An Application to Cylindrical Shell Buckling G. J. Lord, A. R. Champneys, G. W. Hunt Abstract. Donnell equations, a coupled system of elliptic equations describing the equilibrium of an axially compressed cylindrical shell.
Earlier work suggests that axially localized solutions are the physically preferred buckling modes.
Hence the problem is posed on a cylindrical domain that is unbounded axially and solutions are sought which are homoclinic in the axial variable and periodic circumferentially. Methods for location and parameter continuation of homoclinic solutions of ODEs are then adapted, making special use of the symmetry and reversibility properties of solutions observed experimentally. The method for location of solutions makes use of asymptotic approximations where available. The method is illustrated step by step to produce a variety of homoclinic solutions of the equations and compute their bifurcation diagrams as the loading parameter varies. Good agreement with experimental data is found.