scholarly journals Concentrated Loads on a Floating Ice Sheet

1977 ◽  
Vol 19 (81) ◽  
pp. 237-245 ◽  
Author(s):  
D. E. Nevel
Keyword(s):  
Load Distribution ◽  
Elastic Layer ◽  
Plate Theory ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Integral Form ◽  
Maximum Tensile Stress ◽  
Radial Position ◽  
Ice Thickness ◽  
Concentrated Loads

Abstract The safe bearing capacity of a floating ice sheet is usually determined by limiting the maximum tensile stress which occurs under the load at the bottom of the ice sheet. If the size of the load distribution is large compared to the ice thickness, the thin plate theory predicts these stresses correctly. However, if the size of the load distribution becomes small compared to the ice thickness, the plate theory overestimates the stresses. In this case the ice sheet should he treated as a three-dimensional elastic layer. Previous investigators have solved the elastic-layer problem for loads distributed over a circular area, and have limited the results to the stress at the bottom of the ice sheet directly under the center of the load. In the present paper the stresses are evaluated at any radial position, and it is shown how these stresses approach those for the plate theory as the radial position becomes large. The solutions for the stresses are presented in integral form, as well as graphs from the numerical integration. These new results are significant for the superposition of stresses when two concentrated loads act near each other. Similarly for loads distributed over a rectangular area, the plate theory will overestimate the stresses if the dimensions of the load becomes small compared to the ice thickness. For this case integral solutions are presented for the stresses, and are evaluated directly under the center of the load.

scholarly journals Concentrated Loads on a Floating Ice Sheet

1977 ◽  
Vol 19 (81) ◽  
pp. 237-245
Author(s):  
D. E. Nevel
Keyword(s):  
Load Distribution ◽  
Elastic Layer ◽  
Plate Theory ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Integral Form ◽  
Maximum Tensile Stress ◽  
Radial Position ◽  
Ice Thickness ◽  
Concentrated Loads

AbstractThe safe bearing capacity of a floating ice sheet is usually determined by limiting the maximum tensile stress which occurs under the load at the bottom of the ice sheet. If the size of the load distribution is large compared to the ice thickness, the thin plate theory predicts these stresses correctly. However, if the size of the load distribution becomes small compared to the ice thickness, the plate theory overestimates the stresses. In this case the ice sheet should he treated as a three-dimensional elastic layer.Previous investigators have solved the elastic-layer problem for loads distributed over a circular area, and have limited the results to the stress at the bottom of the ice sheet directly under the center of the load. In the present paper the stresses are evaluated at any radial position, and it is shown how these stresses approach those for the plate theory as the radial position becomes large. The solutions for the stresses are presented in integral form, as well as graphs from the numerical integration. These new results are significant for the superposition of stresses when two concentrated loads act near each other.Similarly for loads distributed over a rectangular area, the plate theory will overestimate the stresses if the dimensions of the load becomes small compared to the ice thickness. For this case integral solutions are presented for the stresses, and are evaluated directly under the center of the load.

scholarly journals Basal temperature conditions of the Greenland ice sheet during the glacial cycles

1996 ◽  
Vol 23 ◽  
pp. 226-236 ◽  
Author(s):  
Philippe Huybrechts
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Ice Thickness ◽  
Glacial Cycle ◽  
Glacial Cycles ◽  
Temperature Conditions ◽  
Strongly Damped

A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.

scholarly journals Basal temperature conditions of the Greenland ice sheet during the glacial cycles

1996 ◽  
Vol 23 ◽  
pp. 226-236 ◽  
Author(s):  
Philippe Huybrechts
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Ice Thickness ◽  
Glacial Cycle ◽  
Glacial Cycles ◽  
Temperature Conditions ◽  
Strongly Damped

A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ 180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.

Elastic and Viscoelastic Foundation Models

1964 ◽  
Vol 31 (3) ◽  
pp. 491-498 ◽  
Author(s):  
Arnold D. Kerr
Keyword(s):  
Load Distribution ◽  
Plate Theory ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Critical Study ◽  
Pasternak Foundation ◽  
Modified Bessel Function ◽  
Classical Plate Theory ◽  
Physical Problems ◽  
Further Development

The present paper contains a critical study of a number of foundation models as well as a further development of some of the ideas involved. Among others it is shown that the Pasternak foundation is a mechanical model for the so-called “generalized” foundation. It is also demonstrated that the kernel for the Pasternak foundation in plane stress or plane strain is identical with Wieghardt’s exponential kernel, and that for the three-dimensional case the kernel is a modified Bessel function. It is also shown that the “non solvability” of the problem of a finite beam or plate resting on a continuous foundation as posed by Wieghardt and further elaborated by Pflanz is not correct, and that problems of this type are solvable for any load distribution permissible in classical plate theory. Throughout the paper, emphasis is placed on the proper mathematical formulation of the physical problems in question.

scholarly journals Hydroelastic wave diffraction by a vertical cylinder

2011 ◽  
Vol 369 (1947) ◽  
pp. 2832-2851 ◽  
Author(s):  
Paul Brocklehurst ◽  
Alexander Korobkin ◽  
Emilian I. Părău
Keyword(s):  
Incident Wave ◽  
Wave Diffraction ◽  
Plate Theory ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Cylinder Surface ◽  
Linear Elastic ◽  
Potential Flow Model

A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave.

scholarly journals A substrate for brane shells from $$ T\overline{T} $$

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jeremias Aguilera-Damia ◽  
Louise M. Anderson ◽  
Evan Coleman
Keyword(s):  
Three Dimensional ◽  
Radial Position ◽  
Singular Behavior ◽  
Curvature Singularity ◽  
Closed Timelike Curves ◽  
Finite Radius ◽  
Linear Dilaton ◽  
Singularity Resolution ◽  
New Interpretation ◽  
Single Trace

Abstract A solvable current-current deformation of the worldsheet theory of strings on AdS3 has been recently conjectured to be dual to an irrelevant deformation of the spacetime orbifold CFT, commonly referred to as single-trace $$ T\overline{T} $$ T T ¯ . These deformations give rise to a family of bulk geometries which realize a non-trivial flow towards the UV. For a particular sign of this deformation, the corresponding three-dimensional geometry approaches AdS3 in the interior, but has a curvature singularity at finite radius, beyond which there are closed timelike curves. It has been suggested that this singularity is due to the presence of “negative branes,” which are exotic objects that generically change the metric signature. We propose an alternative UV-completion for geometries displaying a similar singular behavior by cutting and gluing to a regular background which approaches a linear dilaton vacuum in the UV. In the S-dual picture, a singularity resolution mechanism known as the enhançon induces this transition by the formation of a shell of D5-branes at a fixed radial position near the singularity. The solutions involving negative branes gain a new interpretation in this context.

scholarly journals Coherent radar ice thickness measurements over the Greenland ice sheet

2001 ◽  
Vol 106 (D24) ◽  
pp. 33761-33772 ◽  
Author(s):  
S. Gogineni ◽  
D. Tammana ◽  
D. Braaten ◽  
C. Leuschen ◽  
T. Akins ◽  
...  
Keyword(s):  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Coherent Radar ◽  
Thickness Measurements

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

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