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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector (en)
skos:prefLabel	Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector (en)
skos:notation	RIV/61388998:_____/10:00343347!RIV11-MSM-61388998
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA101/07/1471), P(GA101/09/1630), P(ME10114), Z(AV0Z20760514)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Gabriel, Dušan Plešek, Jiří Kopačka, Ján
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav termomechaniky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	247452
http://linked.open...ai/riv/idVysledku	RIV/61388998:_____/10:00343347
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	normal vector; contact; optimization methods (en)
http://linked.open.../riv/klicoveSlovo	normal vector optimization methods contact
http://linked.open...ontrolniKodProRIV	[EA4F66540F5F]
http://linked.open...v/mistoKonaniAkce	Svratka
http://linked.open...i/riv/mistoVydani	Prague
http://linked.open...i/riv/nazevZdroje	Engineering Mechanics 2010
http://linked.open...in/vavai/riv/obor	JC
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Finite element modelling of linear, non-linear and multiscale effects in wave propagation in solids and heterogeneous media Numerical solution to steady-state and transient wave dispersion in mechanical systems on different scales Numerical Solution of Contact-Impact Problems in Nonlinear Finite Element Analysis
http://linked.open...UplatneniVysledku	2010
http://linked.open...iv/tvurceVysledku	Plešek, Jiří Gabriel, Dušan Kopačka, Ján Ulbin, M.
http://linked.open...vavai/riv/typAkce	EUR - Evropská
http://linked.open.../riv/zahajeniAkce	2010-05-10 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Complex dynamical systems in thermodynamics, fluid and solid mechanics
number of pages	13 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Ústav termomechaniky AV ČR
https://schema.org/isbn	978-80-87012-26-0

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