H. Hedia

Finite element modelling with transformation techniques

Transformation methods are a very powerful tool in finite element modelling. In many cases, an adequate mapping transforms the problem into an easier one or allows advantage to be taken of the symmetries. This paper demonstrates that any mapping can be handled automatically provided the classical vector analysis approach is given up for the benefit of a differential geometry approach. As a first example, it is shown that axisymmetrical problems need no more a particular treatment provided the mapping of the cylindrical coordinates on the cartesian ones is considered as it is. Furthermore, a novel axisymmetrical formulation is proposed which relies on one further transformation and improves considerably the quality of the interpolated field. Transformation methods are also of great help to model the infinite space by means of finite elements. Many authors have presented such transformations which are often instances of the same general shell transformation that is presented here.

Modelling of electromechanical relays taking into account movement and electric circuits

This paper presents a numerical modelling of an electromechanical relay connected with an electric excitation circuit. This transient modelling not only takes into account the classical electromagnetic equations of the device but also the movement and circuit equations. The use of the finite element-boundary element coupling method facilitates the computation of the movement while the actual coupling with circuit equations is necessary for an accurate and reliable representation of transient phenomena. >

Error estimation based on a new principle of projection and reconstruction

A new approach for error estimation in finite element computations is presented. This method may be applied to a wide range of modeling (magnetostatics, magnetodynamics, scattering problems). The main idea is to reconstruct, from the finite element solution of a primal formulation, a field belonging to the space of the dual finite element formulation. The error is then computed through the nonfulfilment of the constitutive relation by the couple: primal solution-dual solution. 2-D problems with analytical solutions are treated to prove the efficiency of the method. Then the error estimator is used to adapt the mesh for a 3-D magnetostatic problem.

Arrangement of phases and heating constraints in a busbar

This paper presents the analysis of a busbar for a three-phase system. The best connection of the different phases is proposed to derive the optimal dissipation of the heat flux inside the busbar. The implementation of a magnetothermal coupled model which can take into account radiation exchange and the electric circuit parameters is necessary. A comparison of numerical results with experimental results is made on an industrial busbar.

A New Method for Axisymmetrical Linear and Non-Linear Problems

The problem of unacceptable inaccuracies sometimes observed in the fields computed with the classical axisymmetrical model (i.e., first-order finite elements with auxiliary potential V=A/r) is solved. Two methods are proposed to improve the accuracy of the results: isoparametrical second-order elements and first-order elements with a suitable coordinate transformation. The second method, using first-order elements, gives the exact solution for piecewise linear materials; it has also been generalized for nonlinear systems by defining a quadrilateral axis-dedicated element. >

Determination of equivalent material characteristics for parasitic effects in electrical apparatus

For linear systems excited with sinusoidal constraints, an exact dynamical modelling can be performed with a phasor (complex number) approach. For nonlinear systems (exhibiting saturation, hysteresis and higher harmonics), a time stepping model is very time consuming. A method to model such nonlinear systems with an approximated phasor approach is presented. Determination of equivalent material characteristics is discussed and applications are given.

Optimization of the width of a thin plate in a transverse flux induction furnace

This paper presents the analysis of a transverse flux induction furnace. The originality of the analysis presented in this paper is to use successively three different formulations in order to solve the magneto-thermal coupled problem. The Whitney elements (node based, edge based, facet based and volume based elements) are shown to be a convenient means to perform naturally that coupling and to fulfil convergence conditions for the iterative solver.

A sinusoidal magnetic field computation in nonlinear materials

This paper presents a new approach to solve nonlinear problems using the complex formalism in the finite element method. The main idea is to use a modified Newton Raphson procedure taking into account both the derivative and the conjugate derivative of the unknowns in the Jacobian matrix. To validate this method, the nonlinear complex analysis is compared to a classical time stepping analysis for the computation of the magnetic field outsides shielded three-phase cable.

An optimization method for the design of physical and Maxwellian absorbers

This paper presents a general deterministic optimization procedure to compute the spatial repartition of material property-dissipative and nondissipative part-which minimizes physical or numerical reflection in physical and Maxwellian absorbers. The reflection performances of particular absorbers are compared from many points of view and deeply analyzed. The obtained results can usefully guide the designer in the choice of a particular absorber for the treatment of practical or numerical applications.

Graphical language interpreter and meshing tool for electromagnetic computations

The authors present three software tools that were developed together with an electromagnetic field computation program within the framework of finite and boundary element (possibly coupled) methods. The first tool consists of a two-dimensional or three-dimensional structure generator whose results are transmitted to a second tool: an interactive meshing program or an automatic surface generator. These three programs, written in FORTRAN and associated with the submission of a dynamic memory allocation module, are very simple to use and have proved to be extremely useful by allowing the submission of complicated real cases in a short time. Two examples are considered: a stepping motor and a hairpin transformer. >