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The aim of this paper is to provide a simple yet accurate and efficient geometric method for thermal homogenization of impregnated and non-impregnated coil winding technologies based on the concept of thermal resistance.

For regular windings, the periodic microscopic cell in the winding space is identified. Also, for irregular windings, the average microscopic cell of the winding is determined. An approximation is used to calculate the thermal resistance of the winding cell. Based on this approximation, the winding insulation is considered as a circular ring around the wire. Mathematical equations are obtained to calculate the equivalent thermal resistance of the cell. The equivalent thermal conductivity of the winding is calculated using equivalent thermal resistance of the cell. Winding thermal homogenization is completed by determining the equivalent thermal properties of the cell.

The thermal pattern of different windings is simulated and compared with the results of different homogenization methods. The results show that the proposed method is applicable for a wide range of windings in terms of winding scheme, packing factor and winding insulation. Also, the results show that the proposed method is more accurate than other winding homogenization methods in calculating the equivalent thermal conductivity of the winding.

In this paper, the change of electrical resistance of the winding with temperature and thermal contact between the sub-components are ignored. Also, liquid insulators, such as oils, and rectangular wires were not investigated. Research in these topics is considered as future work.

Unlike other homogenization methods, the proposed method can be applied to non-impregnated and irregular windings. Also, compared to other homogenization methods, the proposed method has a simpler formulation that makes it easier to program and implement. All of these indicate the efficiency of the proposed method in the thermal analysis of the winding.

The purpose of this study is to develop a homogenization approach that ensures both high accuracy and time-efficient solution for elastic-plastic functionally graded composites.

The paper presents a novel two-stage hybrid homogenization approach that combines advantages of the mean field homogenization and homogenization based on the finite element method (FEM). The groundbreaking nature of the developed approach is associated with division of the hybrid homogenization procedure into two stages, which allows to very efficiently determine the solution for arbitrary volume fraction of the reinforcement. This paper concerns also on modelling of composites with randomly distributed prolate and oblate particles. For this purpose, the hybrid homogenization was implemented in the framework of the discrete orientation averaging procedure involving pseudo-grain discretization method.

Agreement between the results obtained using the proposed approach and the standard FEM-based homogenization is very good (up to the volume fraction of 0.3).

The proposed two-stage homogenization approach allows to obtain the solution for materials with arbitrary volume fraction of the reinforcement very efficiently; therefore, it is highly beneficial for the two-scale modeling of nonlinear functionally graded materials and structures.

Effectiveness of the homogenization method for various heat transfer problems of engineering composites is the main aim of the paper. This comparative study is done for layered, fiber and particle reinforced Representative Volume Elements (RVE) for composites made of widely used components. Mathematical model is based on the effective modules method introduced for periodic composites ‐ effective heat conductivity is calculated in the closed form for specific spatial distribution of the components, while effective volumetric heat capacity is obtained from a simple spatial averaging. Such a homogenization scheme makes possible to significantly simplify the numerical analysis of transient heat transfer phenomena in various types of composites. The comparison of temperature histories obtained for the real and homogenized composite models is carried out using the Finite Element Method system ANSYS. As is demonstrated for various boundary problems, a homogenization technique in terms of composites types collected in the paper give satisfactory agreement with the real structure modeling; further numerical studies on composite cells discretization should increase modeling efficiency and diminish the numerical errors.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

In this paper, a homogenization‐based multi‐scale method for predicting the effective thermal conductivity of porous materials with radiation is presented, which considers the effect of geometry and distribution of pores. Using homogenization method to solve the pure conductive problem of porous materials with periodic structure, the effective thermal conductivity without considering radiation is predicted, and a temperature field in a local domain of a unit cell is obtained. This temperature field is taken as the good approximation of the real temperature distribution, and the radiative thermal conductivity is obtained. The effect of the microstructure, the distribution and geometry of pores on heat transfer of porous materials is discussed. It is concluded that the dimension of the pores is an important influence factor on the thermal transfer property of porous materials if radiation is considered. Increasing the pore’s dimension enhances the contribution of radiation to the heat transfer property of porous materials. For porous materials with cylindrical and spherical pores, the radiative thermal conductivity is proportional to pore’s diameter.

