Part-through bending cracks in sea ice plates: Mathematical modeling

Zdenek P. Bazant, J. J H Kim, Yuan N. Li

Research output: Contribution to journalConference article

10 Citations (Scopus)

Abstract

The paper presents a new mathematical model for propagation of part-through bending cracks in floating sea ice plate, which is a problem of considerable practical importance, for example, the load carrying capacity or penetration through the ice plate. After reviewing the previous work on propagation of through-cracks due to transverse loads, the three-dimensional problem of part-through cracks is simplified as two-dimensional using the well known approximation by line springs. These nonlinear springs describe the relation of rotation and additional in-plane expansion due to part-through crack to the bending moment and normal force transmitted through the crack. The problem of several radial cracks emanating from a small loaded area is analyzed. The bending and in-plane elastic responses of the floating plate are described by compliance functions. It is shown that the rotations across the crack cause the compression resultant in the plates and the neutral axis of the stress to shift above the mid-thickness of plates. This represents a dome effect which carries a significant part of the load. The profile of the crack depth propagating upward and the shape of the dome are calculated. A study of the failure loads and the size effect is left for a subsequent paper.

Original languageEnglish
Pages (from-to)97-105
Number of pages9
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume207
Publication statusPublished - 1995 Jan 1

Fingerprint

Sea ice
Cracks
Domes
Load limits
Bending moments
Ice
Mathematical models

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

@article{7ab12e10e4044d758cd654ad7e8e89d1,
title = "Part-through bending cracks in sea ice plates: Mathematical modeling",
abstract = "The paper presents a new mathematical model for propagation of part-through bending cracks in floating sea ice plate, which is a problem of considerable practical importance, for example, the load carrying capacity or penetration through the ice plate. After reviewing the previous work on propagation of through-cracks due to transverse loads, the three-dimensional problem of part-through cracks is simplified as two-dimensional using the well known approximation by line springs. These nonlinear springs describe the relation of rotation and additional in-plane expansion due to part-through crack to the bending moment and normal force transmitted through the crack. The problem of several radial cracks emanating from a small loaded area is analyzed. The bending and in-plane elastic responses of the floating plate are described by compliance functions. It is shown that the rotations across the crack cause the compression resultant in the plates and the neutral axis of the stress to shift above the mid-thickness of plates. This represents a dome effect which carries a significant part of the load. The profile of the crack depth propagating upward and the shape of the dome are calculated. A study of the failure loads and the size effect is left for a subsequent paper.",
author = "Bazant, {Zdenek P.} and Kim, {J. J H} and Li, {Yuan N.}",
year = "1995",
month = "1",
day = "1",
language = "English",
volume = "207",
pages = "97--105",
journal = "American Society of Mechanical Engineers, Applied Mechanics Division, AMD",
issn = "0160-8835",

}

Part-through bending cracks in sea ice plates : Mathematical modeling. / Bazant, Zdenek P.; Kim, J. J H; Li, Yuan N.

In: American Society of Mechanical Engineers, Applied Mechanics Division, AMD, Vol. 207, 01.01.1995, p. 97-105.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Part-through bending cracks in sea ice plates

T2 - Mathematical modeling

AU - Bazant, Zdenek P.

AU - Kim, J. J H

AU - Li, Yuan N.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - The paper presents a new mathematical model for propagation of part-through bending cracks in floating sea ice plate, which is a problem of considerable practical importance, for example, the load carrying capacity or penetration through the ice plate. After reviewing the previous work on propagation of through-cracks due to transverse loads, the three-dimensional problem of part-through cracks is simplified as two-dimensional using the well known approximation by line springs. These nonlinear springs describe the relation of rotation and additional in-plane expansion due to part-through crack to the bending moment and normal force transmitted through the crack. The problem of several radial cracks emanating from a small loaded area is analyzed. The bending and in-plane elastic responses of the floating plate are described by compliance functions. It is shown that the rotations across the crack cause the compression resultant in the plates and the neutral axis of the stress to shift above the mid-thickness of plates. This represents a dome effect which carries a significant part of the load. The profile of the crack depth propagating upward and the shape of the dome are calculated. A study of the failure loads and the size effect is left for a subsequent paper.

AB - The paper presents a new mathematical model for propagation of part-through bending cracks in floating sea ice plate, which is a problem of considerable practical importance, for example, the load carrying capacity or penetration through the ice plate. After reviewing the previous work on propagation of through-cracks due to transverse loads, the three-dimensional problem of part-through cracks is simplified as two-dimensional using the well known approximation by line springs. These nonlinear springs describe the relation of rotation and additional in-plane expansion due to part-through crack to the bending moment and normal force transmitted through the crack. The problem of several radial cracks emanating from a small loaded area is analyzed. The bending and in-plane elastic responses of the floating plate are described by compliance functions. It is shown that the rotations across the crack cause the compression resultant in the plates and the neutral axis of the stress to shift above the mid-thickness of plates. This represents a dome effect which carries a significant part of the load. The profile of the crack depth propagating upward and the shape of the dome are calculated. A study of the failure loads and the size effect is left for a subsequent paper.

UR - http://www.scopus.com/inward/record.url?scp=0029181453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029181453&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0029181453

VL - 207

SP - 97

EP - 105

JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

JF - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

SN - 0160-8835

ER -