Differential geometry and design coupling in MDO

The notion of coupling within a design, particularly within the context of Multidisciplinary Design Optimization (MDO), is much used but ill-defined. There are many different ways of measuring design coupling, but these measures vary in both their conceptions of what design coupling is and how such coupling may be calculated. Within the differential geometry framework which we have previously developed for MDO systems, we put forth our own design coupling metric for consideration. Our metric is not commensurate with similar types of coupling metrics, but we show that it both provides a helpful geo- metric interpretation of coupling (and uncoupledness in particular) and exhibits greater generality and potential for analysis than those similar metrics. Furthermore, we discuss how the metric might be profitably extended to time-varying problems and show how the metric's measure of coupling can be applied to multi-objective optimization problems (in unconstrained optimization and in MDO). © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The influence of room geometry on the overturning of smoke owing to a floor fire

The present paper explores the influence of room geometry on the overturning of smoke owing to a centrally located floor fire, and examines the implications on smoke filling times. The focus is on presenting practical design guidelines based on the theoretical predictions of the model of Kaye and Hunt. An engineering platform is developed for the prediction of smoke filling times, and a rational basis is provided by way of which smoke behaviour can be specified for simple room designs. The time taken for smoke to fill a room to a given height is critically affected by the room aspect ratio and the characteristic size of the buoyancy source. At large times, taller (small aspect ratio) rooms are shown to fill with smoke at a faster rate than wide (large aspect ratio) rooms owing to large-scale overturning and engulfing of ambient air during the initial transients. Larger area sources of buoyancy also decrease significantly the smoke filling times, with important implications for fire and smoke safety design. Simplified design curves incorporating the main findings have been developed for use as a tool by practising fire-safety engineers.

In-plane critical current density measurements of straight and curved tracks in RABiTS-MOD coated conductors

Depending on the temperature and the magnitude and orientation of an external magnetic field, the critical current density, J c , of a coated conductor can be limited either by the properties of the grain boundaries or by those of the grains. In order to ascertain what governs J c under different conditions, we have measured straight and curved tracks, patterned into RABiTS-MOD samples, while a magnetic field was swept in the plane of the films. Significantly different results were obtained at different field and temperature ranges, which we were able to attribute to J c being limited by either grain boundaries or grains.

Influence of tire geometry on the horn effect

A reciprocal-configuration Boundary Element Method calculation of acoustic radiation characteristics has been implemented for a generic tire geometry. The influence of the geometric parameters on the radiation characteristics has been studied. The degree of amplification of noise sources on the tire belt is strongly affected by the overall tire width. In contrast, the tire radius predominantly influences the pattern of the varying amplification around the belt, rather than its absolute level. Radiusing the tire's 'shoulder' region is potentially beneficial in terms of lowering amplification levels, for a tire of fixed overall width. However, it is less effective than maintaining sharp shoulders and reducing the overall width. Thus, for an acoustically optimal belted tire, the overall width should be as small as possible, even if this leads to a larger diameter. The width should not be increased in order to accommodate a radiused crown region. Copyright © (2012) by the Institute of Noise Control Engineering (INCE).

Vibration decay along deepwater moorings with complex geometry and configuration, as a tool for truncation

This paper is concerned with the difficulties in model testing deepwater structures at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation. Passive truncation has traditionally been the preferred method by industry; however, these techniques tend to suffer in capturing accurately line dynamic response and so reproducing peak tensions. In an attempt to improve credibility of model test data the proposed truncation procedure sets up the truncated model, based on line dynamic response rather than quasi-static system stiffness. Vibration decay of transverse elastic waves due to fluid drag forces is assessed and it is found that below a certain length criterion, the transverse vibrational characteristics for each line are inertia driven, hence with respect to these motions the truncated model can assume a linear damper whose coefficient depends on the local line properties and vibration frequency. Initially a simplified taut string model is assumed for which the line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a general guideline for the truncation length criterion, which is suitable for any kind of line with any top motion. The focus of this paper is to extend this work to a more complex line configuration of a conventional deepwater mooring line and so enhance the generality of the truncation guideline. The paper will close with an example case study of a spread mooring system, applying this method to create an equivalent numerical model at a reduced depth that replicates exactly the static and dynamic characteristics of the full depth system. Copyright © 2012 by ASME.

Analytical model and experimental validation of friction laws for composites under low loads

In order to account for interfacial friction of composite materials, an analytical model based on contact geometry and local friction is proposed. A contact area includes several types of microcontacts depending on reinforcement materials and their shape. A proportion between these areas is defined by in-plane contact geometry. The model applied to a fibre-reinforced composite results in the dependence of friction on surface fibre fraction and local friction coefficients. To validate this analytical model, an experimental study on carbon fibrereinforced epoxy composites under low normal pressure was performed. The effects of fibre volume fraction and fibre orientation were studied, discussed and compared with analytical model results. © Springer Science+Business Media, LLC 2012.

Characterization and deformation response of orthotropic fibre networks with auxetic out-of-plane behaviour

In the present paper, highly porous fibre networks made of 316L fibres, with different fibre volume fractions, are characterized in terms of network architecture, elastic constants and fracture energies. Elastic constants are measured using quasi-static mechanical and modal vibration testing, yielding local and globally averaged properties, respectively. Differences between quasi-static and dynamic elastic constants are attributed to through-thickness shear effects. Regardless of the method employed, networks show signs of material inhomogeneity at high fibre densities, in agreement with X-ray nanotomography results. Strong auxetic (or negative Poisson's ratio) behaviour is observed in the through-thickness direction, which is attributed to fibre kinking induced during processing. Measured fracture energies are compared with model predictions incorporating information about in-plane fibre orientation distribution, fibre volume fraction and single fibre work of fracture. Experimental values are broadly consistent with model predictions, based on the assumption that this energy is primarily associated with plastic deformation of individual fibres within a process zone of the same order as the inter-joint spacing. © 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

Numerical study on hydrate bearing sediments during gas production

The fully coupled methane hydrate model developed in Cambridge was adopted in this numerical study on gas production trial at the Eastern Nankai Trough, Japan 2013. Based on the latest experimental data of hydrate soil core samples, the clay parameters at Eastern Nankai site were successfully calibrated. With updated clay parameters and site geometry, a 50 days gas production trail was numerically simulated in FLAC2D. The geomechanical behaviour of hydrate bearing sediments under 3 different depressurization strategies were explored and discussed. The results from both axisymmetrical and plane-strain models suggest, the slope of the seabed only affects mechanical properties while no significant impact on the dissociation, temperature and pore pressure. For mechanical deformation after PT recovery, there are large settlements above the perforation zone and small uplift underneath the production zone. To validate the fully coupled model, numerical simulation with finer mesh in the hydrate production zone was carried out. The simulation results suggest good agreement between our model and JOE's results on history matching of gas and water production during trial. Parameter sensitivity of gas production is also investigated and concluded the sea water salinity is a dominant factor for gas production.