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This paper aims to propose and establish a set of new benchmark models to investigate and confidently validate the modeling and prediction of total stray-field loss inside magnetic and non-magnetic components under harmonics-direct current (HDC) hybrid excitations. As a new member-set (P21^e) of the testing electromagnetic analysis methods Problem 21 Family, the focus is on efficient analysis methods and accurate material property modeling under complex excitations.

This P21^e-based benchmarking covers the design of new benchmark models with magnetic flux compensation, the establishment of a new benchmark measurement system with HDC hybrid excitation, the formulation of the testing program (such as defined Cases I–V) and the measurement and prediction of material properties under HDC hybrid excitations, to test electromagnetic analysis methods and finite element (FE) computation models and investigate the electromagnetic behavior of typical magnetic and electromagnetic shields in electrical equipment.

The updated Problem 21 Family (V.2021) can now be used to investigate and validate the total power loss and the different shielding performance of magnetic and electromagnetic shields under various HDC hybrid excitations, including the different spatial distributions of the same excitation parameters. The new member-set (P21^e) with magnetic flux compensation can experimentally determine the total power loss inside the load-component, which helps to validate the numerical modeling and simulation with confidence. The additional iron loss inside the laminated sheets caused by the magnetic flux normal to the laminations must be correctly modeled and predicted during the design and analysis. It is also observed that the magnetic properties (B27R090) measured in the rolling and transverse directions with different direct current (DC) biasing magnetic field are quite different from each other.

The future benchmarking target is to study the effects of stronger HDC hybrid excitations on the internal loss behavior and the microstructure of magnetic load components.

This paper proposes a new extension of Problem 21 Family (1993–2021) with the upgraded excitation, involving multi-harmonics and DC bias. The alternating current (AC) and DC excitation can be applied at the two sides of the model’s load-component to avoid the adverse impact on the AC and DC power supply and investigate the effect of different AC and DC hybrid patterns on the total loss inside the load-component. The overall effectiveness of numerical modeling and simulation is highlighted and achieved via combining the efficient electromagnetic analysis methods and solvers, the reliable material property modeling and prediction under complex excitations and the precise FE computation model using partition processing. The outcome of this project will be beneficial to large-scale and high-performance numerical modeling.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Because the nanocrystalline core is widely used in power electronic equipment, and the excitation waveform of its working mode is complex, the vibration at medium and high frequencies cannot be ignored. Therefore, this study aims to study the vibration mechanism of nanocrystalline strip and the vibration characteristics of nanocrystalline magnetic ring under different excitation waveforms.

First, the electromagnetic vibration mechanism between nanocrystalline strips is analyzed by finite element analysis, and the force of the magnetic ring with and without air gap is compared and analyzed. Then, the vibration of nanocrystalline magnetic ring under different excitation waveforms such as sine wave, triangular wave, symmetric rectangular wave and asymmetric rectangular wave is analyzed by experimental method. The acceleration time domain waveform measured by the experiment is analyzed by fast Fourier transform, and the vibration is analyzed according to the spectrum.

Because of the increase of magnetic flux leakage, the volume force density and the Maxwell force on the surface of the nanocrystalline magnetic ring will increase after the air gap is opened, resulting in the intensification of vibration. Under symmetric/asymmetric rectangular wave excitation, the vibration acceleration varies with the duty cycle. Due to the influence of harmonic excitation, the relationship between the main frequency of vibration and the excitation frequency is not two times, and its multiple decreases with the increase of excitation frequency.

The research and analysis of this paper can promote the application of new magnetic materials in electrical equipment in small and medium-sized and medium- to high-frequency fields.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This paper aims to develop a model that reflects the current transformer (CT) core materials nonlinearity. The model enables simulation and analysis of the CT excitation current that includes the inductive magnetizing current and the resistive excitation current.

A nonlinear CT model is established with the magnetizing current as the solution variable. This model presents the form of a nonlinear differential equation and can be solved discretely using the Runge–Kutta method.

By simulating variations in the excitation current for different primary currents, loads and core materials, the results demonstrate that enhancing the permeability of the B–H curve leads to a more significant improvement in the CT ratio error at low primary currents.

The proposed model has three obvious advantages over the previous models with the secondary current as the solution variable: (1) The differential equation is simpler and easier to solve. Previous models contain the time differential terms of the secondary current and excitation flux or the integral term of the flux, making the iterative solution complicated. The proposed model only contains the time differential of the magnetizing current. (2) The accuracy of the excitation current obtained by the proposed model is higher. Previous models calculate the excitation current by subtracting the secondary current from the converted primary current. Because these two currents are much greater than the excitation current, the error of calculating the small excitation current by subtracting two large numbers is greatly enlarged. (3) The proposed model can calculate the distorted waveform of the excitation current and error for any form of time-domain primary current, while previous models can only obtain the effective value.

To understand the behavior of the magnetization processes in ferromagnetic materials in function of temperature, a temperature-dependent hysteresis model is necessary. This study aims to investigate how temperature can be accounted for in the energy-based hysteresis model, via an appropriate parameter identification and interpolation procedure.

