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This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

The purpose of this paper is to develop a new and fast three-dimensional (3D) analytical model to study a synchronous axial magnetic coupling with rectangular shaped magnets. This model takes into account edge and curvature 3D effects.

This paper firstly introduces a 3D analytical model for an axial coupler with sector shaped permanent magnet (PM) based on magnetic scalar potential formulation in cylindrical coordinates. The magnetic field in PM, air gap and iron disks is computed by solving Laplace’s and Poisson’s partial differential equation. This solution is then used to compute the field in rectangular shaped magnets. To do so, the adopted approach consists to divide the rectangular magnet into sector radial slices each of which the 3D model allows the determination of the magnetic field distribution. The results obtained by the proposed 3D analytical model are validated through 3D finite element computations. Furthermore, a prototype axial magnetic coupler has been constructed so air gap flux density and static torque measurements are compared to the analytical predictions.

The results obtained by the analytical model show the effectiveness of the proposed geometry transformation approach. The developed model takes into account all the 3D effects without needing any correction factor.

The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process.

The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process.

A new and fast 3D analytical model, to improve the computation of the electromagnetic torque developed by a synchronous magnetic coupler with rectangular shaped magnets, has been developed. The proposed approach is really effective as it leads to consistent results when compared to 3D finite element method ones without any need for correction factor.

3D bulk image effects in high‐NA lens lithography are studied through 3D exposure and development simulations by applying a Mack model to the 3D exposure process.

This paper aims to evaluate the mechanical behaviour of polycarbonate/acrylonitrile butadiene styrene (PC/ABS) filaments for fusion filament fabrication (FFF). PC/ABS have emerged as a promising material for FFF due to their excellent mechanical properties. However, the optimal processing conditions and the effect of the blending ratio on the mechanical properties of the resulting workpieces are still unclear.

A statistical factorial matrix was designed, including infill pattern, printing speed, nozzle size, layer height and printing temperature as factors (with three levels). A total of 810 workpieces were printed using PC/ABS blends filament with the FFF. The workpieces’ finishing and mass were evaluated. Tensile tests were performed. Analysis of variance was performed to determine the main effects of the processing conditions on the mechanical properties.

The results showed that the PC/ABS (70/30) exhibited higher tensile. Tensile rupture corresponded to 30% of the tensile strength. The infill pattern showed the highest contribution to the responses. The concentric pattern showed higher tensile strength. Tensile strength and mass ratio demonstrated the influence of mass on tensile strength. The influence of printing parameters on deformation depended on the blend proportions. Higher printing speed and lower layer height provided better quality workpieces.

This study has implications for the design and manufacturing of three-dimensional printed parts using PC/ABS filaments. An extensive experimental matrix was applied, aiming at a complete understanding of mechanical behavior, considering the main printing parameters and combinations not explored by literature.

The purpose of this paper is to determine the validity of using classical laminated plate theory to predict strain concentration factors in notched laminates under bending.

The objective was accomplished by comparing results predicted by classical theory to those from more refined theories that incorporate transverse shear and other 3D effects in the analysis. Three notch sizes and two laminate types were considered. The results were obtained through finite element analysis.

Strain concentration factors predicted by the classical theory were generally found to be significantly lower than those predicted by the more refined theories. However, these differences tended to be very localized to the vicinity of the notch tip.

This study points out a potential deficiency in a commonly used design tool. The seriousness of this deficiency can best be determined by further research, particularly through a systematic testing program.

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a three‐dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two‐dimensional (2D) cavity.

The second‐order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25‐4) and Reynolds numbers (0.01‐1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier‐Stokes (NS) equations and with available experimental data.

The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side‐walls in transverse direction (in 3D), due to which the vorticity in the core‐region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry‐plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid‐motion are observed; these are weak at low Reynolds numbers, but become quite strong at high Reynolds numbers.

The findings will be useful in the study of variety of enclosed fluid flows.

The purpose of this paper is to develop a novel method for establishing the mathematical link between the restored Hogarth curve and the golden ratio, and to advance the potential application of the Hogarth curves in standardization of the garment pattern design by using this method.

