Summary of Results for Problem 20 (3‐d Static Force Problem)

Takahashi, Norio; Nakata, T.; Morishige, Haruo

doi:10.1108/eb010138

Cited by 23 publications

(5 citation statements)

References 3 publications

(1 reference statement)

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“…As expected nested MG is especially for large scaled problems considerably faster than conventional approaches. In order to verify the calculation scheme, the TEAM pro- blem #20 was calculated with the nonlinear permeablity given in [8]. In Table III the computed magnetic force f mag to the pole was compared to measurement.…”

Section: Numerical Resultsmentioning

confidence: 99%

Nested multigrid methods for the fast numerical computation of 3D magnetic fields

Schinnerl¹,

Schöberl

Kaltenbacher³

2000

IEEE Trans. Magn.

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This paper deals with the numerical solution of static as well as transient 3D magnetic field problems. Thereby, a finite element method (FEM) with the magnetic vector potential as field variable and a discretisation with edge elements is used. For the efficient solution of the obtained matrix equation system a nested geometrical multigrid solver (MG) is presented, which reduces the solution time considerably. Numerical simulations demonstrate the superiority of the proposed method versus conventional solving strategies.

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Section: Numerical Resultsmentioning

confidence: 99%

Nested multigrid methods for the fast numerical computation of 3D magnetic fields

Schinnerl¹,

Schöberl

Kaltenbacher³

2000

IEEE Trans. Magn.

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“…Performing the partial derivations in (27), note that, by definition, the remaining quantities are constant. The expression for the force becomes:…”

Section: A Force Calculationmentioning

confidence: 99%

“…14) coincide well with the measurement from the official results. [27] The dynamic simulations are conducted with an excitation function that forms a smooth step.…”

Section: B Reference Simulationmentioning

confidence: 99%

Computing Forces by ECSW-Hyperreduction in Nonlinear Magnetodynamic FEM Problems

Maierhofer,

Rixen

2024

IEEE Trans. Magn.

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This contribution proposes a novel strategy to apply the hyperreduction principle for the mechanical force calculation of non-linear magnetodynamic problems in a FEM context. The already established Energy Conserving Sampling and Weighting (ECSW) Method is therefore adapted to exploit the structure of mechatronic systems, so the hyperreduction is only applied to the non-linear domain. It is consequently named partial hyperreduction, here the pECSW. Also, the force calculation is formulated such that ECSW is applied as sampling-based integration. The force computation requires a new element sampling and weighting process, here called cECSW, arising from the configurational updates of the geometry corresponding with the possible motions of the mobile part. The advantage is the possibility of avoiding treating the full-order model for the force calculation. Storing the reduced order model with two element sets for field and force calculation is sufficient. The strategy is demonstrated on the TEAM20 problem of the Compumag benchmark systems, which is extended to dynamic excitation. The new methods show the ability to produce accurate results for significantly smaller systems.

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“…Benchmark problem 20 for the TEAM Workshop [41] is a 3D nonlinear magneto-static problem, as shown in Fig. 8.…”

Section: Team Problem 20mentioning

confidence: 99%

A triangular prism solid and shell interactive mapping element for electromagnetic sheet metal forming process

Cui

She

Feng

et al. 2017

Journal of Computational Physics

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In this paper, a novel triangular prism solid and shell interactive mapping element is proposed to solve the coupled magnetic-mechanical formulation in electromagnetic sheet metal forming process. A linear six-node "Triprism" element is firstly proposed for transient eddy current analysis in electromagnetic field. In present "Triprism" element, shape functions are given explicitly, and a cell-wise gradient smoothing operation is used to obtain the gradient matrices without evaluating derivatives of shape functions. In mechanical field analysis, a shear locking free triangular shell element is employed in internal force computation, and a data mapping method is developed to transfer the Lorentz force on solid into the external forces suffered by shell structure for dynamic elasto-plasticity deformation analysis. Based on the deformed triangular shell structure, a "Triprism" element generation rule is established for updated electromagnetic analysis, which means inter-transformation of meshes between the coupled fields can be performed automatically. In addition, the dynamic moving mesh is adopted for air mesh updating based on the deformation of sheet metal. A benchmark problem is carried out for confirming the accuracy of the proposed "Triprism" element in predicting flux density in electromagnetic field. Solutions of several EMF problems obtained by present work are compared with experiment results and those of traditional method, which are showing excellent performances of present interactive mapping element.

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Summary of Results for Problem 20 (3‐d Static Force Problem)

Cited by 23 publications

References 3 publications

Nested multigrid methods for the fast numerical computation of 3D magnetic fields

Nested multigrid methods for the fast numerical computation of 3D magnetic fields

Computing Forces by ECSW-Hyperreduction in Nonlinear Magnetodynamic FEM Problems

A triangular prism solid and shell interactive mapping element for electromagnetic sheet metal forming process

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