Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

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 particle impact problems

Particle impacts are of fundamental importance in many areas and there has been a renewed interest in research on particle impact problems. A comprehensive investigation of the particle impact problems, using finite element (FE) methods, is presented in this thesis. The capability of FE procedures for modelling particle impacts is demonstrated by excellent agreements between FE analysis results and previous theoretical, experimental and numerical results. For normal impacts of elastic particles, it is found that the energy loss due to stress wave propagation is negligible if it can reflect more than three times during the impact, for which Hertz theory provides a good prediction of impact behaviour provided that the contact deformation is sufficiently small. For normal impact of plastic particles, the energy loss due to stress wave propagation is also generally negligible so that the energy loss is mainly due to plastic deformation. Finite-deformation plastic impact is addressed in this thesis so that plastic impacts can be categorised into elastic-plastic impact and finite-deformation plastic impact. Criteria for the onset of finite-deformation plastic impacts are proposed in terms of impact velocity and material properties. It is found that the coefficient of restitution depends mainly upon the ratio of impact velocity to yield Vni/Vy0 for elastic-plastic impacts, but it is proportional to [(Vni/Vy0)*(Y/E*)]-1/2, where Y /E* is the representative yield strain for finite-deformation plastic impacts. A theoretical model for elastic-plastic impacts is also developed and compares favourably with FEA and previous experimental results. The effect of work hardening is also investigated.

Modelling the human accommodation system using finite element analysis

The human accommodation system has been extensively examined for over a century, with a particular focus on trying to understand the mechanisms that lead to the loss of accommodative ability with age (Presbyopia). The accommodative process, along with the potential causes of presbyopia, are disputed; hindering efforts to develop methods of restoring accommodation in the presbyopic eye. One method that can be used to provide insight into this complex area is Finite Element Analysis (FEA). The effectiveness of FEA in modelling the accommodative process has been illustrated by a number of accommodative FEA models developed to date. However, there have been limitations to these previous models; principally due to the variation in data on the geometry of the accommodative components, combined with sparse measurements of their material properties. Despite advances in available data, continued oversimplification has occurred in the modelling of the crystalline lens structure and the zonular fibres that surround the lens. A new accommodation model was proposed by the author that aims to eliminate these limitations. A novel representation of the zonular structure was developed, combined with updated lens and capsule modelling methods. The model has been designed to be adaptable so that a range of different age accommodation systems can be modelled, allowing the age related changes that occur to be simulated. The new modelling methods were validated by comparing the changes induced within the model to available in vivo data, leading to the definition of three different age models. These were used in an extended sensitivity study on age related changes, where individual parameters were altered to investigate their effect on the accommodative process. The material properties were found to have the largest impact on the decline in accommodative ability, in particular compared to changes in ciliary body movement or zonular structure. Novel data on the importance of the capsule stiffness and thickness was also established. The new model detailed within this thesis provides further insight into the accommodation mechanism, as well as a foundation for future, more detailed investigations into accommodation, presbyopia and accommodative restoration techniques.

A sensitivity study of the human crystalline lens using finite element analysis

Finite element analysis is a useful tool in understanding how the accommodation system of the eye works. Further to simpler FEA models that have been used hitherto, this paper describes a sensitivity study which aims to understand which parameters of the crystalline lens are key to developing an accurate model of the accommodation system. A number of lens models were created, allowing the mechanical properties, internal structure and outer geometry to be varied. These models were then spun about their axes, and the deformations determined. The results showed the mechanical properties are the critical parameters, with the internal structure secondary. Further research is needed to fully understand how the internal structure and properties interact to affect lens deformation.

Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

Linking finite-element analysis and computer-aided drafting processes

The aim of this research was to investigate the integration of computer-aided drafting and finite-element analysis in a linked computer-aided design procedure and to develop the necessary software. The Be'zier surface patch for surface representation was used to bridge the gap between the rather separate fields of drafting and finite-element analysis because the surfaces are defined by analytical functions which allow systematic and controlled variation of the shape and provide continuous derivatives up to any required degree. The objectives of this research were achieved by establishing : (i) A package which interpretes the engineering drawings of plate and shell structures and prepares the Be'zier net necessary for surface representation. (ii) A general purpose stand-alone meshed-surface modelling package for surface representation of plates and shells using the Be'zier surface patch technique. (iii) A translator which adapts the geometric description of plate and shell structures as given by the meshed-surface modeller to the form needed by the finite-element analysis package. The translator was extended to suit fan impellers by taking advantage of their sectorial symmetry. The linking processes were carried out for simple test structures, simplified and actual fan impellers to verify the flexibility and usefulness of the linking technique adopted. Finite-element results for thin plate and shell structures showed excellent agreement with those obtained by other investigators while results for the simplified and actual fan impellers also showed good agreement with those obtained in an earlier investigation where finite-element analysis input data were manually prepared. Some extensions of this work have also been discussed.