VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

The Exodus evacuation model applied to building evacuation scenarios

The purpose of this paper is to demonstrate the potential of the EXODUS evacuation model in building environments. The latest PC/workstation version of EXODUS is described and is also applied to a large hypothetical supermarket/restaurant complex measuring 50 m x 40 m. A range of scenarios is presented where population characteristics (such as size, individual travel speeds, and individual response times), and enclosure configuration characteristics (such as number of exits, size of exits, and opening times of exits) are varied. The results demonstrate a wide range of occupant behavior including overtaking, queuing, redirection, and conflict avoidance. Evacuation performance is measured by a number of model predicted parameters including individual exit flow rates, overall evacuation flow rates, total evacuation time, average evacuation time per occupant, average travel distance, and average wait time. The simulations highlight the profound impact that variations in individual travel speeds and occupant response times have in determining the overall evacuation performance. 1. Jin, T., and Yamada T., "Experimental Study of Human Behavior in Smoke Filled Corridors," Proceedings of The Second International Symposium on Fire Safety Science, 1988, pp. 511-519. 2. Galea, E.R., and Galparsoro, J.M.P., "EXODUS: An Evacuation Model for Mass Transport Vehicles," UK CAA Paper 93006 ISBN 086039 543X, CAA London, 1993. 3. Galea, E.R., and Galparsoro, J.M.P., "A Computer Based Simulation Model for the Prediction of Evacuation from Mass Transport Vehicles," Fire Safety Journal, Vol. 22, 1994, pp. 341-366. 4. Galea, E.R., Owen, M., and Lawrence, P., "Computer Modeling of Human Be havior in Aircraft Fire Accidents," to appear in the Proceedings of Combus tion Toxicology Symposium, CAMI, Oklahoma City, OK, 1995. 5. Kisko, T.M. and Francis, R.L., "EVACNET+: A Computer Program to Determine Optimal Building Evacuation Plans," Fire Safety Journal, Vol. 9, 1985, pp. 211-220. 6. Levin, B., "EXITT, A Simulation Model of Occupant Decisions and Actions in Residential Fires," Proceedings of The Second International Symposium on Fire Safety Science, 1988, pp. 561-570. 7. Fahy, R.F., "EXIT89: An Evacuation Model for High-Rise Buildings," Pro ceedings of The Third International Sym posium on Fire Safety Science, 1991, pp. 815-823. 8. Thompson, P.A., and Marchant, E.W., "A Computer Model for the Evacuation of Large Building Populations," Fire Safety Journal, Vol. 24, 1995, pp. 131-148. 9. Still, K., "New Computer System Can Predict Human Behavior Response to Building Fires," FIRE 84, 1993, pp. 40-41. 10. Ketchell, N., Cole, S.S., Webber, D.M., et.al., "The Egress Code for Human Move ment and Behavior in Emergency Evacu ations," Engineering for Crowd Safety (Smith, R.A., and Dickie, J.F., Eds.), Elsevier, 1993, pp. 361-370. 11. Takahashi, K., Tanaka, T. and Kose, S., "An Evacuation Model for Use in Fire Safety Design of Buildings," Proceedings of The Second International Symposium on Fire Safety Science, 1988, pp. 551- 560. 12. G2 Reference Manual, Version 3.0, Gensym Corporation, Cambridge, MA. 13. XVT Reference Manual, Version 3.0 XVT Software Inc., Boulder, CO. 14. Galea, E.R., "On the Field Modeling Approach to the Simulation of Enclosure Fires, Journal of Fire Protection Engineering, Vol. 1, No. 1, 1989, pp. 11-22. 15. Purser, D.A., "Toxicity Assessment of Combustion Products," SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA, pp. 1-200 - 1-245, 1988. 16. Hankin, B.D., and Wright, R.A., "Pas senger Flows in Subways," Operational Research Quarterly, Vol. 9, 1958, pp. 81-88. 17. HMSO, The Building Regulations 1991 - Approved Document B, section B 1 (1992 edition), HMSO publications, London, pp. 9-40. 18. Polus A., Schofer, J.L., and Ushpiz, A., "Pedestrian Flow and Level of Service," Journal of Transportation Engineering, Vol. 109, 1983, pp. 46-47. 19. Muir, H., Marrison, C., and Evans, A., "Aircraft Evacuations: the Effect of Passenger Motivation and Cabin Con figuration Adjacent to the Exit," CAA Paper 89019, ISBN 0 86039 406 9, 1989. 20. Muir, H., Private communication to appear as a CAA report, 1996.

