A Finite Element Formulation for Tetrahedral Elements Based on Reluctivity Tensor

In some cases, the magnetic material's reluctivity becomes a full three-dimensional tensor. In some applications the use of a scalar or a vector reluctivity is accurate enough. However, the consideration of the off-diagonal terms in a reluctivity tensor is necessary in many other calculations. In this paper, a finite element formulation is developed from Maxwell's equations and 4-node tetrahedral element shape function. The uniqueness of the formulation is that the off-diagonal terms of reluctivity tensor are fully considered. A finite element analysis program based on this formulation is compiled, which uses Femap to create a model and to display the magnetic flux distribution. Several simulations of a current-carrying air-core square coil between two iron plates are performed and compared. It shows that off-diagonal terms of reluctivity tensor have influence on distribution of magnetic flux.