Elemento finito
44597 palavras
179 páginas
FEM/BEM NOTESProfessor Peter Hunter
p.hunter@auckland.ac.nz
Associate Professor Andrew Pullan
a.pullan@auckland.ac.nz
Department of Engineering Science
The University of Auckland
New Zealand
June 17, 2003
c Copyright 1997-2003
Department of Engineering Science
The University of Auckland
Contents
1 Finite Element Basis Functions
1.1 Representing a One-Dimensional Field .
1.2 Linear Basis Functions . . . . . . . . .
1.3 Basis Functions as Weighting Functions
1.4 Quadratic Basis Functions . . . . . . .
1.5 Two- and Three-Dimensional Elements
1.6 Higher Order Continuity . . . . . . . .
1.7 Triangular Elements . . . . . . . . . . .
1.8 Curvilinear Coordinate Systems . . . .
1.9 CMISS Examples . . . . . . . . . . . .
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2 Steady-State Heat Conduction
2.1 One-Dimensional Steady-State Heat Conduction . . . . .
2.1.1 Integral equation . . . . . . . . . . . . . . . . . .
2.1.2 Integration by parts . . . . . . . . . . . . . . . . .
2.1.3 Finite element approximation . . . . . . . . . . .
2.1.4 Element integrals . . . . . . . . . . . . . . . . . .
2.1.5 Assembly . . . . . . . . . . . . . . . . . . . . . .
2.1.6 Boundary conditions . . . . . . . . . . . . . . . .
2.1.7 Solution . . . . . . . . . . . . . . . . . . . . . . .
2.1.8 Fluxes . . . . . . . . . . . . . . . . . . . . . . . .
2.2 An -Dependent Source Term . . . . . . . . . . . . . . .
2.3 The Galerkin Weight Function Revisited . . . . . . . . . .
2.4 Two and Three-Dimensional Steady-State Heat Conduction
2.5 Basis Functions - Element