Temporal finite elements in the dynamic analysis of structures

This thesis demonstrates that the use of finite elements need not be confined to space alone, but that they may also be used in the time domain, It is shown that finite element methods may be used successfully to obtain the response of systems to applied forces, including, for example, the accelerations in a tall structure subjected to an earthquake shock. It is further demonstrated that at least one of these methods may be considered to be a practical alternative to more usual methods of solution. A detailed investigation of the accuracy and stability of finite element solutions is included, and methods of applications to both single- and multi-degree of freedom systems are described. Solutions using two different temporal finite elements are compared with those obtained by conventional methods, and a comparison of computation times for the different methods is given. The application of finite element methods to distributed systems is described, using both separate discretizations in space and time, and a combined space-time discretization. The inclusion of both viscous and hysteretic damping is shown to add little to the difficulty of the solution. Temporal finite elements are also seen to be of considerable interest when applied to non-linear systems, both when the system parameters are time-dependent and also when they are functions of displacement. Solutions are given for many different examples, and the computer programs used for the finite element methods are included in an Appendix.

The design of fault tolerant software for loosely coupled distributed systems

Requirements for systems to continue to operate satisfactorily in the presence of faults has led to the development of techniques for the construction of fault tolerant software. This thesis addresses the problem of error detection and recovery in distributed systems which consist of a set of communicating sequential processes. A method is presented for the `a priori' design of conversations for this class of distributed system. Petri nets are used to represent the state and to solve state reachability problems for concurrent systems. The dynamic behaviour of the system can be characterised by a state-change table derived from the state reachability tree. Systematic conversation generation is possible by defining a closed boundary on any branch of the state-change table. By relating the state-change table to process attributes it ensures all necessary processes are included in the conversation. The method also ensures properly nested conversations. An implementation of the conversation scheme using the concurrent language occam is proposed. The structure of the conversation is defined using the special features of occam. The proposed implementation gives a structure which is independent of the application and is independent of the number of processes involved. Finally, the integrity of inter-process communications is investigated. The basic communication primitives used in message passing systems are seen to have deficiencies when applied to systems with safety implications. Using a Petri net model a boundary for a time-out mechanism is proposed which will increase the integrity of a system which involves inter-process communications.

A study of adaptive load balancing algorithms for distributed systems

With the advent of distributed computer systems with a largely transparent user interface, new questions have arisen regarding the management of such an environment by an operating system. One fertile area of research is that of load balancing, which attempts to improve system performance by redistributing the workload submitted to the system by the users. Early work in this field concentrated on static placement of computational objects to improve performance, given prior knowledge of process behaviour. More recently this has evolved into studying dynamic load balancing with process migration, thus allowing the system to adapt to varying loads. In this thesis, we describe a simulated system which facilitates experimentation with various load balancing algorithms. The system runs under UNIX and provides functions for user processes to communicate through software ports; processes reside on simulated homogeneous processors, connected by a user-specified topology, and a mechanism is included to allow migration of a process from one processor to another. We present the results of a study of adaptive load balancing algorithms, conducted using the aforementioned simulated system, under varying conditions; these results show the relative merits of different approaches to the load balancing problem, and we analyse the trade-offs between them. Following from this study, we present further novel modifications to suggested algorithms, and show their effects on system performance.

The relative performance of scalable load balancing algorithms in loosely-coupled distributed systems. Available in 2 volumes.

The computer systems of today are characterised by data and program control that are distributed functionally and geographically across a network. A major issue of concern in this environment is the operating system activity of resource management for different processors in the network. To ensure equity in load distribution and improved system performance, load balancing is often undertaken. The research conducted in this field so far, has been primarily concerned with a small set of algorithms operating on tightly-coupled distributed systems. More recent studies have investigated the performance of such algorithms in loosely-coupled architectures but using a small set of processors. This thesis describes a simulation model developed to study the behaviour and general performance characteristics of a range of dynamic load balancing algorithms. Further, the scalability of these algorithms are discussed and a range of regionalised load balancing algorithms developed. In particular, we examine the impact of network diameter and delay on the performance of such algorithms across a range of system workloads. The results produced seem to suggest that the performance of simple dynamic policies are scalable but lack the load stability of more complex global average algorithms.

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.

