Based on the study of a number of references, the thesis puts forward a safety buckling load design method based on the maximal variation velocity of loading vs displacement. Traditional stable buckling and unstable buckling all have been unified as general bifurcation buckling.
A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method.
The effect of transverse shearing deformations on the buckling and post-buckling of annular plates is studied by using the bifurcation theory and the shooting method-
Using bifurcation theory it is proved that the steady flow of viscous incompressible fluid between two concentric rotating spheres is rigid flow, there is no bifurcation when the Reynolds number changes, if the angle velocities of the two spheres equal.
The flow of incompressible viscous fluid is controlled by Navier-Stokes Equations. The qualititave analysis of the solutions of the equation is important to the studies of bifurcation problems and numerical solutions of the equations.