Boundary Galerkin's method for three-dimensional finite element electromagnetic field computation

Electromagnetic field problems are often formulated as boundary value problems in unbounded regions. For this reason, the application of conventional numerical methods, such as the finite element method, is difficult. The paper describes a new technique to circumvent this difficulty. The technique is based on the reduction of the field equations in unbounded space to equivalent boundary Galerkin's criterion. Such criterion can be combined with the volume Galerkin's criterion for regions occupied by conductors. A new quasi-finite-element discretization based on the coupled boundary/volume Galerkin's criterion is presented.     

Three-dimensional finite element program for magnetic field problems

A finite element program has been developed to solve magnetic field problems in three dimensions. The program is based on the extended Ritz method which employs discrete values of the magnetic vector potential as the unknown parameters. A simple example problem illustrates the use of this program. One of the distributions obtained compares favorably with that calculated from a two-dimensional approximation. In that case, the two-dimensional calculation provides a realistic approximation.     

Evaluation of the stress distribution in CFR-PEEK dental implants by the three-dimensional finite element method

CFR-PEEK (carbon fiber reforced—poly ether ether ketone) has been demonstrated to be excellent substitute titanium in orthopedic applications and can be manufactured with many physical, mechanical, and surface properties, in several shapes. The aim of this study was to compare, using the three-dimensional finite element method, the stress distribution in the peri-implant support bone of distinct models composed of PEEK components and implants reinforced with 30% carbon fiber (30% CFR-PEEK) or titanium. In simulations with a perfect bonding between the bone and the implant, the 30% CFR-PEEK presented higher stress concentration in the implant neck and the adjacent bone, due to the decreased stiffness and higher deformation in relation to the titanium. However, 30% CFR-PEEK implants and components did not exhibit any advantages in relation to the stress distribution compared to the titanium implants and components.     

A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems

A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis. In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula. The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems. In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do. And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods. Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified.     

Topology optimization of a magnetic field in a three-dimensional finite region

This article describes the method of magnetic field topology optimization in an axisymmetric three-dimensional finite region. It is assumed that the region of interest is surrounded by a cylindrical solenoid with an electrical current. The solenoid’s inner and outer surfaces are built-up by rotating plane Bezier curves around the symmetry axis. As a global minimizer a genetic algorithm method is used. Optimal configurations are provided under given constraints.     

Magnetic performance of step-lap joints in distribution transformer cores

The magnetic characteristis of cores with step-lap joints are analyzed by using the finite element method taking into account eddy current and magnetic saturation. The effects of the following factors on the magnetic characteristics such as flux and eddy current distributions and magnetizing current are clarified quantitatively. 1)step-lap length 2)length of air gap at the joint 3)number of laminations per one stagger layer 4)flux density (magnetic saturation) Obtained results give useful suggestions improving the design of the joints of transformer cores.     

A generalized phase field multiscale finite element method for brittle fracture

A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement-based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse elements, where solution of the governing equations is performed. Mapping is achieved by employing a set of numerically derived multiscale shape functions. A set of representative benchmark tests is used to verify the proposed procedure and assess its performance in terms of accuracy and efficiency compared with the standard phase field finite element implementation.     

A method for rendering 3D finite element vector field solutionsnondivergent

The use of the method of constraints for enforcing the zero divergence condition in vectorial finite-element schemes is discussed. An earlier implementation of the method was shown to produce the correct solution for a 3-D resonant cavity problem modeled by a single finite element. Partial success in extending the method to multielement cases is reported. The reduction in matrix size alone would justify the development of the technique for general multielement grids, but it will require the implementation of a global approach to the method of constraints     

The B-spline finite element method applied to axi-symmetrical andnonlinear field problems

A B-spline FEM (finite-element method) using the B-spline functions for rectangular elements as shape functions is presented. It is very effective for solving two-dimensional electromagnetic field problems in regular regions. Compared with the conventional FEM, it gives more accurate potential values and due to the inherent properties of B-spline functions yields much closer field values. Both the computing time and the storage capacity are greatly reduced as well     

A novel method of reducing iron losses in power transformer cores

A method is described in which the iron loss of single phase transformer cores constructed from grain-oriented silicon-iron can be reduced. It is shown in two different sized cores that by assembling the limbs with laminations cut at small angles to the rolling direction (RD) of the steel, and stacked in a certain way, the loss can be reduced. Reductions of up to 6 percent were achieved in cores assembled from high permeability steel.     