A structural method for the design of fault tolerant distributed control systems

Distributed digital control systems provide alternatives to conventional, centralised digital control systems. Typically, a modern distributed control system will comprise a multi-processor or network of processors, a communications network, an associated set of sensors and actuators, and the systems and applications software. This thesis addresses the problem of how to design robust decentralised control systems, such as those used to control event-driven, real-time processes in time-critical environments. Emphasis is placed on studying the dynamical behaviour of a system and identifying ways of partitioning the system so that it may be controlled in a distributed manner. A structural partitioning technique is adopted which makes use of natural physical sub-processes in the system, which are then mapped into the software processes to control the system. However, communications are required between the processes because of the disjoint nature of the distributed (i.e. partitioned) state of the physical system. The structural partitioning technique, and recent developments in the theory of potential controllability and observability of a system, are the basis for the design of controllers. In particular, the method is used to derive a decentralised estimate of the state vector for a continuous-time system. The work is also extended to derive a distributed estimate for a discrete-time system. Emphasis is also given to the role of communications in the distributed control of processes and to the partitioning technique necessary to design distributed and decentralised systems with resilient structures. A method is presented for the systematic identification of necessary communications for distributed control. It is also shwon that the structural partitions can be used directly in the design of software fault tolerant concurrent controllers. In particular, the structural partition can be used to identify the boundary of the conversation which can be used to protect a specific part of the system. In addition, for certain classes of system, the partitions can be used to identify processes which may be dynamically reconfigured in the event of a fault. These methods should be of use in the design of robust distributed systems.

CONNECT challenges: towards emergent connectors for eternal networked systems

The CONNECT European project that started in February 2009 aims at dropping the interoperability barrier faced by today’s distributed systems. It does so by adopting a revolutionary approach to the seamless networking of digital systems, that is, synthesizing on the fly the connectors via which networked systems communicate.

Online approximations for wind-field models

We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations.

Exchanging uncertainty: interoperable geostatistics?

Traditionally, geostatistical algorithms are contained within specialist GIS and spatial statistics software. Such packages are often expensive, with relatively complex user interfaces and steep learning curves, and cannot be easily integrated into more complex process chains. In contrast, Service Oriented Architectures (SOAs) promote interoperability and loose coupling within distributed systems, typically using XML (eXtensible Markup Language) and Web services. Web services provide a mechanism for a user to discover and consume a particular process, often as part of a larger process chain, with minimal knowledge of how it works. Wrapping current geostatistical algorithms with a Web service layer would thus increase their accessibility, but raises several complex issues. This paper discusses a solution to providing interoperable, automatic geostatistical processing through the use of Web services, developed in the INTAMAP project (INTeroperability and Automated MAPping). The project builds upon Open Geospatial Consortium standards for describing observations, typically used within sensor webs, and employs Geography Markup Language (GML) to describe the spatial aspect of the problem domain. Thus the interpolation service is extremely flexible, being able to support a range of observation types, and can cope with issues such as change of support and differing error characteristics of sensors (by utilising descriptions of the observation process provided by SensorML). XML is accepted as the de facto standard for describing Web services, due to its expressive capabilities which allow automatic discovery and consumption by ‘naive’ users. Any XML schema employed must therefore be capable of describing every aspect of a service and its processes. However, no schema currently exists that can define the complex uncertainties and modelling choices that are often present within geostatistical analysis. We show a solution to this problem, developing a family of XML schemata to enable the description of a full range of uncertainty types. These types will range from simple statistics, such as the kriging mean and variances, through to a range of probability distributions and non-parametric models, such as realisations from a conditional simulation. By employing these schemata within a Web Processing Service (WPS) we show a prototype moving towards a truly interoperable geostatistical software architecture.

