Extended Finite Element Methods

A generalized macroscopic representation of electrical steels used in transformer manufacturing industry is developed. The proposed representation is specifically formulated for integration in the finite element method. Usage of the specific technique enables the accurate evaluation of electromagnetic field distribution of transformer cores under heavily saturated conditions. Advantages over conventional techniques include numerical stability, numerical accuracy, and reduction of iterations of the Newton–Raphson method.

In this paper a robust three-dimensional (3D) finite element (FE) anisotropy model is introduced based on a particular scalar potential formulation. The specific 3D FE model is suitable for the accurate evaluation of the peak flux density distribution and no load loss of one-phase and three-phase wound core distribution transformers. The accuracy of the proposed 3D FE anisotropy model is validated by local flux density and no load loss measurements.

Nowadays, transformers are made of conventional magnetic cores which are constructed of a single grainoriented or amorphous, magnetic steel. Even though, the transformer is the most efficient of electrical machines, with efficiencies typically above 90%, it is possible to improve transformer performance by using composite magnetic cores. Patents related to this simple and effective technique can be traced back to 1929. The specific technique can be applied to wound core distribution transformers. By using wound cores constructed with a combination of conventional and high permeability grain-oriented steel the total owing cost (TOC) of the transformer can be reduced effectively. This paper presents a brief review of patents on wound and composite magnetic cores and introduces a generalized technique for the determination of the optimum design variables of a new composite wound core design.

This paper proposes the manufacturing of distribution transformers using a novel type of magnetic core which is called composite wound core. A composite wound core is constructed of a combination of conventional and high magnetization grain-oriented steel. The main advantage of transformers assembled of composite wound cores over conventional transformers is the significant reduction of the manufacturing and operating cost. For the analysis of composite wound core transformers, a FE model considering anisotropy and high saturation conditions, and an advanced 3D hybrid FE-BE model have been developed.

Un elemento finito lineal con sección transversal constante puede adoptar cualquier orientación en el plano y sus extremos o nodos lo ligan al resto de los elementos. La energ a cinética (T ) y potencial (V ) de un elemento elástico dinámico son el basamento en la implementación del principio de Hamilton para la definición de un elemento finito. La definición de la energía cinética y potencial es el primer paso para la formulación variacional preliminar a la enunciación por elementos finitos que se utiliza para resolver, dígase, los problemas de mecanismos que se mueven en el plano utilizando la ecuación de Hamilton. El objetivo general consistió en definir la ecuación del movimiento de un elemento finito lineal plano elástico dinámico utilizando la ecuación de Hamilton, a partir de la lagrangiana (T –V ) obtenida con el uso de un polinomio de quinto y uno de primer grados, con ocho grados de libertad, cuatro en cada nodo, que representaron las deformaciones: axial (u(x)), transversal (w(x)), pendiente ((dw(x)/dx)) y curvatura ((d2w(x)/dx2)). La deformación debido al cizalleo transversal, insignificante comparado con la deformación flexional y la axial, la inercia rotatoria y las fuerzas friccionales en las uniones,fueron desestimadas con el fin de producir un elemento amigo. Los objetivos específicos fueron producir: (a) la matriz de masa de traslación [MD], (b) la matriz giroscópica de traslación [AD], (c) la matriz de rigidez total de traslación [KD], y (d) el vector de deformación (S). Como resultado se forjó la ecuación del movimiento de un elemento finito lineal plano elástico dinámico [MD]( ¨ S) − 2¨_[AD]( ˙S ) + {[K] − _˙2[MD] − ¨_[AD]}(S) = (Q) . Se concluyó que la ecuación obtenida variacionalmente con la aplicación del principio de Hamilton es un modelo cuyo procedimiento puede ser utilizado cuando se requiera aumentar el número de grados de libertad del modelo.

This paper shows experimental results of longitudinal flux density and its harmonics at the limb, the yoke and the corner of a three phase, Si-Fe, five-legged wound transformer core. Results show that the flux density is nonuniform in the cores and there is high level of third harmonic component. Moreover, the lower flux values in the outer cores have been assessed and the simultaneous time variation of the flux in both outer cores has been demonstrated by measurements while the peak magnetic flux density values have been compared to FEM analysis. These findings enable a better understanding of the magnetic behavior of five legged wound transformer cores and their consideration is expected to achieve respective improvement of the design with respect to core losses and magnetostriction noise.

