Mixed and hybrid formulations for the three-dimensional magnetostatic problem

2001 ◽  
Vol 18 (1) ◽  
pp. 85-104 ◽  
Author(s):  
C. Daveau ◽  
J. Laminie
Keyword(s):  
Three Dimensional ◽  
Magnetostatic Problem

A novel direct resolution method for coupled systems in finite element analysis

2020 ◽  
Vol 39 (5) ◽  
pp. 1271-1280
Author(s):  
Youcef Boutora ◽  
Noureddine Takorabet
Keyword(s):  
Finite Elements ◽  
Linear Systems ◽  
Symmetric Matrix ◽  
Direct Method ◽  
Three Dimensional ◽  
Coupled Systems ◽  
Resolution Method ◽  
Element Analysis ◽  
Content Type ◽  
Magnetostatic Problem

Purpose This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems. Design/methodology/approach The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method. Findings The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices. Research limitations/implications This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems. Originality/value The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.

scholarly journals Estimation of Magnetic Field Growth and Construction of Adaptive Mesh in Corner Domain for the Magnetostatic Problem in Three-Dimensional Space

2018 ◽  
Vol 173 ◽  
pp. 03019
Author(s):  
Eugene Perepelkin ◽  
Aleksandr Tarelkin
Keyword(s):  
Magnetic Field ◽  
Smooth Boundary ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Field Growth ◽  
Magnetostatic Problem ◽  
Research Facilities ◽  
The Magnetic Field ◽  
Three Dimensional Space

A magnetostatics problem arises when searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundary-value problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require consideration of the solution behavior in the corner domain. In this work we obtained an upper estimation of the magnetic field growth using integral formulation of the magnetostatic problem and propose a method for condensing the differential mesh near the corner domain of the vacuum in the three-dimensional space based on this estimation.

Three-dimensional magnetostatic problem

1999 ◽  
Vol 46 (1) ◽  
pp. 117-130 ◽  
Author(s):  
B. Bandelier ◽  
C. Daveau ◽  
J. Laminie ◽  
S. M. Mefire ◽  
F. Rioux-Damidau
Keyword(s):  
Three Dimensional ◽  
Magnetostatic Problem

Free-Form Design of Electrical Machine Rotor Cores for Production Using Additive Manufacturing

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Michele Garibaldi ◽  
Christopher Gerada ◽  
Ian Ashcroft ◽  
Richard Hague
Keyword(s):  
Structural Integrity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Free Form ◽  
Electrical Machine ◽  
Element Analysis ◽  
Torque Density ◽  
Magnetostatic Problem ◽  
Form Design ◽  
3D Printed

This work presents a finite element analysis-based, topology optimization (TO) methodology for the combined magnetostatic and structural design of electrical machine cores. Our methodology uses the Bi-directional Evolutionary Structural Optimization (BESO) heuristics to remove inefficient elements from a meshed model based on elemental energies. The algorithm improves the average torque density while maintaining structural integrity. To the best of our knowledge, this work represents the first effort to address the structural-magnetostatic problem of electrical machine design using a free-form approach. Using a surface-mounted permanent magnet motor (PMM) as a case study, the methodology is first tested on linear and nonlinear two-dimensional problems whereby it is shown that the rapid convergence achieved makes the algorithm suitable for real-world applications. The proposed optimization scheme can be easily extended to three dimensions, and we propose that the resulting designs are suitable for manufacturing using selective laser melting, a 3D printing technology capable of producing fully dense high-silicon steel components with good soft magnetic properties. Three-dimensional TO results show that the weight of a PMM rotor can be slashed by 50% without affecting its rated torque profile when the actual magnetic permeability of the 3D-printed material is considered.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document