BRITTLE FRACTURE OF ICE LAYER UNDER WATER LEVEL LOWERING
Journal: BULLETIN OF KSAU
№ 4
, 2018
Rubrics: TEHNICHESKIE NAUKI
Authors:
1.
Krasnoyarsk State Agrarian University
Type:
Article
Pages:
from 120
to 127
Status:
Published
Received:
21.08.2018
Accepted:
23.08.2018
Published:
25.08.2018
Subject area:
UDK 539.3+532.5
Language:
Russian
Keywords:
numerical simulation, elastic plate, or-thogonal polynomials
Abstract (English):
The work continues studying of behavior of thick ice field floating on water surface at abatement of water level. Earlier stationary task of equilibrium of ice layer near flat site of the coast was considered. Various ways of contact with the coast were studied, intense and de-formable fortune of an ice field, as with free top surface, and loaded with some force come into; the assessment of "dangerous zone" is executed. Natural supervision of the destruction of ice testifies about the existence in the ice field of two characteristic cracks: in the place of con-tact with the coast and at the distance of 10-12 thick-ness. However, within stationary task it is not possible to explain the emergence of the second crack. All these results need considering dynamics of behavior of an ice field after the emergence of the first crack. In the study the attempt to simulate the behavior of ice is made so that the tension of an ice layer gave concentration of stretching tension near the coast and at some distance from it that is probable and provides destruction near these sites. In the study approximate solution of dynam-ic contact task considering incompressibility of water on which ice floats was received. The accounting of incom-pressibility brings to the ice field subtime water and to fast emergence of the second crack. At numerical solu-tion of the task there were serious difficulties. The deci-sion was based on the methods of operational calcula-tion. Laplace's transformation on time and Fourier's co-sine transformation on one of spatial variables was ap-plied to regional task to the system of differential equa-tions with private derivative of functions with three vari-ables. Limited decision of received system of ordinary differential equations managed to be written out in the form of meeting not own integrals. Numerical address of transformation of Laplace of the image of unknown func-tion caused the greatest difficulties. Known methods of numerical address were unacceptable as they demand the knowledge of the order of decrease of the image. The address was necessary to do with the help of sine - and Fourier's cosine transformation with a large number of integrating knots. Calculations provided necessary accuracy.
The work continues studying of behavior of thick ice field floating on water surface at abatement of water level. Earlier stationary task of equilibrium of ice layer near flat site of the coast was considered. Various ways of contact with the coast were studied, intense and de-formable fortune of an ice field, as with free top surface, and loaded with some force come into; the assessment of "dangerous zone" is executed. Natural supervision of the destruction of ice testifies about the existence in the ice field of two characteristic cracks: in the place of con-tact with the coast and at the distance of 10-12 thick-ness. However, within stationary task it is not possible to explain the emergence of the second crack. All these results need considering dynamics of behavior of an ice field after the emergence of the first crack. In the study the attempt to simulate the behavior of ice is made so that the tension of an ice layer gave concentration of stretching tension near the coast and at some distance from it that is probable and provides destruction near these sites. In the study approximate solution of dynam-ic contact task considering incompressibility of water on which ice floats was received. The accounting of incom-pressibility brings to the ice field subtime water and to fast emergence of the second crack. At numerical solu-tion of the task there were serious difficulties. The deci-sion was based on the methods of operational calcula-tion. Laplace's transformation on time and Fourier's co-sine transformation on one of spatial variables was ap-plied to regional task to the system of differential equa-tions with private derivative of functions with three vari-ables. Limited decision of received system of ordinary differential equations managed to be written out in the form of meeting not own integrals. Numerical address of transformation of Laplace of the image of unknown func-tion caused the greatest difficulties. Known methods of numerical address were unacceptable as they demand the knowledge of the order of decrease of the image. The address was necessary to do with the help of sine - and Fourier's cosine transformation with a large number of integrating knots. Calculations provided necessary accuracy.
Keywords:
numerical simulation, elastic plate, or-thogonal polynomials
numerical simulation, elastic plate, or-thogonal polynomials
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