This paper presents the life estimation of the diffuser structure. Literature shows that the welds are the source of failure in case of welded structure; hence the estimation of its life is very critical. There are two kinds of methods for life estimation stress life approach and strain life approach which have been validated for simple problems. Stress life approach was identified as appropriate for life estimation of the variable diffuser. There are papers indicating the methodology for life estimation using commercial software for life prediction. Here, Optistruct-Hyper-Works for pre-processing and solver and Hyper-View-Hyper-Works for post processing has been used for the indeterminate structure, complex loading and boundary condition. The mathematical model subjected to the variable pressure contours for a particular Mach No., with the gimbal joint boundary condition at the test section end and the roller support at the other end. In this paper stress and fatigue analysis of the variable diffuser has been carried out and life of the variable diffuser has been estimated. Keywords —fatigue analysis; finite element method; fatigue life. I. INTRODUCTION Fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. Mechanical components and structures used in day today life contain notches and geometrical discontinuities in them. For example, shafts have keyways in them and pressure vessels contain openings for the operational requirements. These notches, holes, keyways produce stress concentrations in the structure. Notches and keyways can be the region where crack initiation takes place which leads to crack propagation and finally failure of the structure when the stresses higher than the nominal value. Therefore predicting fatigue strength of the component is relevant considering design and safety of the component. Hence fatigue crack initiation life can be estimated based on local stress-strain approach. Wind tunnel is used for aerodynamic flow simulation around the scaled models for force and moment measurements. Wind tunnel testing is indispensible in the design phase of any vehicle flying (subsonic to supersonic) for its aerodynamic characterisation. There are two types of wind tunnels open circuit and closed circuit wind tunnels. In open circuit tunnels the high pressure air stored in the reservoir is forced on to the model through a nozzle to get the required Mach no and then is let out to the atmosphere with the aid of a diffuser. Whereas in case of close circuit tunnel the high pressure compressed air is recalculated in a close circuit. Variable diffuser is one of the components in the wind tunnel circuit. The CSIR-NAL trisonic wind tunnel is more than 50 years old. The diffuser of the wind tunnel needs to be analyzed for fatigue life. The literature reviews show that the linear static analysis has to be carried out for the given loads and then wind tunnel runs are to be used for cyclic loading case for fatigue.

This paper concerns the thermal investigation of a surface-mounted permanent-magnet synchronous motor designed for high-temperature aerospace actuation applications. A finite-element package was developed, enabling accurate 3-D transient thermal analysis by considering complex and unsymmetrical actuator housing configurations. Its validity was verified by measurements carried out at different duty cycles and operating conditions.

In recent years, researchers have proposed transformerless solutions for connecting renewable-energy power plants to the grid. Apart from lack of efficiency and increased cost and weight of the transformer, one of the reasons is the dc input current that causes transformer saturation. The purpose of this paper is the development of a finite-element computational tool that is going to aid transformer manufacturers in designing distribution transformers specifically for the renewable-energy market. It is based on a generalized macroscopic representation of electrical steels used in the transformer manufacturing industry that enables the accurate evaluation of electromagnetic field distribution of transformer cores under heavily saturated conditions. Its advantages over conventional formulations include numerical stability, numerical accuracy, and reduction of iterations of the Newton–Raphson method. An experimental verification of the proposed method is carried out.

Distribution transformers losses are equal to almost 2% of the electricity generated worldwide and only in the European Union are estimated at about 33 TWh/year. Approximately 75% of the total losses are due to core losses as a result of the loading characteristics of distribution transformers. Design of the joints of magnetic cores has a profound impact on core losses and transformer efficiency. The paper introduces a finite element methodology for the analysis of transformer joints. The proposed technique consists in the application of certain boundary conditions for the excitation of the joints. The main advantages of the pseudo-source technique include minimization of the computational cost and ease of implementation. The technique is combined with a number of FE formulations and a vector hysteresis model. Two-dimensional as well as 3-D FE analysis is studied. Longitudinal and normal flux measurements were carried out for the validation of the proposed technique.

