Issue 28

B. Ye et alii, Frattura ed Integrità Strutturale, 28 (2014) 32-41; DOI: 10.3221/IGF-ESIS.28.04 35 Figure 3 : The solution regionof FEM: 1-probe 2-aluminumplate 3-defect 4-aluminumplate 5-air region. Region boundary condition (stepC) The solution region boundary AB, BC, AD and CD are the first boundary. AB is the symmetric axis and the source current is opposite on both sides. The magnetic vector potential A equals to zero along the symmetric axis AB. The boundary of region 5BC, AD andCD are independent boundarywhosemagnetic vector potential A is given to zero. The solution region discretization (stepD) Several principles of triangle subdivision are as follows: 1) Avoiding triangle aspect ratiooversize; 2) Only one species of media in one triangle region, subdivision element is incapable of spanning boundary in the defect region 3whose boundary isEFGH; 3) Subdivision regiondenser in the large gradient field, whilemore sparse in the small gradient field. Inside any unit shown inFigure 2, adopting linear interpolation function, themagnetic vector potential A P ( ρ , z ) of any point P ( ρ , z ) canbe represented using themagnetic vector potential A l , A m and A n of the triangle peak points l , m and n .       A SS S AA A S A ( , ) T T P z l m n l m n e    (5) where, A P ( ρ , z ) is themagnetic vector potential of any point P , the T and e of [ A ] e T respectively represent transpose and the finite element, S i is basic interpolation function, namely form function, i = l , m , n , Δ is triangular unit area. The minimum of energy functional and the finite element equations of magnetic vector potential (stepE) By the first order partial derivative of Eq.5 inside the element, it is expressed: A A 1 1 A B A 2 2 A A A 1 1 A C A 2 2 A ( ) [ ][ ] ( ) [ ][ ] l T l m n m e n l T l m n m e n b b b c c c z                                             (6) Based onEqs. (4), (5) and (6), the energy functional F e ( A ) of every element is:                  2 2 2 1 1 1 1 A C A B A S A S A S A 2 2 2 2 ( ) d d e T T T T T e e e e e e j F J z                                           (7) If thewhole solution region is dispersed to M triangular element, the total energy functional of solution region is 1 A A ( ) ( ) M e e F F    (8)