A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Application of finite element method and photo-elasticity to an lap welded connection

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A finite-element method for the solution of turbine-generation end-zone fields

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Shear induced toughening in bonded joints:experiments and analysis

Bonded joint specimens were fabricated from composite adherends and either an epoxy or a urethane adhesive. In mixed-mode fracture experiments, the epoxy bonded specimens generally failed by subinterfacial fracture in the composite, while specimens bonded with urethane failed very close to the adhesive/substrate interface. For the epoxy bonded specimens, fracture toughness did not change significantly with mode-mix, but for urethane bonded joints, fracture toughness increased with increasing shear load. Finite element analysis, which modeled specimens bonded with the two adhesives, showed similar trends. The different toughening behaviors for the two bonded joints can be attributed to dissipation of energy through inelastic deformation, which was insignificant in the epoxy-bonded joints but substantial when the urethane was used as the bonding agent.

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

AC self-bearing motors with a bridge configured winding

Magnetic levitation bearings eliminate friction, wear and the need for lubrication and so have high speed capability and potential for vibration control. One noteworthy development in the realm of magnetic levitation is the self-bearing or bearingless motor - an electromagnetic machine that supports its own rotor by way of magnetic forces generated by windings on its stator. Accordingly, various winding schemes have been proposed to accomplish the task of force production. This thesis proposes a novel concept of winding based on a bridge connection for polyphase self-bearing rotating electrical machines with the following advantages: • the connection uses a single set of windings and thus power loss is relatively low when compared with self-bearing motors with conventional dual set of windings. • the motor and levitation controls are segregated such that only one motor inverter is required for the normal torque production and levitation forces are produced by using auxiliary power supplies of relatively low current and voltage rating. The usual way of controlling the motor is retained. • there are many variant winding schemes to meet special needs. • independent power supplies for levitation control offer redundancy for fault tolerance. This thesis dwells specifically on the conceptual design and implementation of the proposed single set of windings scheme. The new connection has been verified to exhibit characteristics of a self-bearing motor via coupled-field finite element analysis: results are crosschecked analytically. Power loss and other aspects such as cost, design implementation are compared to support the newly proposed connection as a potential alternative to present designs.

The Mechanics of the drawing of polygonal sections from round at elevated temperature

Economic factors such as the rise in cost of raw materials, labour and power, are compelling manufacturers of cold-drawn polygonal sections, to seek new production routes which will enable the expansion in the varieties of metals used and the inclusion of difficult-to-draw materials. One such method generating considerable industrial interest is the drawing of polygonal sections from round at elevated temperature. The technique of drawing mild steel, medium carbon steel and boron steel wire into octagonal, hexagonal and square sections from round at up to 850 deg C and 50% reduction of area in one pass has been established. The main objective was to provide a basic understanding of the process, with particular emphasis being placed on modelling using both experimental and theoretical considerations. Elevated temperature stress-strain data was obtained using a modified torsion testing machine. Data were used in the upper bound solution derived and solved numerically to predict drawing stress strain, strain-rate, temperature and flow stress distribution in the deforming zone for a range of variables. The success of this warm working process will, of course, depend on the use of a satisfactory elevated temperature lubricant, an efficient cooling system, a suitable tool material having good wear and thermal shock resistance and an efficient die profile design which incorporates the principle of least work. The merits and demerits of die materials such as tungsten carbide, chromium carbide, Syalon and Stellite are discussed, principally from the standpoint of minimising drawing force and die wear. Generally, the experimental and theoretical results were in good agreement, the drawing stress could be predicted within close limits and the process proved to be technically feasible. Finite element analysis has been carried out on the various die geometries and die materials, to gain a greater understanding of the behaviour of these dies under the process of elevated temperature drawing, and to establish the temperature distribution and thermal distortion in the deforming zone, thus establishing the optimum die design and die material for the process. It is now possible to predict, for the materials already tested, (i) the optimum drawing temperature range, (ii) the maximum possible reduction of area per pass, (iii) the optimum drawing die profiles and die materials, (iv) the most efficient lubricant in terms of reducing the drawing force and die wear.

A temporary connection for an aluminium space frame

This thesis examines theoretically and experimentally the behaviour of a temporary end plate connection for an aluminium space frame structure, subjected to static loading conditions. Theoretical weld failure criterions are derived from basic fundamentals for both tensile and shear fillet welds. Direct account of weld penetration is taken by incorporating it into a more exact poposed weld model. Theoretical relationships between weld penetration and weld failure loads, failure planes and failure lengths are derived. Also, the variation in strength between tensile and shear fillet welds is shown to be dependent upon the extent of weld penetration achieved/ The proposed tensile weld failure theory is extended to predict the theoretical failure of the welds in the end plate space frame connection. A finite element analysis is conducted to verify the assumptions made for this theory. Experimental hardness and tensile tests are conducted to substantiate the extent and severity of the heat affected zone in aluminium alloy 6082-T6. Simple transverse and longitudinal fillet welded specimens of the same alloy, are tested to failure. These results together with those of other authors are compared to the theoretical predictions made by the proposed weld failure theories and by those made using Kamtekar's and Kato and Morita's failure equations, the -formula and BS 8118. Experimental tests are also conducted on the temporary space frame connection. The maximum stresses and displacements recorded are checked against results obtained from a finite element analysis of the connection. Failure predictions made by the proposed extended weld failure theory, are compared against the experimental results.

Theoretical modelling of the sulcated spring

Replacement of the traditional coil spring with one of more fibre-reinforced plastic sulcated springs is a future possibility. Spring designers of metallic coil springs have design formulae readily available, and software packages specific to coil spring design exist. However, the sulcated spring is at the prototype stage of development, so literature on these springs is very sparse. The thesis contains information on the market for sulcated springs, and their advantages and disadvantages. Literature on other types of fibre reinforced plastic springs has also been reviewed. Design software has been developed for the sulcated spring along similar lines to coil spring design software. In order to develop the software, a theoretical model had to be developed which formed the mathematical basis for the software. The theoretical model is based on a choice of four methods for calculating the flexural rigidity; beam theory, plate theory, and lamination theory assuming isotropic and orthoropic material properties. Experimental results for strain and spring stiffness have been compared with the theoretical model, and were in good agreement. Included in the design software are the results of experimental work on fatigue, and design limiting factors to prevent or warn against impractical designs. Finite element analysis has been used to verify the theoretical model developed, and to find the better approximation to the experimental results. Applications and types of assemblies for the sulcated spring were discussed. Sulcated spring designs for the automotive applications of a suspension, clutch and engine valve spring were found using the design computer software. These sulcated spring designs were within or close to the space of the existing coil spring and yield the same performance. Finally the commercial feasibility of manufacturing the sulcated spring was assessed and compared with the coil spring, to evaluate the plausibility of the sulcated spring replacing the coil spring eventually.