Original title: Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector
Authors: Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří ; Ulbin, M.
Document type: Papers
Conference/Event: ENGINEERING MECHANICS 2010, Svratka (CZ), 2010-05-10 / 2010-05-13
Year: 2010
Language: eng
Abstract: The stability of the contact algorithm using the penalty method is significantly affected by choosing of the penalty function. The penalty function is defined like a magnitude of the penetration vector multiplied by the users-defined constant - the penalty parameter. The penetration vector is obtained by solution of the minimum distance problem between the node/Gaussian integration point and the segment of the element. For a general quadrilateral contact segment this task leads to the system of two nonlinear equations. It is shown that the popular Newton-Raphson method is inadvisable for this problem. In this paper, alternative methods like quasi-Newton methods, gradient methods and the simplex method are presented. Especial attention is put on the line-search method that is crucial for a general success of quasi-Newton methods as well as gradient methods. All mentioned methods are tested by means of numerical example, which involves bending of two rectangular plates over a cylinder.
Keywords: contact; normal vector; optimization methods
Project no.: CEZ:AV0Z20760514 (CEP), GA101/07/1471 (CEP), GA101/09/1630 (CEP), ME10114 (CEP)
Funding provider: GA ČR, GA ČR, GA MŠk
Host item entry: Engineering Mechanics 2010, ISBN 978-80-87012-26-0

Institution: Institute of Thermomechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0185848

Permalink: http://www.nusl.cz/ntk/nusl-42032


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