The hysteresis model used for simulating the material response is energy-consistent and relies on thermodynamic principles. The material parameters have been identified by unidirectional alternating measurements, and the model has been tested for both simple and complex excitation waveforms. Measurements and simulations have been performed on a soft ferrite toroidal sample characterized in a wide temperature range.

The analysis shows that the model is able to represent accurately arbitrary excitation waveforms in function of temperature. The identification method used to determine the model parameters has proven its robustness: starting from simple excitation waveforms, the complex ones can be simulated precisely.

As parameters vary depending on temperature, a new parameter variation law in function of temperature has been proposed.

A complete static hysteresis model able to take the temperature into account is now available. The identification is quite simple and requires very few measurements at different temperatures.

The results suggest that it is possible to predict magnetization curves within the measured range, starting from a reduced set of measured data.

The purpose of this paper is to perform experimental tests on fatigue characteristics of chip scale package (CSP) assembly under vibration. Some suggestions for design to prolong fatigue life of CSP assembly are provided.

The CSP assembly which contains different package structure modes and chip positions was manufactured. The fatigue characteristics of CSP assembly under vibration were tested. The fatigue load spectrum of CSP assembly was developed under different excitation. The fatigue life of chips can be estimated by using the high-cycle fatigue life formula based on different stress conditions. The signal–noise curve shows the relationship between fatigue life and key factors. The design strategy for improving the fatigue life of CSP assembly was discussed.

The CSP chip has longer fatigue life than the ball grid array chip under high cyclic strain. The closer to fixed point the CSP chip, the longer fatigue life chips will have. The chip at the edge of the printed circuit board (PCB) has longer fatigue life than the one in the middle of the PCB. The greater the excitation imposed on the assembly, the shorter the fatigue life of chip.

It is very difficult to set up a numerical approach to illustrate the validity of the testing approach because of the complex loading modes and the complex structure of CSP assembly. The research on an accurate mathematical model of the CSP assembly prototype is a future work.

It builds a basis for high reliability design of high-density CSP assembly for engineering application. In addition, vibration fatigue life prediction method of chip-corner solder balls is deduced based on three-band technology and cumulative damage theory under random vibration so as to verify the accuracy of experimental data.

This paper fulfils useful information about the dynamic reliability of CSP assembly with different structural characteristics and material parameters.

This paper aims to derive a simple and effective but still a reasonably accurate model for electromagnetic problems with hysteretic magnetic properties and/or induced currents in heterogeneous regions in 2D, meant particularly for non‐destructive testing (NDT) of steel cables by eddy‐currents.

It is assumed that the diffusion of electromagnetic fields in a heterogeneous cable, which consists of many strands, can be described by the Maxwell equations with periodically oscillating coefficients. A computationally efficient model can then be derived. The idea behind this is to replace the heterogeneous material in the cross‐section by a fictitious homogeneous one, whose behaviour at the macroscopic level is a good approximation of the one of the composite material. Such a homogenized model is obtained by employing the two‐scale convergence.

The model is validated based on experimental electromagnetic data from a steel cable (measured magnetic hysteresis loops) to show that the model is applicable for NDT of cables. The model is useful for studying NDT of cables, both for excitation at low frequency (where changes in magnetic properties are investigated) and at higher frequency (eddy current testing). It is valid for a wide range of amplitudes and frequencies.

From the mathematical point of view the model incorporated a non‐local boundary condition that has to be included in the analysis. From the engineering point of view, by solving an inverse problem based on this model and on measured hysteresis loops at several frequencies, a broader range of defects in the cable can be detected.

Under different ground motion excitation modes, the spatial coupling effect of seismic response for the arch bridge with thrust, seismic weak parts and the internal force components of the control section of main arch ribs are analyzed.

Taking a 490 m deck type railway steel truss arch bridge as the background, the dynamic calculation model of the whole bridge was established by SAP2000 software. The seismic response analyses under one-, two- and three-dimension (1D, 2D and 3D) uniform ground motion excitations were carried out.

For the steel truss arch bridge composed of multiple arch ribs, any single direction ground motion excitation will cause large axial force in the chord of arch rib. The axial force caused by transverse and vertical ground motion excitation in the chord of arch crown area is 1.4–3.6 times of the corresponding axial force under longitudinal seismic excitation. The in-plane bending moment caused by the lower chord at the vault is 4.2–5.5 times of the corresponding bending moment under the longitudinal seismic excitation. For the bottom chord of arch rib, the arch foot is the weak part of earthquake resistance, but for the upper chord of arch rib, the arch foot, arch crown and the intersection of column and upper chord can all be the potential earthquake-resistant weak parts. The normal stress of the bottom chord of the arch rib under multidimensional excitation is mainly caused by the axial force, but the normal stress of the upper chord of the arch rib is caused by the axial force, in-plane and out of plane bending moment.

The research provides specific suggestions for ground motion excitation mode and also provides reference information for the earthquake-resistant weak part and seismic design of long-span deck type railway steel truss arch bridges.

The purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.

In a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

An overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.

The uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.