Numerous C 0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a non-differentiable term due to the frictional contact. We prove that these C 0 DG methods are consistent and stable, and derive optimal order error estimates for the quadratic element. A numerical example is presented to show the performance of the C 0 DG methods; and the numerical convergence orders confirm the theoretical prediction. Keywords. Variational inequality of fourth-order, discontinuous Galerkin method, plate frictional contact problem, optimal order error estimate

An XFEM multiscale approach is adopted in order to investigate the mechanical properties and fracture behavior of carbon nanotube reinforced concrete specimen. At the nanoscale, molecular dynamics simulation is used to find the mechanical properties of carbon nanotube (CNTs). Afterwards, a hydration model is adopted to find the chemical composition of cement paste. The hydrated model and CNTs are then converted into a finite element mesh for further analysis. Finally, at the meso scale the fracture behavior of the CNT reinforced concrete is simulated by the XFEM approach. The results indicate that the fracture energy of samples with similar volume fractions but reinforced by longer CNTs increase significantly , but addition of CNTs has little influence on the elastic modulus. In addition, the extent of crack propagation under a similar load level becomes considerably lower for the concrete samples reinforce by longer CNTs.

This paper develops a model based on an original lumped-parameter network configuration for the thermal transient analysis of a permanent magnet synchronous motor (PMSM). The specific PMSM was designed and optimized for a demanding aerospace application. The validity of the proposed lumped-parameter model is verified by measurements carried out in a thermal chamber.

This paper proposes a three-phase five legged wound transformer core constructed of two high permeability Si-Fe wound cores and two conventional Si-Fe wound cores. The two large internal wound cores are manufactured of high permeability, grain-oriented electrical steel. The two small outer wound cores are manufactured of conventional, grain-oriented electrical steel. The specific arrangement is based on experimental evidence concerning the peak flux density non-uniformity of the typical three-phase five legged wound transformer core, constructed of the high magnetization grain-oriented steel. Since the peak flux density of the two outer cores is lower than the two internal cores, low cost, low permeability, conventional grain-oriented electrical steel can \ be used for the outer cores. Losses, excitation currents, flux waveforms, and their harmonics contents are presented in this paper. A comparison of the mixed three-phase transformer core and the typical one is also carried out.

Purpose – This paper aims to present an accurate representation of laminated wound cores with a low computational cost using 2D and 3D finite element (FE) method.
Design/methodology/approach – The authors developed an anisotropy model in order to model laminated wound cores. The anisotropy model was integrated to the 2D and 3D FE method. A comparison between 2D and 3D FE techniques was carried out. FE techniques were validated by experimental analysis.
Findings – In the case of no-load operation of wound core transformers both 2D and 3D FE techniques yield the same results. Computed and experimental local flux density distribution and no-load loss agree within 2 per cent to 6 per cent.
Originality/value – The originality of the paper consists in the development of an anisotropy model specifically formulated for laminated wound cores, and in the effective representation of electrical steels using a composite single-valued function. By using the aforementioned techniques, the FE computational cost is minimised and the 3D FE analysis of wound cores is rendered practical.

This paper introduces a novel technique for iron loss minimization of wound core transformers. The proposed technique involves the evaluation of appropriate design variables of wound cores constructed by a combination of standard and high magnetization grade steel. The evaluation of the optimum design variables of the multiple grade lamination wound core is achieved by combining a permeability tensor finite-element model and simulated annealing with restarts.

Introduction: Torque of the maxillary incisors is essential in esthetics and proper occlusion, while torque expression is influenced by many factors. The aim of this finite element study was to assess the relative effect of tooth morphology, bracket prescription, and bracket positioning on tooth displacement and developed stresses/strains after torque application. Methods: A three-dimensional upper right central incisor with its periodontal ligament (PDL) and alveolus was modelled. The tooth varied in the crown–root angle (CRA) between 156°, 170°, and 184°. An 0.018-inch slot discovery® (Dentaurum, Ispringen, Germany) bracket with a rectangular 0.018 × 0.025-inch β-titanium wire was modelled. Bracket torque prescription varied between 0°, 12°, and 22°, with bracket placement at the centre of the middle, gingival or incisal third of the crown. A total of 27 models were generated and a buccal root torque of 30° was applied. Afterwards, crown and apex displacement, strains in the PDL, and stresses in the bracket were calculated and analysed statistically. Results: The palatal crown displacement was significantly affected by bracket positioning (up to 94 per cent), while the buccal apex displacement was significantly affected by bracket prescription (up to 42 per cent) and bracket positioning (up to 23 per cent). Strains in the PDL were affected mainly by CRA (up to 54 per cent), followed by bracket positioning (up to 45 per cent). Finally, bracket prescription considerably affected the stresses in the bracket (up to 144 per cent). Limitations: These in silico results need to be validated in vivo before they can be clinically extrapolated. Conclusion: Tooth anatomy and the characteristics of the orthodontic appliance should be considered during torque application.

