Premium
Numerical Mountain Pass and its Applications
Author(s) -
Horák Jiří,
Lord Gabriel J.,
Peletier Mark A.
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610003
Subject(s) - continuation , mountain pass , numerical continuation , buckling , nonlinear system , numerical analysis , numerical approximation , mathematics , shell (structure) , calculus (dental) , computer science , mathematical analysis , bifurcation , structural engineering , engineering , physics , mechanical engineering , medicine , dentistry , quantum mechanics , programming language
The mountain pass theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. The mountain pass structure can be exploited numerically, as well. We explain the main ideas on an example of buckling of a cylindrical shell. First, we prove existence of an MP‐solution for almost all values of a given load parameter. Then, we find a numerical approximation of such a solution. Finally, we compare the results of a numerical continuation in the load parameter with results of physical experiments and make a few comments about further numerical investigations of the problem. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)