The Hogarth curve was fully restored by using the plant design system (PDS) software package and divided the restored curve into two fragments based on the intersection point between the curve and the straight line joining the curve endpoints. The ratios between two fragments of curves and straight lines were calculated and compared with the golden ratio, respectively, which was set as a normalized value. The potential application of the restored Hogarth curves in the normalization of the garment pattern design was therefore studied by using the standard mannequins.

The ratio in the most beautiful curve, i.e., the fourth Hogarth curve, was found to be infinitely approaching to the golden ratio. Furthermore, the incorporation of the Hogarth curves into the garment pattern design demonstrated that the fourth Hogarth curve was the most aesthetic line.

This work offered a novel method for bridging the gaps between arts and maths, i.e., the mathematical relation between the Hogarth curves and the golden ratio. Such a method will provide the protocol to promote the potential applications of the Hogarth curves in the garment pattern design and the human body decoration.

This study aims to perform flow simulations inside the acinus with fine alveolar pores (Kohn pores) using hexagonal cells and bottom-up geometric modeling, which enabled the elimination of invalid voids using previous top-bottom methods and spherical or circular cells.

Regular hexagonal cells were used to construct alveoli with no gaps via tessellation. Some hexagonal cells were fused to eliminate the inner boundaries to represent the structure of the bronchial tree. For the remaining hexagonal cells, the side lengths of the shared walls were adjusted to construct alveolar pores. Periodic moving boundaries with the same phase were set for all walls to describe synchronous contraction and expansion of the bronchi and alveoli.

More realistic flow characteristics in the distal lung were obtained. The effects of pore size and the mechanism of auxiliary ventilation of alveolar pores were revealed.

To the best of the authors’ knowledge, this is the first numerical simulation study on the function of multiple alveolar pores at the level of pulmonary acini, which will be helpful for simulating the dynamic process of cough and sputum excretion in the future.

The purpose of this study is to develop a novel comprehensive three-dimensional computational model to predict the transient thermal behavior and residual stresses resulting from the layer-by-layer deposition in the direct metal laser sintering process.

In the proposed model, time integration is performed with an implicit scheme. The equations for heat transfer are discretized by a finite volume method with thermophysical properties of the metal powder and an updated convection coefficient at each time step. The model includes convective and radiative boundary conditions for the exposed surfaces of the part and constant temperatures for the bottom surface on the build plate. The laser source is modeled as a moving radiative heat flux along the scanning pattern, while the thermal gradients are used to calculate directional and von Mises residual thermal stresses by using a quasi-steady state assumption.

In this study, four different scanning patterns are analyzed, and the transient temperature and residual thermal stress fields are evaluated from these patterns. It is found that the highest stresses occur where the laser last leaves off on its scanning pattern for each layer.

The proposed model is designed to capture the layer-by-layer deposition for a three-dimensional geometry while considering the effect of the instantaneous melting of the powder, melt pool, dynamic calculation of thermophysical properties, ease of parametrization of various process parameters and the vectorization of the code for computational efficiency. This versatile model can be used for process parameter optimization of other laser powder bed fusion additive manufacturing techniques. Furthermore, the proposed approach can be used for analyzing different scanning patterns.

The use of three-dimensional virtual worlds (3DVWs) is increasingly becoming a common practice in language education to provide digital learning environments for second-language (L2) communicative classes. This study aimed to identify the key factors underlying communication in 3DVWs that can improve the communication skills of L2 learners.

To achieve this, exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) were conducted to validate the identified factors affecting communication in 3DVWs. A self-reported questionnaire with 47 items on a five-point Likert scale was administered to 513 pre-service teachers, teachers and lecturers in the field of language education.

The results of the EFA revealed four factors that contribute to communication in 3DVWs, namely learner motivation, interaction pattern, language development and learner autonomy. CFA results provided support for the updated model, with statistically significant Chi-square results (χ² (df = 83) = 181.049, p < 0.001) indicating a good fit between the model and the data.

The findings suggest that the four EFA-derived parameters are valid and can assist instructional designers and L2 instructors in creating 3DVWs that enhance L2 learners' communication abilities. This study provides valuable insights for educators, instructional designers and researchers in the field of language education and technology-enhanced learning.