Computation of homoclinic orbits in partial differential equations: An application to cylindrical shell buckling. (English) Zbl 0954.74021

Lord, G. J.; Champneys, A. R.; Hunt, G. W.

SIAM J. Sci. Comput. 21, No. 2, 591-619 (1999).

This paper deals with cylindrical shell buckling. First of all, the authors use a Galerkin procedure in circumferential direction (perhaps it is more correct to name this procedure Kantorovich procedure, because we reduce the system of PDEs to an infinite system of ODEs). The choice of approximation functions is based on experimental results. Then the authors use a shooting method which involves the solution of an initial value problem to give a corrected solution. It is interesting that quite well-developed techniques for continuing homoclinic solutions can be used for this problem with great success. Comparision with experimental results shows a good agreement, but it should be noted that the calculations are done only for an infinite cylinder whereas experimental data are available for a clampled cylinder of finite length.

Reviewer: Igor Andrianov (Gumperda)

MSC:

74G60	Bifurcation and buckling
74K25	Shells
37N15	Dynamical systems in solid mechanics

Keywords:

initial approximations; boundary value problem; cylindrical shell; buckling; Galerkin procedure; shooting method; initial value problem; homoclinic solutions; infinite cylinder

Software:

HomCont