碳弧气刨温度场的三维有限元模型

为了分析碳弧气刨过程的温度场分布特征,根据碳弧气刨过程特点,结合"单元死活"技术,建立了一个既考虑电弧热作用又考虑材料去除的碳弧气刨温度场三维有限元模型.在此基础上,对碳弧气刨温度场的特点进行了分析.计算结果表明,电弧强烈的热作用使坡口附近产生了很大的温度梯度,而材料的去除使得该处的温度梯度变得更为剧烈.有限元结果和实验结果对比表明,本文建立的碳弧气刨温度场有限元模型是正确的.     

3-D open boundary magnetic field analysis using infinite elementbased on hybrid finite element method

A method for analyzing 3-D open-boundary magnetic field problems using infinite elements has been developed. The infinite problem has the advantage that the bandwidth of the coefficient matrix and the number of unknown variables are reduced. Moreover, no experience is necessary in determining decay parameters. The effectiveness of the infinite-element method is illustrated by the accuracy and the CPU time obtained when various boundary conditions are applied     

A new approach to magnetic field analysis by the dual reciprocity boundary element method

This paper presents an application of the dual reciprocity boundary element method to non-linear magnetic field analysis. Advanced techniques employed in the procedure include discontinuous elements, quasi-singular and hyper-singular integration schemes and the Galerkin formulation. Numerical results are included to show the performance of the proposed approach.     

A finite element weighted residual solution to one-dimensional field problems

The one-dimensional diffusion-convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two-dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.     

Extended finite element method and fast marching method for three-dimensional fatigue crack propagation

A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modeled by finite elements with no explicit meshing of the crack surfaces. The initial crack geometry is represented by level set functions, and subsequently signed distance functions are used to compute the enrichment functions that appear in the displacement-based finite element approximation. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. Stress intensity factors for planar three-dimensional cracks are computed, and fatigue crack growth simulations for planar cracks are presented. Good agreement between the numerical results and theory is realized.     

Parallel simulations of three-dimensional cracks using the generalized finite element method

This paper presents a parallel generalized finite element method (GFEM) that uses customized enrichment functions for applications where limited a priori knowledge about the solution is available. The procedure involves the parallel solution of local boundary value problems using boundary conditions from a coarse global problem. The local solutions are in turn used to enrich the global solution space using the partition of unity methodology. The parallel computation of local solutions can be implemented using a single pair of scatter–gather communications. Several numerical experiments demonstrate the high parallel efficiency of these computations. For problems requiring non-uniform mesh refinement and enrichment, load unbalance is addressed by defining a larger number of small local problems than the number of parallel processors and by sorting and solving the local problems based on estimates of their workload. A simple and effective estimate of the largest number of processors where load balance among processors is maintained is also proposed. Several three-dimensional fracture mechanics problems aiming at investigating the accuracy and parallel performance of the proposed GFEM are analyzed.     

A new finite element method in micromagnetics

A finite-element method is presented in which the magnetization is linearly interpolated within each tetrahedral element and the magnetostatic interaction is accurately obtained by integration. The equilibrium magnetizations at the nodal points can be found by minimizing the total energy of the system. Two different minimization schemes are compared     

An apporach to automatic three-dimensional finite element mesh generation

Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)^{3, 4, 8, 16, 18, 25, 38}. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.     

A three-dimensional least-squares finite element technique for deformation analysis

The development of a three-dimensional least-squares finite element technique suitable for deformation analysis was presented. By adopting a spatial viewpoint, a consistent rate formulation that treats deformation as a process was established. The technique utilized the least-squares variational principle that minimizes the squares of errors encountered in any attempt to meet the field equations exactly. Both velocity and Cauchy stress rate fields were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-definite coefficient matrix. A conjugate gradient iterative solver with incomplete-Choleski preconditioner was used to solve the resulting linear system of equations. Issues such as finite element formulation, mesh design, code efficiency, and time integration were addressed. A set of linear elastic problems was used for patch-test; both homogeneous and non-homogeneous deformations were considered. Additionally, two finite elastic deformation problems were analysed to gauge the overall performance of the technique. The results demonstrated the computational feasibility of a three-dimensional least-squares finite element technique for deformation analysis. © 1997 John Wiley & Sons, Ltd.