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Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

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dc.creator Serpa Alberto Luiz
dc.creator Iguti Fernando
dc.date 2000
dc.date.accessioned 2013-05-30T11:30:22Z
dc.date.available 2013-05-30T11:30:22Z
dc.date.issued 2013-05-30
dc.identifier http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-73862000000200011
dc.identifier http://www.doaj.org/doaj?func=openurl&genre=article&issn=01007386&date=2000&volume=22&issue=2&spage=273
dc.identifier.uri http://koha.mediu.edu.my:8181/jspui/handle/123456789/4645
dc.description This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.
dc.publisher The Brazilian Society of Mechanical Sciences
dc.source Journal of the Brazilian Society of Mechanical Sciences
dc.subject Finite Elements
dc.subject Contact Problem
dc.subject Friction
dc.subject Mathematical Programming
dc.subject Augmented Lagrangian
dc.title Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

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