P. Alotto, P. Molfino, G. Molinari, M. Nervi and R. Orlando
In this paper a code for the solution of nonlinear thermo‐magnetic problems, arising in the transient analysis of thermal and electromagnetic fields in resistive toroidal field…
Abstract
In this paper a code for the solution of nonlinear thermo‐magnetic problems, arising in the transient analysis of thermal and electromagnetic fields in resistive toroidal field coils of tokamak devices, is presented. A formulation based on the electric vector potential T and the magnetic total scalar potential Ψ for the analysis of the thermo‐magnetic skin effect phenomenon in the toroidal field coils of proposed tokamaks has been used, and the results obtained are reported, reviewed and discussed.
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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…
Abstract
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.
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Federico Delfino, Andrea Manella, Paolo Molfino and Mansueto Rossi
The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated…
Abstract
The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.
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Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed”…
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Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed” formulations have been elusive up to now. We propose one, based on a particular gauge, div(σ α)=−σ 2μ v, close to the “Lorenz gauge” of several recent publications, but not identical if one does not assume a piecewise uniform conductivity.
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Iveta Petrasova, Václav Kotlan, Lenka Šroubová, Pavel Karban and Ivo Doležel
The purpose of this paper is to present the calibration of a laser welding model suitable for solving problems with input data that are either unknown or known only approximately.
Abstract
Purpose
The purpose of this paper is to present the calibration of a laser welding model suitable for solving problems with input data that are either unknown or known only approximately.
Design/methodology/approach
The calibration starts from the measured temperature profile of the weld, and the aim is to get a similar profile by the solution of the model. The corresponding procedure is based on replacing the material characteristics that are known only approximately by polynomial or rational functions whose coefficients are determined using a suitable optimization process. The algorithm is supplemented with a simplified model of the keyhole shape.
Findings
The big advantage of the proposed approach is the velocity of solution of the problem and low consumption of the sources (hardware and software). In comparison with solving the full model of laser welding, the methodology provides results of a still acceptable accuracy by several orders faster. On the other hand, the results also depend on the strategy of selecting the points at which the temperature is verified and on “manual” setting of the deformation parameters.
Research limitations/implications
Application of the methodology is conditioned by several experiments with the used material (without experiment it is impossible to carry out the calibration and set the shape of the keyhole), while the full model allows it. On the other hand, the full model is not able to predict the errors in the case when some input data is unknown or known only approximately and the results have to be also confirmed experimentally.
Practical implications
The presented methodology may be used for determining unknown material characteristics and faster modelling of laser welding.
Originality/value
This paper proposes a novel methodology for evaluation of quality of laser welds in cases of unknown or partially unknown material parameters and substantial acceleration (by 2-3 orders) of the numerical solution of the model of laser welding.
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P. Alotto and I. Perugia
An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation…
Abstract
An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation minimises the residual of the constitutive equation, and exactly imposes Maxwell’s equations with Lagrange multipliers. Finite elements satisfying the physical continuity properties for both the magnetic and the magnetic induction fields are used in the numerical approximation. The possibility of decoupling the formulation in two separate sets of equations is discussed. A preconditioned iterative method to solve the final algebraic linear system is presented. Finally, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure.
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The purpose of this paper is to demonstrate how Monte Carlo methods can be applied to the solution of field theory problems.
Abstract
Purpose
The purpose of this paper is to demonstrate how Monte Carlo methods can be applied to the solution of field theory problems.
Design/methodology/approach
This objective is achieved by building insight from Laplacian field problems. The point solution of a Laplacian field problem can be viewed as the solid angle average of the Dirichlet potentials from that point. Alternatively it can be viewed as the average of the termination potential of a number of random walks. Poisson and Helmholtz equations add the complexity of collecting a number of packets along this walk, and noting the termination of a random walk at a Dirichlet boundary.
Findings
When approached as a Monte Carlo problem, Poisson type problems can be interpreted as collecting and summing source packets representative of current or charge. Helmholtz problems involve the multiplication of packets of information modified by a multiplier reflecting the conductivity of the medium.
Practical implications
This method naturally lends itself to parallel processing computers.
Originality/value
This is the first paper to explore random walk solutions for all classes of eddy current problems, including those involving velocity. In problems involving velocity, the random walk direction enters depending on the walk direction with respect to the local velocity.
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Marco Cioffi, Alessandro Formisano and Raffaele Martone
The role of the parameters uncertainness in the optimal design of electromagnetic devices is discussed and an efficient strategy to look for robustness of feasible solutions is…
Abstract
The role of the parameters uncertainness in the optimal design of electromagnetic devices is discussed and an efficient strategy to look for robustness of feasible solutions is proposed. A suitable modification of the objective function (OF) is used to rank different device configurations on the basis of their ability to maintain the required performances against small parameters modifications due to construction tolerances. In the frame of a genetic algorithm approach, the modified OF has been able to address the evolutionary optimisation towards more robust solutions.
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E. Schlemmer, W. Harb, J. Schoenauer and F. Mueller
In this paper, stochastic optimisation and risk estimation techniques are applied to the problem of hydroelectric generator design. Optimisation results from deterministic…
Abstract
In this paper, stochastic optimisation and risk estimation techniques are applied to the problem of hydroelectric generator design. Optimisation results from deterministic simulations can involve considerable risks due to unavoidable variations in system properties as well as environmental conditions. Therefore, stochastic simulation is used to include the effects of parameter scatter and noise effects in the computer models. This allows the evaluation of the scatter in performance and thus an assessment of reliability and quality of the simulated system.
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P. Alotto, P. Molfino and G. Molinari
The common approach to continuous and discrete optimisation problems in electromagnetics does not take into account uncertainties and variations of the design variables. Local…
Abstract
The common approach to continuous and discrete optimisation problems in electromagnetics does not take into account uncertainties and variations of the design variables. Local sensitivity analysis is usually performed only after the optimisation run to study the behaviour of the objective function in the neighbourhood of the optimum. However, this procedure may prove inefficient if the optimum has to be rejected due to sensitivity considerations and a new run has then to be performed. In this paper an alternative approach, which takes into account uncertainties in the design variables and physical data, is presented, and an analytical function is used to highlight the features of the proposed method. The essence of the technique is to couple the optimisation with a series of worst case analyses which are embedded in the optimisation loop. The method is fully general and can be applied to any optimisation method. The additional computational costs associated with the procedure maybe relatively high, but in the authors’ opinion the obtained gains in user confidence in the solution and the computational savings in some cases far offset the possible drawbacks of the method.