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Physical phenomena interact with each other in ways that one cannot be analyzed without considering the other. To account for such interactions between multiple phenomena, partitioning has become a widely implemented computational approach. Partitioned analysis involves the exchange of inputs and outputs from constituent models (partitions) via iterative coupling operations, through which the individually developed constituent models are allowed to affect each other’s inputs and outputs. Partitioning, whether multi-scale or multi-physics in nature, is a powerful technique that can yield coupled models that can predict the behavior of a system more complex than the individual constituents themselves. The paper aims to discuss these issues.

Although partitioned analysis has been a key mechanism in developing more realistic predictive models over the last decade, its iterative coupling operations may lead to the propagation and accumulation of uncertainties and errors that, if unaccounted for, can severely degrade the coupled model predictions. This problem can be alleviated by reducing uncertainties and errors in individual constituent models through further code development. However, finite resources may limit code development efforts to just a portion of possible constituents, making it necessary to prioritize constituent model development for efficient use of resources. Thus, the authors propose here an approach along with its associated metric to rank constituents by tracing uncertainties and errors in coupled model predictions back to uncertainties and errors in constituent model predictions.

The proposed approach evaluates the deficiency (relative degree of imprecision and inaccuracy), importance (relative sensitivity) and cost of further code development for each constituent model, and combines these three factors in a quantitative prioritization metric. The benefits of the proposed metric are demonstrated on a structural portal frame using an optimization-based uncertainty inference and coupling approach.

This study proposes an approach and its corresponding metric to prioritize the improvement of constituents by quantifying the uncertainties, bias contributions, sensitivity analysis, and cost of the constituent models.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

Highly anisotropic zirconium is a material used in the cladding of nuclear fuel rods, ensuring containment of the radioactive material within. The complex material structure of anisotropic zirconium requires model developers to replicate not only the macro-scale stresses but also the meso-scale material behavior as the crystal structure evolves; leading to strongly coupled multi-scale plasticity models. Such strongly coupled models can be achieved through partitioned analysis techniques, which couple independently developed constituent models through an iterative exchange of inputs and outputs. Throughout this iterative process, biases, and uncertainties inherent within constituent model predictions are inevitably transferred between constituents either compensating for each other or accumulating during iterations. The paper aims to discuss these issues.

A finite element model at the macro-scale is coupled in an iterative manner with a meso-scale viscoplastic self-consistent model, where the former supplies the stress input and latter represents the changing material properties. The authors present a systematic framework for experiment-based validation taking advantage of both separate-effect experiments conducted within each constituent’s domain to calibrate the constituents in their respective scales and integral-effect experiments executed within the coupled domain to test the validity of the coupled system.

This framework developed is shown to improve predictive capability of a multi-scale plasticity model of highly anisotropic zirconium.

For multi-scale models to be implemented to support high-consequence decisions, such as the containment of radioactive material, this transfer of biases and uncertainties must be evaluated to ensure accuracy of the predictions of the coupled model. This framework takes advantage of the transparency of partitioned analysis to reduce the accumulation of errors and uncertainties.

The purpose of this paper is to extend statistical energy analysis (SEA)‐like modeling to fluid‐structure coupled systems.

An equivalent approach of aerodynamic loads is applied to a SEA‐like modeling of a panel‐cavity coupled system with rain‐on‐the‐roof excitation. Two aerodynamic excitations are presented: turbulent boundary layer (TBL) and diffuse field excitation. The energetic description of the coupled system is studied with both aerodynamic excitations, taking in account the coincidence effects. In order to extent the approach to more general systems, some parameters of the coupled system are also modified and the accuracy of the coupled system modeling is investigated.

The boundary conditions of the panel and the coupling strength between the panel and the cavity have been modified. As it was expected, the accuracy of equivalent approach is shown to be independent of such modifications. The interest of such calculation is thus highlighted: modelings of systems and aerodynamic excitations are independent, and can be treated separately.

This result is interesting in the space industry, for launch vehicles are excited by different types of random excitations. Those excitations can be modeled by SEA‐like with low calculation time and memory and applied to a unique system modeling.

The purpose of this paper is to propose an analytical model for estimating propagation delay in coupled resistance-inductance-capacitance (RLC) interconnects.

With higher frequency of operation, longer length of interconnect and fast transition time of the signal, the resistor capacitor (RC) models are not sufficient to estimate the delay accurately. To mitigate this problem, accurate delay models for coupled interconnects are required. In this paper, an analytical model for estimation of interconnect delay is developed for simultaneously switching lines. Two distributed RLC lines coupled inductively and capacitively are considered. To validate the proposed model, SPICE results are compared with the proposed analytical results. Each line in the coupled structure is terminated by a capacitive load of 30fF. The driving signal is considered symmetrical with equal rise and fall time of 5 ps and OFF/ON time of 45 ps. The model is validated for both in-phase and out of phase switching of lines.

It is observed that the model works well for both the phases of inputs switching. The derived expressions of delay exhibit complete physical insight, and the results obtained are in excellent agreement with SPICE results. Comparison of analytical delay with SPICE delay shows an average error of < 2.7 per cent.

The analytical expressions for interconnect delay are derived for the first time under simultaneously switching scenario. This model is useful to estimate delay across the inductively and capacitively coupled interconnects.

Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

To develop new and existing coupled thermal and mechanical models of electromagnetic solids for the simulation of coupled field problems based on a consistent theoretical and computational framework.

The finite element computational models we describe involve the combination of classical electrodynamics, continuum mechanics, and thermodynamics. In order to create consistent coupled models, we employ the fundamental principles of thermodynamics as a common framework.

Our procedure requires the necessary thermodynamical considerations for building consistent multiphysics models and develops some novel implementation issues that are important from the designers' point of view. Additionally, efficient numerical algorithms for solving the arising static and dynamic nonlinearities are discussed.

The paper targets the simulation of coupled problems in macroscopic electromagnetic continua.

The application areas of the coupled field models are identified and illustrated by the solution of complex industrial problems.

We introduce new computational models and techniques for the solution of some coupled field problems in electromagnetic solids. While some elements of these computational models and techniques have been used for decades, the complete theoretical and computational framework is presented for the first time here.

The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation.

The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis.

This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation.

The presentation of winding functions allows to generically describe the coupling, embed the circuit equations into the de Rham complex and visualize them by Tonti diagrams. This is of value for scientists interested in differential geometry and engineers that work in the field of numerical simulation of field-circuit coupled problems.

This paper aims to use a scaling approach to scale the solutions of a beforehand-simulated finite element (FE) solution of an induction machine (IM). The scaling procedure is coupled to an analytic three-node-lumped parameter thermal network (LPTN) model enabling the possibility to adjust the machine losses in the simulation to the actual calculated temperature.

The proposed scaling procedure of IMs allows the possibility to scale the solutions, particularly the losses, of a beforehand-performed FE simulation owing to temperature changes and therefore enables the possibility of a very general multiphysics approach by coupling the FE simulation results of the IM to a thermal model in a very fast and efficient way. The thermal capacities and resistances of the three-node thermal network model are parameterized by analytical formulations and an optimization procedure. For the parameterization of the model, temperature measurements of the IM operated in the 30-min short-time mode are used.

This approach allows an efficient calculation of the machine temperature under consideration of temperature-dependent losses. Using the proposed scaling procedure, the time to simulate the thermal behavior of an IM in a continuous operation mode is less than 5 s. The scaling procedure of IMs enables a rapid calculation of the thermal behavior using FE simulation data.

The approach uses a scaling procedure for the FE solutions of IMs, which results in the possibility to weakly couple a finite element method model and a LPTN model in a very efficient way.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.