Pragmatic approach to the development of robust real-time protocols

This research is concerned with the development of distributed real-time systems, in which software is used for the control of concurrent physical processes. These distributed control systems are required to periodically coordinate the operation of several autonomous physical processes, with the property of an atomic action. The implementation of this coordination must be fault-tolerant if the integrity of the system is to be maintained in the presence of processor or communication failures. Commit protocols have been widely used to provide this type of atomicity and ensure consistency in distributed computer systems. The objective of this research is the development of a class of robust commit protocols, applicable to the coordination of distributed real-time control systems. Extended forms of the standard two phase commit protocol, that provides fault-tolerant and real-time behaviour, were developed. Petri nets are used for the design of the distributed controllers, and to embed the commit protocol models within these controller designs. This composition of controller and protocol model allows the analysis of the complete system in a unified manner. A common problem for Petri net based techniques is that of state space explosion, a modular approach to both the design and analysis would help cope with this problem. Although extensions to Petri nets that allow module construction exist, generally the modularisation is restricted to the specification, and analysis must be performed on the (flat) detailed net. The Petri net designs for the type of distributed systems considered in this research are both large and complex. The top down, bottom up and hybrid synthesis techniques that are used to model large systems in Petri nets are considered. A hybrid approach to Petri net design for a restricted class of communicating processes is developed. Designs produced using this hybrid approach are modular and allow re-use of verified modules. In order to use this form of modular analysis, it is necessary to project an equivalent but reduced behaviour on the modules used. These projections conceal events local to modules that are not essential for the purpose of analysis. To generate the external behaviour, each firing sequence of the subnet is replaced by an atomic transition internal to the module, and the firing of these transitions transforms the input and output markings of the module. Thus local events are concealed through the projection of the external behaviour of modules. This hybrid design approach preserves properties of interest, such as boundedness and liveness, while the systematic concealment of local events allows the management of state space. The approach presented in this research is particularly suited to distributed systems, as the underlying communication model is used as the basis for the interconnection of modules in the design procedure. This hybrid approach is applied to Petri net based design and analysis of distributed controllers for two industrial applications that incorporate the robust, real-time commit protocols developed. Temporal Petri nets, which combine Petri nets and temporal logic, are used to capture and verify causal and temporal aspects of the designs in a unified manner.

Novel hydrogel polymers

Hydrogels may be conveniently described as hydrophilic polymers that are swollen by, but do not dissolve in water. In this work a series of copolymer hydrogels and semi-interpenetrating polymer networks based on the monomers 2-hydroxyethyl methacrylate, N-vinyl pyrrolidone and N'N' dimethyl acrylamide, together with some less hydrophilic hydroxyalkyl acrylates and methacrylates have been synthesised. Variations in structure and composition have been correlated both with the total equilibrium water content of the resultant hydrogel and with the more detailed water binding behaviour, as revealed by differential scanning calorimetry studies. The water binding characteristics of the hydrogels were found to be primarily a function of the water structuring groups present in gel. The water binding abilities of these groups were, however, modified by steric effects. The mechanical properties of the hydrogels were also investigated. These were found to be dependent on both the polymer composition and the amount and nature of the water present in the gels. In biological systems, composite formation provides a means of producing strong, high water content materials. As an analogy with these systems hydrogel composites were prepared. In an initial study of these materials the water binding and mechanical properties of semi-interpenetrating polymer networks of N'N'dimethyl acrylamide with cellulosic type materials, with polyurethanes and with ester containing polymers were examined. A preliminary investigation of surface properties of both the copolymers and semi-interpenetrating polymer networks has been completed, using both contact angle measurements and anchorage dependent fibroblast cells. Measurable differences in surface properties attributable to structural variations in the polymers were detected by droplet techniques in the dehydrated state. However, in the hydrated state these differences were masked by the water in the gels. The use of cells enabled the underlying differences to be probed and the nature of the water structuring group was again found to be the dominant factor.

Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Deformations of the pneumatic tyre

A mathematical model is developed for the general pneumatic tyre. The model will permit the investigations of tyre deformations produced by arbitrary external loading, and will enable estimates to be made of the distributions of applied and reactive forces. The principle of Finite Elements is used to idealise the composite tyre structure, each element consisting of a triangle of double curvature with varying thickness. Large deflections of' the structure are accomodated by the use of an iterative sequence of small incremental steps, each of' which obeys the laws of linear mechanics. The theoretical results are found to compare favourably with the experimental test data obtained from two different types of ttye construction. However, limitations in the discretisation process has prohibited accurate assessments to be made of stress distributions in the regions of high stress gradients ..

The role of models@run.time in supporting on-the-fly interoperability

Models at runtime can be defined as abstract representations of a system, including its structure and behaviour, which exist in tandem with the given system during the actual execution time of that system. Furthermore, these models should be causally connected to the system being modelled, offering a reflective capability. Significant advances have been made in recent years in applying this concept, most notably in adaptive systems. In this paper we argue that a similar approach can also be used to support the dynamic generation of software artefacts at execution time. An important area where this is relevant is the generation of software mediators to tackle the crucial problem of interoperability in distributed systems. We refer to this approach as emergent middleware, representing a fundamentally new approach to resolving interoperability problems in the complex distributed systems of today. In this context, the runtime models are used to capture meta-information about the underlying networked systems that need to interoperate, including their interfaces and additional knowledge about their associated behaviour. This is supplemented by ontological information to enable semantic reasoning. This paper focuses on this novel use of models at runtime, examining in detail the nature of such runtime models coupled with consideration of the supportive algorithms and tools that extract this knowledge and use it to synthesise the appropriate emergent middleware.