Publication detail

Semiregular finite elements in solving some nonlinear problem

ZLÁMALOVÁ, J.

Czech title

Semiregulární konečné prvky při řešení některých nelineárních problémů

English title

Semiregular finite elements in solving some nonlinear problem

Type

journal article - other

Language

en

Original abstract

The finite element analysis of the variational problem which is formally equivalent to a two-dimensional nonlinear elliptic boundary value problem with mixed nonhomogeneous boundary conditions. The given problem is solved in the case of a bounded domain whose boundary consists of two circles with the same centre. Difference between the radii of circles is very small with respect to radidus. An elliptic problem given on such a domain has many practical applications (let us mention, for example, the cartilage between a joint and hip, or an air-crevice between a rotor and stator in an electromachine). The finite element analysis of this problem is restricted to the case of semiregular triangular finite elements with polynomials of the first degree.

Czech abstract

Metodou konečných prvků je analyzován variační problém, který je formálně ekvivalentní dvojrozměrnému eliptickému okrajovému problému se smíšenými nehomogenními podmínkami na hranici. Daný problém je řešen pro případ ohraničené oblasti, jejíž hranice je tvořena dvema soustřednými kružnicemi, jejichž rozdíl poloměrů je mnohem menší, než poloměr kružnic. Taková oblast má mnoho praktických aplikací, např. chrupavka kyčelního kloubu, vzduchová štěrbina bezi rotorem a statorem v elektromotoru. Analýza je omezena na případ semiregulárních konečných prvků s lineárním polynomem.

English abstract

The finite element analysis of the variational problem which is formally equivalent to a two-dimensional nonlinear elliptic boundary value problem with mixed nonhomogeneous boundary conditions. The given problem is solved in the case of a bounded domain whose boundary consists of two circles with the same centre. Difference between the radii of circles is very small with respect to radidus. An elliptic problem given on such a domain has many practical applications (let us mention, for example, the cartilage between a joint and hip, or an air-crevice between a rotor and stator in an electromachine). The finite element analysis of this problem is restricted to the case of semiregular triangular finite elements with polynomials of the first degree.

Keywords in English

finite element method, semiregular elements

Released

01.01.2001

ISSN

0862-7940

Journal

APPLICATIONS OF MATHEMATICS

Volume

46

Number

1

Pages from–to

53–77

Pages count

24

BIBTEX


@article{BUT42418,
  author="Jana {Hoderová},
  title="Semiregular finite elements in solving some nonlinear problem",
  journal="APPLICATIONS OF MATHEMATICS",
  year="2001",
  volume="46",
  number="1",
  month="January",
  pages="53--77",
  issn="0862-7940"
}