Transformer no load loss optimization is crucial for transformer manufacturers as well as for electric utilities, since it results to significant economic benefits. In this article, the three-dimensional finite element analysis is applied to power transformers in order to predict and minimize the iron loss. The proposed model is based on a particular reduced scalar potential formulation, necessitating no prior source field calculation, and employs detailed modeling of the core geometry and material, considering for manufacturing core formation process effects by convenient hysteresis phenomenological models. Comparisons between this method and test values for a number of commercial transformers, prove its validity and accuracy, rendering it a reliable tool for customized design of an industrial plant

This paper investigates the effects of rotor skew on the performance of permanent magnet synchronous generators. The main effects are concerning reduction of the electromotive force induced, stator current harmonics and torque ripple. The analysis performed is based on various 2D and 3D finite element techniques. Simulation results are compared to measurements.

Erosion of ductile materials by waterjet machining is still a complex phenomenon. This paper presents a finite element model of the waterjet machining (WJM) process. Cutting forces, deformations and stresses occurring in the workpiece material in the vicinity of the cutting interface as a result of erosion impact by the waterjet could be obtained. The results indicate that the finite element method is a useful tool in the analysis of this process. Further research work is currently being conducted by the authors.

In this study, the boundary element method-finite element method (BEM-FEM) model is employed to investigate the sloshing and flexibility terms of elastic submerged structures on the behavior of a coupled domain. The methods are finite element and boundary elements which are utilized for structural dynamic and sloshing modeling, respectively. The applied models are used to assess dynamic parameters of a fluid-structure system. Based on the proposed model, a code is developed which can be applied to an arbitrary two-and three-dimensional tank with an arbitrarily shaped elastic submerged structure. Results are validated based on the existing methods represented in the literature and it is concluded that the absolute relative deviation is lower than 2%. Finally, the interactive influences of submerged components which are more meaningful are investigated. ARTICLE HISTORY KEYWORDS fluid-structure interaction; boundary element method (BEM); reduced order modeling; submerged elastic structure; finite element method (FEM)

The importance of distribution transformer no-load loss on the operation of modern electrical grids is often underestimated. Internationally, distribution transformer no-load loss constitutes nearly 25% of the transmission and distribution losses of electrical grids. The losses in European Union distribution transformers are estimated at about 33 TWh/year whereas, reactive power and harmonic losses add a further 5 TWh/year. In the Greek electrical grid the no-load losses of 140,000 distribution transformers are estimated at about 490 GWh/year. This paper has two goals the first one is to illustrate the significance of distribution transformer no-load loss in periods of high electric energy cost and the second goal is the presentation of a novel numerical methodology for wound core transformers no-load loss analysis, enabling to determine the economically and technically optimum transformer for every use.

The paper presents a three-dimensional finite element (3D FEM) anisotropy model, based on a particular scalar potential formulation, for the no load loss evaluation of wound core shell type distribution transformers. The specific 3D FEM anisotropy model is combined with a hybrid finite element-boundary element (FEM-BE) model, used for the calculation of the transformer’s short circuit impedance, and various optimization algorithms in order to minimize the total owing cost (TOC) of a distribution transformer.

