioned above, especially the self- adjoint property of the stability equations. In our study, the basic equations of shells are simplified under the following assumptions. 1) Rotations to the normal axis of the middle surface may be neglected. 2) The shell is sufficiently thin, therefore the shell is assumed to be loaded with loads distributed over the middle surface.Under the two assumptions mentioned above, three types of equations, eg. the type considering the transverse shear deformation, Sanders type and Vlassoy type, are expressed. And then using these types equations respectively, numerical analysis of cylindrical shells and spherical shells under the non-conservative external forces are performed by using Galerkin method and finite difference method together with Newton - Raphson method. Consequently it was shown that the finite difference method is very effective to make up the stiffness matrix for the analysis of equilibrium state and the stability analysis. Furthermore the limit cycle described in complicated state were found out in the flutter domain by the usual method of analysis by using Calerkin method, finite difference method together with Newton - Raphson method, Newmark b method and the new method of stability analysis.