The use of a biased heuristic by a genetic algorithm applied to the design of multipoint connections in a local access network

This paper presents a genetic algorithm for finding a constrained minimum spanning tree. The problem is of relevance in the design of minimum cost communication networks, where there is a need to connect all the terminals at a user site to a terminal concentrator in a multipoint (tree) configuration, while ensuring that link capacity constraints are not violated. The approach used maintains a distinction between genotype and phenotype, which produces superior results to those found using a direct representation in a previous study.

Finite volume methods applied to the computational modelling of welding phenomena

This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of computational fluid dynamics (CFD) and computational solid mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred finite volume (FV) methods are employed. Additionally, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted.

Multilevel approaches applied to the capacitated clustering problem

This paper presents two multilevel refinement algorithms for the capacitated clustering problem. Multilevel refinement is a collaborative technique capable of significantly aiding the solution process for optimisation problems. The central methodologies of the technique are filtering solutions from the search space and reducing the level of problem detail to be considered at each level of the solution process. The first multilevel algorithm uses a simple tabu search while the other executes a standard local search procedure. Both algorithms demonstrate that the multilevel technique is capable of aiding the solution process for this combinatorial optimisation problem.

A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

Does flexibility in secondary level mathematics curriculum affect degree performance?

The authors have much experience in developing mathematics skills of first-year engineering students and attempting to ensure a smooth transition from secondary school to university. Concerns exist due to there being flexibility in the choice of modules needed to obtain a secondary level (A-level) mathematics qualification. This qualification is based on some core (pure maths) modules and a selection from mechanics and statistics modules. A survey of aerospace and mechanical engineering students in Queen’s University Belfast revealed that a combination of both mechanics and statistics (the basic module in both) was by far the most popular choice and therefore only about one quarter of this cohort had studied mechanics beyond the basic module within school maths. Those students who studied the extra mechanics and who achieved top grades at school subsequently did better in two core, first-year engineering courses. However, students with a lower grade from school did not seem to gain any significant advantage in the first-year engineering courses despite having the extra mechanics background. This investigation ties in with ongoing and wider concerns with secondary level mathematics provision in the UK.

How does Oyster work? The simple interpretation of Oyster mathematics

Oyster® is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.

A-level Mathematics Module Choice and Subsequent Performance in First Year of an Engineering Degree

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules. The flexibility in choice of applied modules has led to concerns that many students would proceed to study engineering at university with little background in mechanics. A survey of aerospace and mechanical engineering students in our university revealed that a combination of mechanics and statistics (the basic module in both) was by far the most popular choice of optional modules in A-level Mathematics, meaning that only about one-quarter of the class had studied mechanics beyond the basic module within school mathematics. Investigation of student performance in two core, first-year engineering courses, which build on a mechanics foundation, indicated that any benefits for students who studied the extra mechanics at school were small. These results give concern about the depth of understanding in mechanics gained during A-level Mathematics.

Interpreting A-level Mathematics grades – as easy as A, B, C?

Many concerns have been expressed that students’ basic mathematical skills have deteriorated during the 1990s and there has been disquiet that current A-level grading does not distinguish adequately between the more able students. This study reports the author’s experiences of teaching maths to large classes of first-year engineering students and aims to enhance understanding of levels of mathematical competence in more recent years. Over the last four years, the classes have consisted of a very large proportion of highly qualified students – about 91% of them had at least grade B in A-level Mathematics. With a small group of students having followed a non-traditional route to university (no A-level maths) and another group having benefitted through taking A-level Further Mathematics at school, the classes have contained a very wide range of mathematical backgrounds. Despite the introductory maths course at university involving mainly repetition of A-level material, students’ marks were spread over a very wide range – for example, A-level Mathematics grade B students have scored across the range 16 – 97%. Analytical integration is the topic which produced the largest variation in performance across the class but, in contrast, the A-level students generally performed well in differentiation. Initial analysis suggests some stability in recent years in the mathematical proficiency of students with a particular A-level Mathematics grade. Allowing choice of applied maths modules as part of the A-level maths qualification increases the variety of students’ mathematical backgrounds and their selection from mechanics, statistics or decision maths is not clear from the final qualification.

A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.