In this paper, a Stable Generalized/eXtended Finite Element Method (SGFEM) is combined with mesh adap-tivity for the robust and computationally efficient simulation of mixed-mode brittle fracture propagation. Both h-refinement around the fracture front and p-enrichment of the analysis domain are used to control discretization errors. A Linear Elastic Fracture Mechanics (LEFM) model based on Grif-fith's criterion is adopted. LEFM scaling relations are used at each fracture propagation step to back calculate SIFs that meet Griffith's criterion. As a result, no iterations are necessary to find loading scaling parameters or fracture size that meet Griffith's criterion. The method is validated against several experimental data sets for mode I and mode I+II fracture propagation problems. Very good agreement between SGFEM and experimental results are observed. These include fracture path, Crack Opening Displacement (COD), and load and fracture length versus COD curves. The computational efficiency of the method is also assessed.

Recent studies demonstrated an association between atypical femoral fracture (AFF) and long-term bisphosphonate (BP) use for osteoporosis treatment. Due to BP treatment, bone undergoes alterations including increased microcrack density and reduced tissue compositional heterogeneity. However, the effect of these changes on the fracture response of bone is not well understood. As a result, the goal of the current study is to evaluate the individual and combined effects of microcracks and tissue compositional heterogeneity on fracture resistance of cortical bone using finite element modeling (FEM) of compact tension (CT) specimen tests with varying microcrack density, location, and clustering, and material heterogeneity in three different bone samples. The simulation results showed that an increase in microcrack density improved the fracture resistance irrespective of the local material property heterogeneity and microcrack distribution. A reduction in material property heterogeneity adversely affected the fracture resistance in models both with and without microcracks. When the combined changes in microcrack density and tissue material property heterogeneity representing BP treatment were evaluated, the models corresponding to BP-treated bone demonstrated reduced fracture resistance. The simulation results also showed that although microcrack location and clustering, and microstructure significantly influenced fracture resistance, the trends observed on the effect of microcrack density and tissue material property heterogeneity did not change. In summary, these results provide new information on the interaction of microcracks, tissue material property heterogeneity, and fracture resistance and may improve the understanding of the influence of mechanical changes due to prolonged BP use on the fracture behavior of cortical bone.

This paper presents the life estimation of the diffuser structure. Literature shows that the welds are the source of failure in case of welded structure; hence the estimation of its life is very critical. There are two kinds of methods for life estimation stress life approach and strain life approach which have been validated for simple problems. Stress life approach was identified as appropriate for life estimation of the variable diffuser. There are papers indicating the methodology for life estimation using commercial software for life prediction. Here, OptistructHyper-Works for pre-processing and solver and Hyper-ViewHyper-Works for post processing has been used for the indeterminate structure, complex loading and boundary condition. The mathematical model subjected to the variable pressure contours for a particular Mach No., with the gimbal joint boundary condition at the test section end and the roller support at the other end. In this paper stress and fatigue analysis of the ...

Erosion of ductile materials by waterjet machining is still a complex phenomenon. This paper presents a finite element model of the waterjet machining (WJM) process. Cutting forces, deformations and stresses occurring in the workpiece material in the vicinity of the cutting interface as a result of erosion impact by the waterjet could be obtained. The results indicate that the finite element method is a useful tool in the analysis of  this process. Further research work is currently being conducted by the authors.

Even though, the flux distribution at joints of stacked type transformer cores has been  investigated thoroughly many issues remain unclear in the case of wound transformer cores. The  paper addresses this lack of information by longitudinal and normal flux measurements at step-lap  joints of Si-Fe wound cores. Flux measurements are verified by an original finite element analysis  where the necessary excitation is performed by means of a pseudo-source. The advantage of the  proposed technique is the accurate estimation of the flux distribution at step-lap joints, with a two  dimensional model of simple geometry and low computational cost, by using any commercial finite  element code.

The iron loss and manufacturing cost of a strip-wound core can be reduced by constructing the wound core with  combination of average and high magnetization grade steel. The present paper introduces a two-dimensional finite element (2D FEM) package for the flux density distribution and iron loss computation of two grade lamination wound cores. The specific 2D FEM package is combined with deterministic and stochastic optimization algorithms in order to compute specific design variables of a two grade lamination wound core, that ensure the minimization of its iron loss and manufacturing cost.

