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.

Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .

Discrete element modelling of a rotating drum and drum granulation

This thesis reports the results of DEM (Discrete Element Method) simulations of rotating drums operated in a number of different flow regimes. DEM simulations of drum granulation have also been conducted. The aim was to demonstrate that a realistic simulation is possible, and further understanding of the particle motion and granulation processes in a rotating drum. The simulation model has shown good qualitative and quantitative agreement with other published experimental results. A two-dimensional bed of 5000 disc particles, with properties similar to glass has been simulated in the rolling mode (Froude number 0.0076) with a fractional drum fill of approximately 30%. Particle velocity fields in the cascading layer, bed cross-section, and at the drum wall have shown good agreement with experimental PEPT data. Particle avalanches in the cascading layer have been shown to be consistent with single layers of particles cascading down the free surface towards the drum wall. Particle slip at the drum wall has been shown to depend on angular position, and ranged from 20% at the toe and shoulder, to less than 1% at the mid-point. Three-dimensional DEM simulations of a moderately cascading bed of 50,000 spherical elastic particles (Froude number 0.83) with a fractional fill of approximately 30% have also been performed. The drum axis was inclined by 50 to the horizontal with periodic boundaries at the ends of the drum. The mean period of bed circulation was found to be 0.28s. A liquid binder was added to the system using a spray model based on the concept of a wet surface energy. Granule formation and breakage processes have been demonstrated in the system.

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

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A semi- analytic finite element approach to the stress analysis of circular plate

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The application of finite element analysis to fracture mechanics.

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Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

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.

The mechanical behaviour of cylindrical GRP panels

Glass reinforced plastic (GRP) is now an established material for the fabrication of sonar windows. Its good mechanical strength, light weight, resistance to corrosion and acoustic transparency, are all properties which fit it for this application. This thesis describes a study, undertaken at the Royal Naval Engineering College, Plymouth, into the mechanical behaviour of a circular cylindrical sonar panel. This particular type of panel would be used to cover a flank array sonar in a ship or submarine. The case considered is that of a panel with all of its edges mechanically clamped and subject to pressure loading on its convex surface. A comprehensive program of testing, to determine the orthotropic elastic properties of the laminated composite panel material is described, together with a series of pressure tests on 1:5 scale sonar panels. These pressure tests were carried out in a purpose designed test rig, using air pressure to provide simulated hydrostatic and hydrodynamic loading. Details of all instrumentation used in the experimental work are given in the thesis. The experimental results from the panel testing are compared with predictions of panel behaviour obtained from both the Galerkin solution of Flugge's cylindrical shell equations (orthotropic case), and finite element modelling of the panels using PAFEC. A variety of appropriate panel boundary conditions are considered in each case. A parametric study, intended to be of use as a preliminary design tool, and based on the above Galerkin solution, is also presented. This parametric study considers cases of boundary conditions, material properties, and panel geometry, outside of those investigated in the experimental work Final conclusions are drawn and recommendations made regarding possible improvements to the procedures for design, manufacture and fixing of sonar panels in the Royal Navy.

On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Numerical modelling of complex femtosecond laser inscribed fiber gratings - comparison wih experiment

We present experimental studies and numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Modeling that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.

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.