Allowing for hysteresis in the calculation of fields in the elements of accelerator magnetic systems

Iron magnetic circuit residual magnetization may contribute as much as several Gs to the magnetic field in charged-particle accelerators. This contribution depends on the magnetization “history.” It is not taken into account in most of the existing software that uses the main magnetization curve. Therefore, an error in field calculations usually exceeds 1%, which is unacceptable for accelerators. In this article, a simple phenomenological magnetic-hysteresis model that is suitable for numerical computations is suggested. Approximations based on the proposed model are compared to the results of measurements on partial hysteresis cycles in a steel ring.     

ANN approach to sorption hysteresis within a coupled hygro‐thermo‐mechanical FE analysis

Non‐linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN‐FE code has been developed and tested for 1‐D and 2‐D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary‐porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN‐FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro‐thermal behaviour of capillary‐porous materials. Copyright © 2001 John Wiley & Sons, Ltd.     

Prediction of the behaviour of copper alloy components under complex loadings by electro-thermomechanical coupled simulations

ABSTRACT

Electronic devices must be served with electric power for different reasons. A robust and reliable electric connectivity is often realised by electric connectors. For its leading properties, precipitation hardened copper alloys are widely used for designing connectors with high level mechanical or conductance properties. However, copper alloys show a characteristic stress relaxation under mechanical or thermal loads. Finite element analysis is a standard method to design and optimise components with respect to reliability and performance. Hence, a material model considering the characteristic of the mechanical properties and allowing for the simulation of time and temperature dependent elasto-viscoplastic material behavior was developed at the Fraunhofer IWM. The parameters of the model were determined using tensile and relaxation test data of a C19010 alloy. The material model is applied to electro-thermomechanical coupled finite element simulations of connectors with different load histories. The goal of the simulations is the analysis of the impact of stress relaxation on the mechanical properties of systems over time. From the numerical results with the new model it is shown, how stress relaxation influences the connector clamping forces or contact pressure, respectively, in dependence with time or temperature. The simulation results documents that stress relaxation has to be taken into account in finite element simulations during the designing process of electrical devices.

This paper is part of a Thematic Issue on Copper and its Alloys.     

Biofluid flow in a channel under the action of a uniform localized magnetic field

In this work the fundamental problem of the biomagnetic (blood) fluid flow in a channel under the influence of a steady localized magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and blood is considered as a homogeneous Newtonian fluid. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is adopted. The solution is obtained by the development of an efficient numerical technique based on finite differences. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the magnetic field influences considerably the flow field. It is also obtained that the electrical conductivity of blood should be taken into account at the area of the uniform magnetic field.     

Quench propagation and stability analysis of Rutherford resistive core cables

The complex phenomena occurring in superconducting cables involve thermal, electromagnetic, fluid-dynamic and mechanical problems that require multiphysics analysis codes. In this paper varied methods of analysis are studied, comparing a detailed model of a resistive core Rutherford cable with simplified models, in order to show at what extent the simplified models can be applied. The detailed model considers every single strand and its core as thermal and electric independent elements, while in the simplified models equivalent electric and thermal parameters are calculated to group several strands into equivalent superstrands. The minimum quench energy and quench propagation velocities are taken as parameters for the comparison, evaluating the scaling of the numerical results with the number of electric and thermal elements considered. Computation times for the different models are compared, indicating possible ways to reduce the numerical burden and making desired accuracies.     

Self-consistent model of a low-pressure rf capacitive discharge

A simple self-consistent model of a low-pressure rf capacitive discharge is formulated. Effects associated with stochastic heating of the electrons and the nonlocal nature of the electric field are taken into account. The relations obtained can be used for a qualitative analysis of the main features of these low-pressure discharges. The results of the numerical calculations show good agreement with available experimental data. Pis’ma Zh. Tekh. Fiz. 23, 39–45 (January 12, 1997)     

Subharmonic ferroresonance in an LCR circuit with hysteresis

We use the Preisach model of magnetic hysteresis to model the inductance in a series LCR circuit. By introducing a hysteresis parameter into the Preisach functions used, we are able to continuously vary the width of the hysteresis loop and thereby investigate the effects of magnetic hysteresis on the circuit's behavior. In particular, it is shown that the stability region of a period-3 subharmonic ferroresonant solution can increase significantly as the hysteresis losses are reduced. The bifurcations leading to the appearance and disappearance of this subharmonic solution are examined. Also, strong numerical evidence is provided for the unsuitability of single-valued M-H curves in the analysis of ferroresonant phenomena     

蚁群算法求解弹性本构参数区间反问题

建立了弹性本构参数区间反问题的数值模型,利用区间参数摄动有限元方法和基于网格划分策略的连续域蚁群算法进行求解,探讨了非均质、不确定区间半径、初值选择及数据噪音对反演结果的影响,数值验证给出令人满意的结果。     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

An Improved Magnetic Equivalent Circuit Model for Iron-Core Linear Permanent-Magnet Synchronous Motors

The aim of this work is to establish an accurate yet simple method for predicting flux density distribution and iron losses in linear permanent-magnet synchronous motors (LPMSMs) for iterative design procedures. For this purpose, an improved magnetic equivalent circuit for calculation of the teeth and yoke flux densities in the LPMSMs is presented. The magnetic saturation of iron core is considered by nonlinear elements and an iterative procedure is used to update these elements. The armature reaction is also taken into account in the modeling by flux sources located on the teeth of motors. These sources are time dependent and can model every winding configuration. The relative motion between the motor primary and secondary is considered by wisely designing air gap elements simplifying the permeance network construction and preventing permeance matrix distortion during primary motion. Flux densities in different load conditions are calculated by means of the proposed model. The effects of saturation and armature reaction on the flux density distribution are shown in detail. Using these flux densities, iron losses in the motor are examined and its variations versus motor parameters are then studied. All results obtained by proposed model are verified by finite-element method based on an extensive analysis.     

