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

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.

Express Diagnostic Method of the Stress State of Weakly Magnetized Ferromagnetic Rods

A method for express diagnostics of weakly magnetized ferromagnetic rods is proposed. It is based on measuring the stray magnetic field of the rod. We analyze the inverse magnetostatic problem and formulate the conditions when its regularization is possible. In this case, it is possible to connect the value of the average transverse component of magnetization with the results of the measured stray magnetic field. The distributions of transverse magnetization values were experimentally studied using rods made of SV08G2S [transliterated from Russian] and ER-308LSi steels as an example. The studied samples were subjected to impact plastic deformation, tensile deformation, and torsion deformation. It is shown that this method allows to register areas with stress concentrations without additional magnetization of the test sample. A feature of the method is the use of once calculated system functions without solving large systems of equations and using unstable spectral methods. The method is applicable for cylindrical objects of small radius far from the edge of the test sample, when the magnetization in the cross section of the sample can be considered as constant.

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

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.

Estimation of Magnetic Field Growth and Construction of Adaptive Mesh in Corner Domain for the Magnetostatic Problem in 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.