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Quasistatic inflation processes within rigid tubes
Author(s) -
Steigenberger J.,
Abeszer H.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700166
Subject(s) - quasistatic process , constraint (computer aided design) , tube (container) , symmetry (geometry) , work (physics) , inflation (cosmology) , rotational symmetry , classical mechanics , mechanics , physics , computer science , mathematics , theoretical physics , geometry , mechanical engineering , engineering , quantum mechanics
In this paper the authors consider mechanical devices of rotational symmetry that can be seen as segments of an artificial worm or as a balloon for angioplasty. Continuing former work [7] 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.