Vol.6, No 1, 2008 pp. 1 - 12
UDC 515.3 : 519.853
COST-EFFECTIVE GEOMETRICALLY NONLINEAR FE-FORMULATION FOR SOFT TISSUES' DEFORMATION
Dragan Marinković1, 2, Katja Joechen3
1Institut für Mechanik, TU Berlin, Straße des 17. Juni, 10623 Berlin, Deutschland 2Mechanical Engineering Faculty, University of Niš, A. Medvedeva 14, 18000 Niš, Serbia
3Institut für Technische Mechanik, Universität Karlsruhe (TH), Kaiserstr. 10, 76131 Karlsruhe, Deutschland
E-mail: Dragan.Marinkovic@TU-Berlin.de
Abstract. Accurate prediction of the behavior of soft bodies' deformation is a demanding task, since it involves geometrical and material nonlinearities as well as variable boundary conditions, i.e. contact problems. This paper represents the first step in handling the issue by proposing development of cost-effective 3D finite element for analyzing geometrical-only nonlinear deformations. The proposed geometrically nonlinear formulation is of the updated Lagrange type and can relatively easily be extended so as to account for other nonlinear aspects (material nonlinearities, contact). It also represents a good compromise between the numerical effort and achieved accuracy. A set of examples, starting from very simple ones and going toward more complex ones, is given to demonstrate the application of developed element and formulation.
Key Words: Finite Element Method, Geometrically Nonlinear Analysis, Tetrahedron Element.
EFIKASNA GEOMETRIJSKI NELINEARNA FE-FORMULACIJA ZA ANALIZU DEFORMACIJA MEKIH MATERIJALA
Precizno određivanje deformacije mekih tela je zahtevan zadatak, jer uključuje i geometrijski i materijalno nelinearno ponašanje, kao i promenljive granične uslove, odnosno probleme kontakta. Rad predstavlja prvi korak autora u ovladavanju ovom problematikom i opisuje razvoj efikasnog 3D konačnog elementa za modeliranje geometrijski nelinearnih deformacija. Predložena geometrijski nelinearna formulacija je tipa updated Lagrange i može se relativno lako proširiti tako da uzme u obzir i druge aspekte nelinearnog ponašanja (materijalnu nelinearnost, kontakt). Ona, takođe, predstavlja dobar kompromis između potrebnog numeričkog napora i ostvarene tačnosti analize. Skup primera, počev od vrlo jednostavnih i idući ka složenijim, je dat sa ciljem da se prikaže primena razvijenog elementa i formulacije.
Ključne reči: metoda konačnih elemenata, geometrijski nelinearna analiza, tetraedar element