Application of asymptotic expansions to model two-dimensional induction heating systems. Part I: calculation of electromagnetic field distribution

We analyze the effect of a radio-frequency alternating magnetic field generated in the vicinity of solid or liquid electrically conducting components, such as used in induction heating processes. The field can penetrate only into a thin magnetic skin located beneath the conductor surface, where the generated heat and stresses are concentrated. This most often leads to major numerical difficulties, especially for very thin magnetic skins. Therefore, we have developed a mathematical model of the electromagnetic field distribution inside the conductors for planar and axisymmetric configurations by using a matched asymptotic expansion technique. Among other features, our method takes the curvature of the conductor surfaces into account. A practical numerical implementation of our model is detailed here, and numerical calculations are carried out in order to extend the model to limiting cases such as curvature discontinuities and corners. These calculations compare successfully with complete numerical computations.     

Diffusion-limited aggregation at multiple centers: Model of dendrite growth at ion beam synthesis of magnetic films in external field

Computer simulations are used to generate two-dimensional dendrites from atoms carrying magnetic moment being parallel to the external magnetic field. The numerical model is based on the model of diffusion-limited aggregation at multiple centers. The magnetic dipole–dipole interaction between diffusing implanted atoms and growing ferromagnetic dendrites is taken into account. It is shown that magnetically induced anisotropy of grown dendrites follows to elongation of them in external field direction. The process of growth of these dendrites is analyzed by measuring mean relative elongation versus number of deposited particles within the grid.     

振动系统中磁流变流体阻尼模型的研究

研究了磁流体的阻尼力特性,提出了基于粘性阻尼和回滞阻尼组成的迟滞阻尼力模型,进行了磁流变阻尼器阻尼力的响应谱分析,并用Newmark数值积分方法分析了带有磁流变流体阻尼器梁结构的多自由度振动系统在不同磁场强度和激励频率作用下的位移响应.结果表明:迟滞阻尼力模型能够很好地描述磁流体阻尼器的力学性能,而且形式简单,概念明确,适合实际应用.     

THE DAMAGE PROCESS IN A FINITE-SIZED BRITTLE SPECIMEN WITH INTERACTING MICROCRACKS

Abstract— The whole damage process in a finite sized specimen with interacting microcracks is simulated by a method combining the closed form crack solutions with boundary elements. Interactions among microcracks and boundary elements are taken into account with an explicit interaction matrix. A coalescence criterion is assumed to rule the intersection behaviour and propagation arrest. The fatal coalescence cluster resulting in the failure of the specimen, out of many intersections of propagating microcracks, is identified with a particular coalescence matrix. The numerical model proposed in this paper can be used to simulate the damage process in a brittle specimen of any shape, under arbitrary plane stress conditions.     

电磁功能梯度材料层合板中表面波的弥散特性

应用混合数值法研究电磁复合材料层合板中表面波的弥散特性。假设材料的材料常数和电、磁常数沿板厚方向呈线性变化,首先用线条元将电磁复合材料层合板划分为单元,建立单元的动力学微分方程,然后根据单元之间的连续条件将单元控制方程装配成系统的控制方程,将单元的位移向量表示成波动形式的解,得到波数域内的系统控制方程,求解系统的特征方程,得到波数与频率的关系即弥散关系,考察电、磁效应对波的弥散特性的影响。     

钢梁-钢筋混凝土柱梁柱中节点非线性有限元模拟

借助ANSYS有限元分析软件,对5个"梁贯通"式RCS梁柱中节点进行三维非线性有限元分析,并和试验结果相比较。分析中考虑材料非线性以及混凝土的开裂与压碎。对单元类型的选取、钢和混凝土材料模型的定义、整体有限元模型的建立、施加荷载、设置求解选项并求解等数值模拟技术进行了深入的研究。研究表明,通过合理设置参数,ANSYS有限元软件能够模拟RCS梁柱节点在静力荷载作用下的性能,并和试验结果吻合较好。     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.     

A nonlinear bilayer beam model for an interfacial crack in dielectric bimaterials under mechanical/electrical loading

A bilayer beam model is extended to study the fracture behavior of dielectric interfacial cracks. In this model, a semi-infinite crack with an original opening value is oriented along the interface between two dielectric layers which are under mechanical/electrical loading. Taking into account the effect of the electrostatic traction on the interfacial crack, a nonlinear analytical solution is derived, along with also a developed finite element analysis method where a special constitutive equation for the capacitor element in ANSYS is utilized to simulate the electrostatic tractions. Both the analytical and numerical solutions predict the same results which further show that the elastic and dielectric mismatches can play a significant role in the interfacial cracking behavior under mechanical and electrical loading. Furthermore, the electrostatic tractions may cause hysteresis loops in the curve of crack opening versus applied mechanical displacement or versus applied electric voltage. An applied mechanical load is the driving force for the interfacial cracking, while an applied electric field retards it.