Vol.3, No 12, 2002 pp. 393-404
UDC 518.12 517.546:531
ON THE RELIABILITY OF THE NEW FINITE ELEMENT
HC8/27
Dubravka Mijuca
Faculty of Mathematics, University of Belgrade, Studentski trg 16,
P.0. Box 550
11000 Belgrade, Yugoslavia, e-mail: dmijuca@matf.bg
ac.yu
It is now generally recognized that reliable finite element procedure,
must fulfill specific mathematical convergence requirements, as consistency
and stability conditions, before it is recommended for general use in solid
and fluid mechanics. In the present paper it will be shown that three-dimensional
finite element HC8/27, based on the primal-mixed formulation in linear
elasticity, is consistent and stable. In addition, numerical evaluation
of the inf-sup condition for the full three-dimensional primal-mixed scheme
in elasticity will be presented. It should be noted that present finite
element is stable without use of any stabilization technique.
Key words: Finite element method, Reliability.
O POUZDANOSTI KONAČNOG ELEMENTA HC8/27
U radu je pokazano da je konačni element HC8/27 primalno-mešovite formulacije
u punoj trodimenzionoj elastičnosti pouzdan, što podrazumenva da je konzistentan
i stabilan. Kao takav, može da se preporuči kao univerzalan konačni element
element u mehanici čvrstog tela za analizu problema proizvoljne geometrije,
uslova oslanjanja, zadatih opterećenja i vrednosti koeficijenta smicanja.
Na taj način se uobičajene biblioteke elemenata, bazirane na familijama
jednodimenzionih, ravnih i trodimenzionih elemenata, zamenjuju samo jednim
trodimenzionim elementom, kome korisnik može da bira broj lokalnih čvorova
po elementu za aproksmaciju napona, a u zavisnosti od toga da li je polazni
fizički problem problem regularan ili ne.
