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1996 | Buch

Preamble Kapitel lesen Erstes Kapitel lesen

Moving Loads on Ice Plates

verfasst von: Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne

Verlag: Springer Netherlands

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Professional Book Archive

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Über dieses Buch

Moving Loads on Ice Plates is a unique study into the effect of vehicles and aircraft travelling across floating ice sheets. It synthesizes in a single volume, with a coherent theme and nomenclature, the diverse literature on the topic, hitherto available only as research journal articles. Chapters on the nature of fresh water ice and sea ice, and on applied continuum mechanics are included, as is a chapter on the subject's venerable history in related areas of engineering and science. The most recent theories and data are discussed in great depth, demonstrating the advanced state of the modelling and experimental field programmes that have taken place. Finally, results are interpreted in the context of engineering questions faced by agencies operating in the polar and subpolar regions.
Although the book necessarily contains some graduate level applied mathematics, it is written to allow engineers, physicists and mathematicians to extract the information they need without becoming preoccupied with details. Structural, environmental, civil, and offshore engineers, and groups who support these industries, particularly within the Arctic and Antarctic, will find the book timely and relevant.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Preamble
Abstract
The wisdom and experience of the later Vikings of Norway and Iceland evidently shunned contemporary political correctness, but was alert to treacherous ice crossings.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 2. Structure and Properties of Ice Plates
Abstract
In order to make any problem tractable, the applied mathematician must make some assumptions about nature. It is an aim of this chapter to introduce the reader to the physical and mechanical properties of ice sheets, so that they may judge for themselves the validity of the assumptions made throughout the remainder of the book. We shall begin with an outline of the atomic structure of ice in Section 2.2. Sea ice occupies up to 15% of the earth’s surface in the months of January and February, and because of this enormous areal extent its growth and physical properties must be reviewed. This is done in Section 2.3. With some notable exceptions, lake and river ice formation is largely based on the same principles as sea ice and may be regarded as a special case in the limit of very low salinity. We add features peculiar to freshwater ice in Section 2.4. In Section 2.5 we describe the mechanical behaviour of freshwater ice and sea ice pertinent to the subject matter of the remainder of the book. We treat all ice sheets without regard to their geographical location.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 3. Continuum Mechanics
Abstract
This chapter introduces the equations of continuum mechanics used in the book to describe the action of a load moving over a continuously supported plate. We shall bias our discussion towards the case of a floating ice plate, although at least qualitatively the discussion is applicable more generally to continuously supported plates subject to moving loads.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 4. Historical Perspectives
Abstract
In Chapter 3 we have seen that the mathematical modelling of a continuously supported plate subjected to a moving load (Figure 4.1) involves coupled equations for the plate and for the supporting fluid base. The moving load is included by considering its weight and possibly its inertial effects. The purpose of this chapter is to introduce the reader to the subject area of moving loads over floating ice covers, by first discussing some relatively simple historical examples to illustrate certain mechanical and mathematical features of problems of this type. This discussion therefore anticipates some aspects of the more complete theory that we approach towards the end of this chapter, and then develop systematically in Chapter 5.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 5. Theoretical Advances
Abstract
The theoretical response of a floating ice sheet to a moving load is discussed further in this chapter. The results described are mainly derived from our simplest acceptable mathematical model, corresponding to a thin elastic or viscoelastic plate of infinite extent resting on an incompressible inviscid fluid of finite depth. Towards the end of Chapter 3 we formulated the elastic equation (3.44) for this model, noting that the water beneath should satisfy the Laplace equation (3.33) together with a linearized kinematic (noncavitation) condition (3.37) applied at the surface z = 0 and a normal flow condition (3.39) at the bottom z = -H. The system to be solved is therefore
$$ {\nabla^2}\phi = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = - H}}} \right. = 0,\quad \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. = \frac{{\partial \zeta }}{{\partial t}} $$
(5.1a)
$$ D{\nabla^4}\zeta + \rho 'h\frac{{{\partial^2}\zeta }}{{\partial {t^2}}} + \rho g\zeta = - \rho \frac{{\partial \phi }}{{\partial z}}\left| {_{{z = 0}}} \right. - f\left( {x,y,t} \right) $$
(5.1b)
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 6. Experiments Involving Moving Loads
Abstract
There have been various experiments to investigate the effects of loads moving across floating ice sheets. In chronological order, field experiments reported in the open literature are due to Wilson (1955, 1958), Anderson (1958a), Sunberg-Falkenmark (1963), Eyre (1977), Goodman and Holdsworth (1978), Takizawa (1978), Kubo (1980), Beltaos (1981), Davys (1984), Takizawa (1985), Squire et al. (1985, 1986), Takizawa (1987), Squire et al. (1988), and Takizawa (1988). The field work spans both hemispheres, although there is some bias toward the northern hemisphere simply because transport across ice sheets in the Arctic has been more common. Some laboratory experiments also have been reported by Hinchey (1987) and Whitten and Hinchey (1988). Some of these publications naturally contain a theoretical element.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Chapter 7. Implications and Conclusions
Abstract
While theory and field experiment are in good accord, the computation of the deflexions, strains, and consequently, the stresses initiated within an ice sheet due to a passing vehicle or a landing aircraft requires the thickness of the sheet to be known together with other particulars of the physical and mechanical character of the ice. This information may be found by direct measurement, usually by coring and perhaps cantilever tests, or inferred from instruments capable of monitoring the effect of the load directly.
Vernon A. Squire, Roger J. Hosking, Arnold D. Kerr, Patricia J. Langhorne
Backmatter
Metadaten
Titel
Moving Loads on Ice Plates
verfasst von
Vernon A. Squire
Roger J. Hosking
Arnold D. Kerr
Patricia J. Langhorne
Copyright-Jahr
1996
Verlag
Springer Netherlands
Electronic ISBN
978-94-009-1649-4
Print ISBN
978-94-010-7238-0
DOI
https://doi.org/10.1007/978-94-009-1649-4