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This paper considers correction aspects of computer communication networks modelling with emphasis on their performance evaluation. In general, the problem is to achieve the highest possible performance given constraints on the system.

The paper reviews the application of the analytical methods, based on the queueing theory, to the computer communication systems and makes an extension of theory to the improvement of the developed analytical models. In this sense the paper describes the derivation of a correction factor for analytical models to study more precise their basic parameters (end‐to‐end delay, performance, etc.).

The contribution is in incorporating the derived correction factor to account for the real non‐exponential nature of the input to the transmission channels of computer communication systems. The produced results by corrected analytical model are compared with results previously reported in the literature to estimate the magnitude of improvement.

The improved analytical models were tested under various ranges of parameters, which influence the architecture of the computer communication networks and which are important for practical use.

The rapid rate of growth of computer‐based communication systems (e.g. distributed computer networks, mobile data networks) has resulted in a renewed and intensive interest in this area. Efficient design of their service facilities leads to the sharing of resources among users. Such public shared networks are largely oversubscribed by independent users, which make random demands on the network resources. The optimal resource allocation to satisfy such demands and the proper settlement of contention when demands exceed the capacity of the resources, constitute the problem of being able to understand and to predict system behaviour.

To behaviour analysis we can use both analytical and simulation methods. Modelling and simulation are methods, which are commonly used by performance analysts to represent constraints and optimise performance. Principally the application of analytical queuing theory results belongs to the preferred method in comparison to the simulation method, because of their ability to analyse also very large networks.

The purpose of this study was to investigate the changes in solder joint stress when subjected to mechanical bending. The analytical theory pertaining to the stresses in the solder joint between the components (including the molding compound, the chip and the substrate) was described, and the printed circuit board (PCB) with a discontinuity function when the PCB assembly is subjected to mechanical bending was developed. Thus, the findings reported here may lead to a better understanding of the solder joint failure based on the Physics of Failure model.

This paper discusses the analytical model for calculating the stress in solder joints, as well as presents a simulation model that can be used for calculating the strain energy density of solder joint. First, the multilayer plate theory is used in discussing the composite material for the component, including the molding compound, the silicon chip and the substrate, or the PCB, including the copper layers, the fiber and the epoxy. Finally, the complete structure of the analytical model developed as a part of this current work is presented.

For the analytical model of multilayer structures in which the interconnection layer is discrete, mechanical bending has been modeled with respect to varying silicon chip length. The analytical model that describes the stress of the outermost solder joint experiences is chosen, as this is the typical solder joint failure. The analytical model can be applied to discrete solder joints, which are evaluated by calculating the matrix form. Owing to its use of the matrix equation, the analytical model can be highly combinatorial and thus more capable of calculating the solution.

The analytical solution based on a simple concept was presented and validated using the finite element model for the stress experienced by solder joints subjected to mechanical bending. To verify that the simulation represents a real PCB case, the authors use the finite element method (FEM) to compare their case with the multilayer plate theory. Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

The analytical model is validated with the FEM model and provides the way to physically examine the solder joint failure mechanism. In this paper, the analytical model is developed as a means to assess the solder joint stress subjected to mechanical bending.

The analytical model treats the solder joint as discrete and has been successfully validated against the finite element model. The complete structure model (the second analytical model) is presented to discuss the effects of varying silicon chip length on the normal stress in solder joints. When the silicon chip length exceeds to 80 per cent of the total package length, the stress of the outermost solder joint increases rapidly. The design analysis findings have suggested that the failure of the outermost solder joint subjected to mechanical bending on the PCB assembly can be reduced by analyzing the analytical model.

The purpose of this study is to propose an analytical model with consideration of the permeability of soft-magnetic materials, which can predict the magnetic field distribution more accurately and facilitate the initial design and parameter optimization of the machine.

This paper proposes an analytical model of stator yokeless radial flux dual rotor permanent magnet synchronous machine (SYRFDR-PMSM) with the consideration of magnetic saturation of soft-magnetic material. The analytical model of SYRFDR-PMSM is divided into seven regions along the radial direction according to the different excitation source and magnetic medium, and the iron permeability in each region is considered based on the Maxwell–Fourier method and Cauchy’s product theorem. The magnetic vector potential of each region is obtained by the Laplace’s or Poisson’s equation, and the magnetic field solution is determined using the boundary conditions of adjacent regions.

