scholarly journals Modeling of relative shear deformation zones before strong earthquakes in Kamchatka from 2018-2021

2021 ◽  
pp. 53-66
Author(s):  
М.И. Гапеев ◽  
Ю.В. Марапулец
Keyword(s):  
Point Source ◽  
Shear Deformation ◽  
Comparative Modeling ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Strong Earthquakes ◽  
Relative Shear ◽  
Rectangular Area ◽  
Single Force ◽  
Different Sources

Представлено сравнительное моделирование зон относительных сдвиговых деформаций для четырех камчатских землетрясений с Mw ≥ 4.8, произошедших в период с декабря 2018 г. по март 2021 г., основанное на статической модели деформационного поля в рамках теории упругости. Земная кора рассмотрена как однородное изотропное упругое полупространство, в котором присутствуют различные источники напряжения, описывающие очаг землетрясения: точечный источник в виде единичной силы, точечный источник в виде комбинации девяти двойных сил, распределенный источник в виде прямоугольной площадки. We present a comparative modeling of the zones of relative shear deformation for four Kamchatka earthquakes Mw≥4.8 that occurred between December 2018 and March 2021. Modeling based on a static model of the deformation field in the framework of the theory of elasticity. The Earth’s crust is considered as a homogeneous isotropic elastic half-space, in which there are different sources of stress describing the source of the earthquake: a point source in the form of a single force, a point source in the form of a combination of nine double forces, a distributed source in the form of a rectangular area.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

scholarly journals Contact interaction of prestressed annular punch and half-space

2020 ◽  
pp. 24-30
Author(s):  
S.Yu. Babich ◽  
◽  
N.O. Yaretska ◽  
Keyword(s):  
Half Space ◽  
Contact Interaction ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Natural State ◽  
Small Perturbations ◽  
Linearized Theory Of Elasticity ◽  
Annular Punch ◽  
Linearized Theory ◽  
Deformed State

The article is devoted to the task of contact interaction of the pressure of a pre-stressed cylindrical annular punch on the half-space with initial (residual) stresses without friction. It is solved for the case of unequal roots of the characteristic equation. In general, the research was carried out for the theory of great initial (ultimate) deformations and two variants of the theory of small initial ones within the framework of linearized theory of elasticity with the elastic potential having any structure. It is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. It is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials.

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

2019 ◽  
Vol 968 ◽  
pp. 475-485 ◽  
Author(s):  
Stanislav Koval’chuk ◽  
Alexey Goryk
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Theory Of Elasticity ◽  
Transverse Shear Deformation ◽  
Uniform Load ◽  
Principle Of Superposition ◽  
Elastic Bending ◽  
Transverse Bending

An exact solution of the theory of elasticity is presented for the problem of a narrow multilayer bar section transverse bending under the action of a normal uniform load on longitudinal faces. The solution is built using the principle of superposition, by imposing common solutions to the problems of bending a multilayer cantilever with uniform loads on the longitudinal faces and an arbitrary load on the free end, and allows to take into account the orthotropy of the materials of the layers, as well as transverse shear deformation and compression. On the basis of a built-in general solution, a number of particular solutions are obtained for multi-layer beams with various ways of the ends fixing.

scholarly journals Impact of cutting face profile angle upon shear deformation degree

2017 ◽  
Vol 2 (6) ◽  
pp. 14-20 ◽  
Author(s):  
Александр Ямников ◽  
Aleksandr Yamnikov ◽  
Дмитрий Волков ◽  
Dmitry Volkov
Keyword(s):  
Shear Deformation ◽  
Metal Cutting ◽  
Cutting Tools ◽  
Deformation Degree ◽  
Thread Cutting ◽  
Profile Angle ◽  
Chip Flow ◽  
Relative Shear ◽  
Definition Of ◽  
The Impact

It is established that cutting with gear-cutting and thread-cutting tools is not free that results in the increase of loading upon tool tips and their quick wear. The layers of metal cut are subjected to considerable shear deformation and also to other kinds of deformation. In this connection the wear character of a tool and its properties will change. There is considered a process of chip removal by trapezoidal and triangular cutters (as in case of metal cutting off with teeth of a hob may be used not three but two tool tips) and the impact of a cutting face profile angle upon a shear deformation degree is also considered. There are shown analytical dependences for the definition of angles of a chip flow, a relative shear, a deformation degree of a shear and a value of tangential stresses in the cutting area taking into account the influence of the strength of material machined, width and thickness of a layer cut and a friction factor. The dependences are checked up at cutting with a trapezoidal cutter.

scholarly journals Thermomechanical Slip in Elastic Contact Between Identical Materials

2021 ◽  
Vol 15 (4) ◽  
pp. 187-192
Author(s):  
Yurii Streliaiev ◽  
Rostyslav Martynyak ◽  
Kostyantyn Chumak
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Thermal Loading ◽  
Boundary Integral Equations ◽  
Contact Region ◽  
Elastic Half Space ◽  
Boundary Integral ◽  
Subsequent Stage ◽  
Relative Shear ◽  
Increasing Temperature

Abstract The contact problem for interaction between an elastic sphere and an elastic half-space is considered taking into account partial thermomechanical frictional slip induced by thermal expansion of the half-space. The elastic constants of the bodies are assumed to be identical. The Amontons–Coulomb law is used to account for friction. The problem is reduced to non-linear boundary integral equations that correspond to the initial stage of mechanical loading and the subsequent stage of thermal loading. The dependences of the contact stress distribution, relative displacements of the contacting surfaces, dimensions of the stick and slip zones on temperature of the half-space are studied numerically. It was revealed that an increase in temperature causes increases in the shear contact stress and the relative shear displacements of the contacting surfaces. The absolute values of the shear contact stress reach their maximum at the boundaries of the stick zones. The greatest value of the moduli of the relative shear displacements are reached at the boundary of the contact region. The stick zone radius decreases monotonically according to a nonlinear law with increasing temperature.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 101-103
Author(s):  
І. Kalinyuk ◽  
Keyword(s):  
Phase Velocity ◽  
Point Source ◽  
Dispersion Equation ◽  
Zero Mode ◽  
Elastic Half Space ◽  
Homogeneous Layer ◽  
Sediment Thickness ◽  
Complex Phase ◽  
Waveguide Model ◽  
Liquid Precipitation

In this paper, two hydro acoustic waveguide model with absorption, which consists of a homogeneous layer of water, a uniform layer of liquid precipitation and an elastic half-space, which is a point source. Numerically solved the dispersion equation that defined the complex phase velocity. The influence of sediment thickness on the phase velocity of the zero mode.

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