Florea I. Hantila

Polarization method for static fields

An overview of the polarization method is presented. The method can by applied for different regimes of the electromagnetic field as well as for electric circuits. Criteria for the choice of the permeability are proposed, so that the iterative scheme leads to a Picard-Banach fixed point procedure. The errors are evaluated. An efficient overrelaxation method is presented. The modality of using FEM numerical method is analyzed in order to ensure the convergence of the method.

Nonlinear FEM-BEM formulation and model-free inversion procedure for reconstruction of cracks using pulse eddy currents

Pulse eddy currents are proposed as a nondestructive testing (NDT) technique to detect flaws in conductive structures with large thickness. The harmonic component of a pulse is rich, so that the pick-up signal containing the amount of information corresponds to a multifrequency analysis. Due to the short time length of the pulse, the amplitude of the excitation increases up to 100 times of the amplitude for an AC signal. Both direct simulation of pulse eddy-currents phenomena using an A-/spl phi/ FEM-BEM code and neural network-based inversion techniques are performed. Numerical results for the inversion of signals due to outer defects are shown.

Integral Formulation and Genetic Algorithms for Defects Geometry Reconstruction Using Pulse Eddy Currents

A method for reconstruction of zero-thickness defects, buried deep under material surface, using pulse eddy currents, is proposed. Both an integral-FEM method for simulation of transient eddy-currents and genetic algorithms, as a model-free inversion technique, are proposed. Numerical results for the inversion of the eddy-currents signals, using genetic algorithms, are shown.

Modelling eddy currents in thin shields

Purpose – The purpose of this paper is to present a simplified rigorous mathematical formulation of the problem of electric currents induced in thin shields with holes yielding more efficient numerical computations with respect to available methods.Design/methodology/approach – A surface integral equation satisfied by the current density was constructed, which is, subsequently, represented at any point by linear combinations of novel vector basis functions only associated with the interior nodes of the discretization mesh, such that the current continuity is everywhere insured. The existence of the holes in the shield is taken into account by associating only one surface vector function with each hole. A method of moments is then applied to compute the scalar coefficients of the vector functions employed.Findings – It was found that the induced current distribution for shields with holes having the complexity of real world structures can be determined with a satisfactory accuracy utilizing a moderate size...

Novel Solution to Eddy-Current Heating of Ferromagnetic Bodies With Nonlinear

An efficient solution is presented for coupled nonlinear eddy currents-thermal diffusion problems. Applying the fixed-point polarization method to the nonlinear eddy-current field problem, with the magnetization dependent on magnetic induction and on temperature, allows the field computation to be performed for each harmonic separately. Since the fictitious permeability can be chosen to be everywhere that of free space, the matrices of the linear systems to be solved at each iteration remain unchanged even when the nonlinear characteristic changes with the temperature. A simple integral equation is used to compute the eddy currents, the inversion of the matrices corresponding to the harmonics being performed only once, before starting the iterative process. The heat conduction-diffusion equation is solved at each time step by the finite-element method. Three illustrative examples are also presented.

{\mbi B}\hbox{–}{\mbi H}

A new procedure for the study of the evolution of the solid phase in a moving solidifying ferromagnetic metal is proposed. The temperature distribution is controlled using eddy currents induced by a coil that covers partially the crucible surface and by cooling the rest of it, with an imposed crucible velocity. Analysis of the thermal field requires the solution of the time-periodic eddy-current problem coupled with the thermal diffusion problem. The nonlinearity of the B-H relation within the ferromagnetic material of the yoke and inside the solidified material cooled below the Curie point, as well as its dependence on temperature, are taken into consideration. Application of the polarization fixed point method allows the construction of an integral equation for eddy currents and always ensures the convergence of the iterative solution. At each time step, the heat diffusion equation is solved through a standard finite element technique, with the thermal conductivity and the specific heat capacity dependent on temperature.

Characteristic Dependent on Temperature

The piezoelectric effect occurs in materials for which an externally applied elastic strain causes a change in electric polarization which produces a charge and a voltage across the material. The converse piezoelectric effect is produced by an externally applied electric field, which changes the electric polarization, which in turn produces an elastic strain. The most known piezoelectric material is quartz crystal. Many other natural crystalline solids, as Rochelle salt, ammonium dihydrogen phosphate, lithium sulfate, and tourmaline as well as some man-made crystal as gallium orthophosphate, aluminium nitride (AlN), and langasite exhibit piezoelectric properties. A lot of artificial ceramics as barium titanate, lead titanate, lead zirconate titanate (PZT), potassium niobate, lithium niobate, and lithium tantalite have similar properties. The most known technical application is the piezoelectric transducer. In the last years electromechanical AlN resonators emerged as a very efficient solution for mobile communications filters due to the possibility to be integrated at a relatively low cost together with CMOS circuits in systems on a chip and systems in a package. In most applications the piezoelectric devices have a linear behaviour. In Section 2 the linear and nonlinear equations of the piezoelectric effect are described, a new iterative procedure for solving the nonlinear equations is given, and some aspects of the Finite Element solution are discussed. An electromechanical field analysis of a displacement transducer is presented in Section 3. Sections 4 and 5 show some recent applications in the mobile communication technology. The field analysis of a bulk acoustic wave (BAW) resonator using 3D linear models is presented in Section 4. Some nonlinear effects in power BAW resonators together with their circuit models are discussed in Section 5.

Efficient Analysis of the Solidification of Moving Ferromagnetic Bodies With Eddy-Current Control

An efficient boundary integral equation solution for magnetic field problems is presented, based on a novel magnetic vector potential formulation and using edge elements and tree-cotree spanning. A zero normal component of this vector potential A and the condition for its line integral along any closed path on the boundary are imposed such that the continuity of the normal component of the magnetic flux density is rigorously satisfied. The unknowns employed are the tangential components of /spl nabla//spl times/A and only the tree edge element values. Multiply connected domains are easily dealt with by introducing certain pairs of cotree edges in the set of tree edges, which are used to construct the cuts that transform a multiply connected domain into a simply connected one. The line integrals of A along the cut loops are determined by the respective magnetic fluxes. The stiffness matrix can easily be obtained. Three illustrative examples are given.

Modeling and Simulation of Piezoelectric Devices

Solution of the equation of motion for conductors in external magnetic fields requires the knowledge of the magnetic forces due to the induced eddy currents that, in turn, can be determined if the position and the velocity of the bodies are known. An iterative technique is adopted, where, at each time step, an initial value of the magnetic force is used to determine the position and the velocity of the body at the end of the time step and, then, the value of the force is corrected. To reduce the computational effort in the case of thin metallic sheets, it is proposed to use the surface integral equation of the induced eddy currents, with a supplementary term added to account for the motion. A sinusoidal with time variation of the excitation field is considered and a phasor representation of various physical quantities is employed. An average magnetic force over each period is used to solve the equation of motion.

Magnetic vector potential tree edge values for boundary elements

A method for reconstruction of defects buried deep under material surface of conductive nonlinear materials is proposed. Defects are approximated as zero thickness. Simulation of pulse eddy currents is done using an integral FEM method, with a polarization method with over-relaxation to speed up the nonlinear iterations, and a neural network method is used for the reconstruction of defects shape from the simulated signals.