The inner and outer air-gap flux density, flux linkage, output torque, etc., of SYRFDR-PMSM are predicted by analytical model, resulting in good agreement with that of finite element model. Additionally, the SYRFDR-PMSM prototype is manufactured and the correctness of analytical model is further verified by experiments on no-load back electromotive force and current–torque curve. Reasonable design of the slot opening width and pole arc coefficient can improve the average output torque and reduce output torque ripple.

The analytical model proposed in this paper assumes that the permeability of soft-magnetic material is a fixed value. However, the actual iron’s permeability varies nonlinearly; thus, the prediction results of the analytical model will have some deviations from the actual machine.

The main contribution of this paper is to propose an accurate magnetic field analytical model of SYRFDR-PMSM. It takes into account the permeability of soft-magnetic material and slot opening, which can quickly and accurately predict the electromagnetic performance of SYRFDR-PMSM. It can provide assistance for the initial design and optimization of SYRFDR-PMSM.

To reduce the computational costs for electromagnetic simulations of permanent magnet synchronous machines maintaining a high accuracy.

An analytical model is introduced regarding multiple designs of permanent magnet synchronous machines. This electromagnetic model is coupled to a numerical simulation. Thereby, the advantages of both computational methods are combined by parameterizing the analytical model to the numerical solution. This results in a high‐efficient analytical model with the accuracy of the numerical simulation. The results of the analytical model are compared to measurements of a permanent magnet synchronous machine. Various machine modifications are simulated to evaluate possible limitations of the analytical model.

It can be stated, that a once parameterized analytical model achieves a high accuracy. Furthermore, geometric variations can be applied without the need of a new parameterization through a numerical simulation. Only changing the permanent magnet height or the air gap height results in a significant deviation and a new numerical simulation is recommended.

Only measurements for machines up to 5 kW were available. In consequence, the model is only validatet in this range.

With the presented analytical model, an electromagnetic design of a permanent magnet synchronous machine can be performed very time efficient achieving accurate results. Furthermore, optimization studies can be performed with low‐computational costs.

The introduced analytical model can be parameterized by a numerical simulation. The numeric simulation process and the parameterization are performed automatically according to the data calculated by the analytical model. Measurements demonstrate the effectiveness and the limitations of the model.

The machine design with optimization method using analytical models is efficient to evaluate a large number of variables because these models are faster to solve. Nevertheless, the validation of the final optimal solution by FE simulation often shows that some specification constraints are not verified. To solve the problem, it is possible to apply a hybrid approach for the design method while combining analytical methods and 3D FE simulations to compensate analytical model errors. The paper addresses this.

Each intermediate optimal solution is evaluated by FE simulation to quantify the analytical model errors. Correction coefficients are derived from this evaluation and another optimization process is performed. With this method, the convergence of the hybrid optimal design process is obtained with a limited number of FE simulations.

This study shows that it is possible to compensate errors of analytical models with a limited number of 3D field calculations during a global optimization design process. The 3D FE software validates the optimal solution but this solution is also a function of the sensitivity of analytical models that is not improved by the correction method.

This error compensation of analytical models using FE simulations can be applied for the design of a wide range of electromagnetic devices with optimization methods.

This paper presents a correction method that guaranteed the validity of the solution after the optimization process when analyzed with a FE software.

As new computer communication systems, such as distributed computer networks or mobile data networks, grow in scale and complexity, the problem of being able to understand and to predict system behaviour becomes increasingly important. To their behaviour analysis we can use both analytical and simulation methods. Principally the application of analytical queuing theory results belongs to the preferred method in comparison to the simulation method. In this sense the article describes the development, realisation and verification of the new analytical model for the study of the basic parameters (end‐to‐end delay, performance etc.) of distributed data networks (computer networks, mobile data networks). The suggested model considers for every node of the data network one part for its own node's activities (communication functions) and another one for the modelling of each node channel for data transmission. When using a multiprocessor system, as the modern node communication processor, the model for its own node activities is the more realistic M/D/r system (Poisson arrival process/Deterministic service time distribution/r server system) and for the every node transmission channel the M/M/1 system (Exponential service time, Single server system). The new developed analytical model includes the influence of the communication functions to the whole delay in each node of a computer communication network. The achieved results of the developed model are compared with the results of the commonly used analytical and simulation models to estimate the magnitude of improvement. Likewise the developed analytical model was tested under various ranges of parameters, which influence the architecture of the distributed data networks and which are important for practical use.