The purpose of this paper is to propose a general approach for the frequency‐domain homogenization of electromagnetic periodic structures. The method allows calculating macroscopic equivalent properties including local effects. It is based on the equivalence of active and reactive electromagnetic powers on an elementary cell. This work is applied to the modelling of eddy current losses in windings, by the use of the finite element method in 2D and 3D.

The approach is based on an homogenization technique, allowing describing local properties (permeability and conductivity) and local effects (eddy currents) of periodical structures, through macroscopic homogenized behaviour laws.

It was found that the presence of local loops of eddy currents at the local scale implies that the average values of the electric and magnetic field are different from the macroscopic fields. This implies some precautions to implement the homogenization. Furthermore, the question of the coupling of the macroscopic laws has been clarified.

The proposed method is limited to the frequency domain. Some additional work is necessary to extend the researches in the time domain.

The proposed methodology is applied for determining losses in coils with the finite element method. The major interest of the method is that it allows taking into account local effects (losses in particular), with a reduced computational time.

The method proposed in this paper is general and clarifies the principle of homogenization in the case of periodical structure in presence of local eddy currents (local loops of current).

Using finite element (FE) method corrects the microstress field resulting from the theory of homogenization in the region of composite in vicinity of the boundary. Obtains the corrected microstress field via an unsmearing procedure based on the known global solution and local peturbation. Analyses two examples: near a free boundary and next to a constrained border. FE models are constructed using both commercial FE code and the authors’ program for homogenization with some interfacing procedures. Shows qualitative results of computations and estimates influence on the microstress description of the local perturbation near the boundary.

Three-dimensional (3D) mesh generation for shape optimizations needs long computational time. This makes it difficult to perform 3D shape optimizations. The purpose of this paper is to present a new meshing method with light computational cost for 3D shape optimizations.

This paper presents a new meshing method on the basis of nonconforming voxel finite element method. The 3D mesh generation is performed with light computational cost keeping the computational accuracy.

It is shown that the computational cost for 3D mesh generation can be reduced without deteriorating numerical accuracy in the FE analysis. It is reported the performance of the present method.

The validity of the nonconforming voxel elements is tested to apply it to the optimization of 3D optimizations.

This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM).

The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied.

A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze.

By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance.

This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

The purpose is to analyze the mechanical behavior of the arterial wall in the degraded region of the arterial wall and to determine the stress distribution, as an important factor for predicting the potential failure mechanisms in the wall. In fact, while the collagen fiber degradation process itself is not modeled, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed. To do so, a local weakness in the media layer is considered by defining representative volume elements (RVEs) with different fiber collagen contents in the degraded area to investigate the mechanical response of the arterial wall.

A three-dimensional (3D) large strain hierarchical multiscale technique, based on the homogenization and genetic algorithm (GA), is utilized to numerically model collagen fiber degradation in a typical artery. Determination of material constants for the ground matrix and collagen fibers in the microscale level is performed by the GA. In order to investigate the mechanical degradation, two types of RVEs with different collagen contents in fibers are considered. Each RVE is divided into two parts of noncollagenous matrix and collagen fiber, and the part of collagen fiber is further divided into matrix and collagen fibrils.

The von Mises stress distributions on the inner and outer surfaces of the artery and the influence of collagen fiber degradation on thinning of the arterial wall in the degraded area are thoroughly studied. Comparing the maximum stress values on outer and inner surfaces in the degraded region shows that the inner surface is under higher stress states, which makes it more prone to failure. Furthermore, due to the weakness of the artery in the degraded area, it is concluded that the collagen fiber degradation considerably reduces the wall thickness in the degraded area, leading to an observable local inflation across the degraded artery.

Considering that little attention has been paid to multiscale numerical modeling of collagen fiber degradation, in this paper a 3D large strain hierarchical multiscale technique based on homogenization and GA methods is presented. Therefore, while the collagen fiber degradation process itself is not modeled in this study, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed.