Quasistatic inflation processes within rigid tubes

In this paper the authors consider mechanical devices that can be seen as segments of an artificial worm or as a balloon for angioplasty. Continuing former work \cite{St 2003} the segment is now placed within a cylindrical or constricted rigid tube that will be touched or pressed during inflation of the segment. Both the segment's shape and the forces of contact are investigated. The main mathematical tool is the Principle of Minimal Potential Energy - handled as an optimal control problem with state constraint. The necessary optimality conditions are carefully analyzed and simulation results for characteristic examples are presented.\\ The treatment of the problem is primarily mathematical but aiming at application.


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