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A stable nodal integration method for static and quasi-static electromagnetic field computation

JOURNAL OF COMPUTATIONAL PHYSICS 2017年 336卷 580-594页

作者： Feng, Hui Cui, Xiangyang Li, Guangyao Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Joint Ctr Intelligent New Energy Vehicle Shanghai 201804 Peoples R China

A stable nodal integration method (SNIM) is presented to solve static and quasi-static electromagnetic problems in this paper. The analysis domain is firstly discretized into a set of triangular or tetrahedral elements, and linear interpolation is adopted within each element. A weakened weak formulation based on the nodes is further considered, framing the so-called node-based smoothing domains. Equivalent smoothing domains are then acquired as circular or spherical regions, where the gradient of shape function is expanded as the first order Taylor form. Subsequently, four or six temporary integration points on the region are picked to obtain items of the stiffness matrix and the external load vector. By simplifying the equations, the stiffness matrix can be received in quite concise form with one point integration and stabilization terms, which are calculated on original node based smoothing domains. The implementation of SNIM on electromagnetic problems is thus realized. The proposed formulation is validated against both analytical solutions and traditional methods, and its effectiveness and potentialities can be well represented and clarified by numerical examples. (C) 2017 Elsevier Inc. All rights reserved.

关键词： stable nodal integration method Computational electromagnetics Node-based smoothed finite element method Linear triangular or tetrahedral mesh

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Coupled-field simulation of electromagnetic tube forming process using a stable nodal integration method

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2017年 128卷 332-344页

作者： Feng, H. Cui, X. Y. Li, G. Y. Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Joint Ctr Intelligent New Energy Vehicle Shanghai 201804 Peoples R China

This paper proposes a stable nodal integration method for analyzing coupling problems of electromagnetic field and mechanical field using linear triangular mesh. For transient electromagnetic field analysis, the node-based smoothed solution is firstly formulated to compute system matrices, and then the equivalent smoothing domain and temporal integration points are constructed to achieve a stable nodal integration method (SNIM), whose coefficient matrix is finally computed using the smoothed shape function derivatives together with the variance terms over the equivalent smoothing domain associated with nodes of the mesh. For dynamic large-deformation analysis, the node-based smoothed finite element method (NS-FEM) is utilized after testifying its stability and effectiveness in thin-walled structures of electromagnetic forming (EMF) process. Furthermore, by treating the morphing region as a static mechanical problem, a weighted elastomer method is presented to accomplish the mesh updating in sequential coupling simulation. Finally, it turns out that the proposed methodologies can be applied successfully to simulate EMF process, and numerical examples for both tube bulging and tube compression are investigated to demonstrate the validity, accuracy and efficiency of the proposed methods. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： stable nodal integration method Electromagnetic tube forming Coupled-field simulation Transient electromagnetic field analysis Dynamic large-deformation analysis

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An electromagnetic forming analysis modelling using nodal integration axisymmetric thin shell

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JOURNAL OF MATERIALS PROCESSING TECHNOLOGY 2017年 244卷 62-72页

作者： Li, She Cui, Xiangyang Feng, Hui Wang, Gang Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 PR Peoples R China Collaborat Innovat Ctr Intelligent New Energy Veh Shanghai 200092 PR Peoples R China

A novel modelling approach for the electromagnetic forming process (EMF) is proposed in this paper. In the present work, a stable nodal integration method (SNIM) is used to calculate the electromagnetic field and an axisymmetric thin shell element is firstly employed for mechanical field analysis to improve the computational efficiency. A layered approach is adopted to predict the gradual spread of plasticity in a shell. To solve the coupled electromagnetic-mechanical problem, a mapping rule is developed to transfer the nodal Lorentz force from the electromagnetic field to the mechanical field. Simultaneously, a solid element with the finite element method (FEM) is employed in the mechanical field for comparison to validate the efficiency of the proposed modelling approach;the FEM is customarily adopted in a conventional numerical method of EMF simulation. Several electromagnetic forming examples are presented to demonstrate the applicability of the proposed model for EMF problems, and the model is validated by comparing its results with available experimental results in the literature. The numerical results obtained by the proposed model are in good accordance with the experiments and show that the proposed model has much lower computational costs than the conventional one. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Electromagnetic forming (EMF) Transient eddy current Axisymmetric thin shell element stable nodal integration method Node-based smoothed finite element method

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

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JOURNAL OF COMPUTATIONAL PHYSICS 2017年 336卷 192-211页

作者： Cui, Xiangyang Li, She Feng, Hui Li, Guangyao Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Collaborat Innovat Ctr Intelligent New Energy Veh Shanghai 200092 Peoples R China

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. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Electromagnetic sheet metal forming Coupled magnetic-mechanical analysis "Triprism" element Shell element stable nodal integration method

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