Issue 39

S. Harzallah et alii, Frattura ed Integrità Strutturale, 39 (2017) 282-290; DOI: 10.3221/IGF-ESIS.39.26 284 Mathematical division may be achieved by the following partial differential equation. The FEM for EC phenomena 2D revolution has been developed in numerous works. For axisymmetric geometries set equations to 2D. We suggest that two-dimensional cylindrical coordinates are considered in order to study these system components of the current density     0, 0, , s s J J r z   . The Magnetic Vector Potential     0, 0, , A A r z   and the two-dimensional cylindrical components of the Magnetic Vector Potential (MVP) diffusion are related as follows;         c k 1 0 in in 1 1 1 1 in in nc s k k k N coils s k k k j rA r rA rA I n r r r z r z S I n S                                                       (2) where, j is the complex number,  is the angular frequency, sk I , k k S ds    [9].Applying the Galerkine’s method, with approximation functions of the Magnetic Vector Potential (MVP), and using Dirichlet boundary conditions, we can write every mesh nodes into discrete forms as follows;   c 1 1 1 0 in . in 1 in nc n m n j j n s m n j k m k k j k N coil s k m k k j N N d A I N N d A N n d S I N n S                                               k in s k d                 (3) where N n is the approximation function at node n, N m is the shape function for all nodes in a given region. Then, we get the following algebraic equations [10] c k 1 0 in [ ][ ] in [F] in [ ] [ ] in nc k N coils k j K A M F                  (4) where 1 mn m n M N N d                    (5) . . mn m n k K N N d      (6) s k m m k k I F N n d S      (7)