Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector

0343347 - ÚT 2011 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Kopačka, Ján - Gabriel, Dušan - Plešek, Jiří - Ulbin, M.
Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector.
Engineering Mechanics 2010. Prague: Institute of Thermomechanics AS CR, v. v. i., 2010 - (Zolotarev, I.), s. 77-89. ISBN 978-80-87012-26-0.
[ENGINEERING MECHANICS 2010. Svratka (CZ), 10.05.2010-13.05.2010]
Grant CEP: GA ČR(CZ) GA101/07/1471; GA ČR(CZ) GA101/09/1630; GA MŠMT(CZ) ME10114
Výzkumný záměr: CEZ:AV0Z20760514
Klíčová slova: normal vector * contact * optimization methods
Kód oboru RIV: JC - Počítačový hardware a software

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.
Trvalý link: http://hdl.handle.net/11104/0185848