This paper aims to present new analytical model for the filling times prediction in flip-chip underfill encapsulation process that is based on the surface energetic for post-bump flow.

The current model was formulated based on the modified regional segregation approach that consists of bump and post-bump regions. Both the expansion flow and the subsequent bumpless flow as integrated in the post-bump region were modelled considering the surface energy–work balance.

Upon validated with the past underfill experiment, the current model has the lowest root mean square deviation of 4.94 s and maximum individual deviation of 26.07%, upon compared to the six other past analytical models. Additionally, the current analytically predicted flow isolines at post-bump region are in line with the experimental observation. Furthermore, the current analytical filling times in post-bump region are in better consensus with the experimental times as compared to the previous model. Therefore, this model is regarded as an improvised version of the past filling time models.

The proposed analytical model enables the filling time determination for flip-chip underfill process at higher accuracy, while providing more precise and realistic post-bump flow visualization. This model could benefit the future underfill process enhancement and package design optimization works, to resolve the productivity issue of prolonged filling process.

The analytical underfill studies are scarce, with only seven independent analytical filling time models being developed to date. In particular, the expansion flow of detachment jump was being considered in only two previous works. Nonetheless, to the best of the authors’ knowledge, there is no analytical model that considered the surface energies during the underfill flow or based on its energy–work balance. Instead, the previous modelling on post-bump flow was based on either kinematic or geometrical that is coupled with major assumptions.

The purpose of this study is to develop an analytical model that is capable of predicting the behavior of shear endplate beam-column assemblies when exposed to fire, taking into account the thermal creep effect.

An analytical model is developed and validated against finite element (FE) models previously validated against experimental tests in the literature. Major material and geometrical parameters are incorporated in the analysis to investigate their influence on the overall response of the shear endplate assembly in fire events.

The analytical model can predict the induced axial forces and deflections of the assembly. The results show that when creep effect is considered explicitly in the analysis, the beam undergoes excessive deformation. This deformation needs to be taken into account in the design. The results show the significance of thermal creep effect on the behavior of the shear endplate assembly as exposed to various fire scenarios.

However, the user-defined constants of the creep equations cannot be applied to other connection types. These constants are limited to shear endplate connections having the material and geometrical parameters specified in this study.

The importance of the analytical model is that it provides a time-effective, simple and comprehensive technique that can be used as an alternative to the experimental tests and numerical methods. Also, it can be used to develop a design procedure that accounts for the transient thermal creep behavior of steel connections in real fire.

Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode.

The proposed model is based on the multi-layer models with the convolution theorem (i.e. Cauchy’s product theorem) by using complex Fourier’s series and the separation of variables method. This technique takes into the different thermal conductivities of the machine parts. The heat sources are determined by calculating the different power losses in the PMSM with the finite-element method (FEM).

To validate the proposed analytical model, the analytical results are compared with those obtained by thermal FEM. The comparisons show good results of the proposed model.

A new 2D analytical model based on the PDE in steady-state for full prediction of temperature distribution in the PMSM takes into account the heat transfer by conduction, convection and radiation.

The purpose of this study is to evaluate the capability and performance of analytical models to predict the structural mechanical behaviour of parts fabricated by fused deposition modelling (FDM).

A total of eight existing and newly proposed analytical models, tailored to satisfy the structural behaviour of FDM parts, are evaluated in terms of their capability to predict the ultimate tensile stress (UTS) and the elastic modulus (E) of parts made of polylactic acid (PLA) by the FDM process. This evaluation is made by comparing the structural properties predicted by these models with the experimental results obtained from tensile tests on FDM specimens fabricated with variable infill percentage, perimeter layers and build orientation.

Some analytical models are able to predict with high accuracy (prediction errors smaller than 5%) the structural behaviour of FDM and categories of similar additive manufactured parts. The most accurate model is Gibson’s and Ashby, followed by the efficiency model and the two new proposed exponential and variant Duckworth models.

The study has been limited to uniaxial loading conditions along three different build orientations.

The structural properties of FDM parts can be predicted by analytical models based on the process parameters and material properties. Product engineers can use these models during the design for the additive manufacturing process.

Existing methods to estimate the structural properties of FDM parts are based on experimental tests; however, such methods are time-consuming and costly. In this work, the use of analytical models to predict the structural properties of FDM parts is proposed and evaluated.