Evaluation of Slope stability is one of the day-today practices of geotechnical engineers. Nowadays, different methods are available to evaluate the stability of a particular slope. Despite the advances that have been made in site exploration, evaluating the stability of slopes remains a challenge. Recently, Ethiopia has been trying to construct a newly planned railway routes to connect the country's development centers and link with ports of neighboring countries. However, this newly planned railway routes will pass in the heart of highly fragile mountainous terrains and earthquake prone regions. Therefore, the prime objective of this paper is to investigate the stability of the railway embankment by using three different stochastic approaches (First Order Reliability Method, Point Estimate Method and Monte Carlo Simulation) with commercially available finite element and finite difference programs. Moreover, the seismic response of the railway Vol. 22 [2017], Bund. 01 52 embank...

This article presents a modeling approach to estimate the energy release due to ductile crack initiation in conjunction to the energy dissipation associated with the formation and propagation of transient stress waves typically referred to as Acoustic Emission. To achieve this goal, a ductile fracture problem is investigated computationally using the Finite Elements Method based on a compact tension geometry under Mode I loading conditions. To quantify the energy dissipation associated with Acoustic Emission, a crack increment is produced given a predetermined notch size in a 3D cohesive-based extended finite element model. The computational modeling methodology consists of defining a damage initiation state from static simulations and linking such state to a dynamic formulation used to evaluate wave propagation and related energy redistribution effects. The model relies on a custom traction separation law constructed using full field deformation measurements obtained experimentally using the Digital Image Correlation method. The amount of energy release due to the investigated first crack increment is evaluated through three different approaches both for verification purposes and to produce an estimate of the portion of the energy that radiates away from the crack source in the form of transient waves. The results presented herein propose an upper bound for the energy dissipation associated to Acoustic Emission, which could assist the interpretation and implementation of relevant nondestructive evaluation methods and the further enrichment of the understanding of effects associated with fracture.

Iron losses of grain-oriented electrical steels, is sensitive to the distortion of the supply voltage waveform of the excitation winding. As a result, magnetic cores of electrical machines and transformers manufactured of grain-oriented electrical steels present significant increase of iron losses when working under distorted supply voltage waveform. In the present paper, an experimental apparatus is developed in order to evaluate the effect of distorted supply voltage
waveform on iron losses of grain-oriented electrical steels. Also, a  theoretical analysis based on the hysteresis design tool of Matlab and the finite element method considering hysteresis is carried out.

An XFEM multiscale approach is adopted in order to investigate the mechanical properties and fracture behavior of carbon nanotube reinforced concrete specimen. At the nanoscale, molecular dynamics simulation is used to find the mechanical properties of carbon nanotube (CNTs). Afterwards, a hydration model is adopted to find the chemical composition of cement paste. The hydrated model and CNTs are then converted into a finite element mesh for further analysis. Finally, at the meso scale the fracture behavior of the CNT reinforced concrete is simulated by the XFEM approach. The results indicate that the fracture energy of samples with similar volume fractions but reinforced by longer CNTs increase significantly , but addition of CNTs has little influence on the elastic modulus. In addition, the extent of crack propagation under a similar load level becomes considerably lower for the concrete samples reinforce by longer CNTs.

Recent studies demonstrated an association between atypical femoral fracture (AFF) and long-term bisphosphonate (BP) use for osteoporosis treatment. Due to BP treatment, bone undergoes alterations including increased microcrack density and reduced tissue compositional heterogeneity. However, the effect of these changes on the fracture response of bone is not well understood. As a result, the goal of the current study is to evaluate the individual and combined effects of microcracks and tissue compositional heterogeneity on fracture resistance of cortical bone using finite element modeling (FEM) of compact tension (CT) specimen tests with varying microcrack density, location, and clustering, and material heterogeneity in three different bone samples. The simulation results showed that an increase in microcrack density improved the fracture resistance irrespective of the local material property heterogeneity and microcrack distribution. A reduction in material property heterogeneity a...

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from Keywords Strain gradient plasticity · Extended finite element method · Crack tip fields · Material length scale · MATLAB

The paper introduces a finite element methodology for the magnetic field analysis of transformer joints. The proposed technique consists in the application of certain boundary conditions for the excitation of the joints region. The main advantages of the pseudo-source technique include minimization of the computational cost and ease of implementation. Longitudinal and normal flux measurements were carried out for the validation of the proposed technique.