scholarly journals Modeling of deformation of the bimaterial with thin Non-linear interface inclusion

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 40-57
Author(s):  
Y. Z. Piskozub ◽  
H. T. Sulym
Keyword(s):  
Singular Integral Equations ◽  
Variable Coefficients ◽  
Concentrated Force ◽  
Linear Deformation ◽  
Static Loads ◽  
Force System ◽  
Analytical Functions ◽  
Antiplane Problem ◽  
Non Linear ◽  
Deformation Models

An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (SSIE) on jump functions with variable coefficients allowing us to describe any quasi-static loads (monotonous or not) and their influence on the stress-strain state in the bulk. To solve the SSIE problem, an iterative analytical-numerical method is offered for various non-linear deformation models. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analyzed for a deformed body under a load of a balanced concentrated force system.

scholarly journals Antiplane Deformation of a Bimaterial with Thin Interfacial Nonlinear Elastic Inclusion

2018 ◽  
Vol 12 (3) ◽  
pp. 190-195
Author(s):  
Heorhiy Sulym ◽  
Yosyf Piskozub ◽  
Julian Polanski
Keyword(s):  
Elastic Inclusion ◽  
Singular Integral Equations ◽  
Longitudinal Shear ◽  
Variable Coefficients ◽  
Thin Inclusion ◽  
Shear Stresses ◽  
Antiplane Deformation ◽  
Characteristic Parameters ◽  
Analytical Functions ◽  
Nonlinear Elastic

Abstract The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.

scholarly journals Antiplane Deformation Of A Bimaterial Containing An Interfacial Crack With The Account Of Friction 2. Repeating And Cyclic Loading

2015 ◽  
Vol 9 (3) ◽  
pp. 178-184 ◽  
Author(s):  
Heorhiy Sulym ◽  
Lyubov Piskozub ◽  
Yosyf Piskozub ◽  
Iaroslav Pasternak
Keyword(s):  
Cyclic Loading ◽  
Function Method ◽  
Sliding Friction ◽  
Normal Load ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Longitudinal Direction ◽  
Antiplane Deformation ◽  
Concentrated Force ◽  
Antiplane Problem

Abstract The paper presents the exact solution of the antiplane problem for an inhomogeneous bimaterial with the interface crack exposed to the normal load and cyclic loading by a concentrated force in the longitudinal direction. Using discontinuity function method the problem is reduced to the solution of singular integral equations for the displacement and stress discontinuities at the domains with sliding friction. The paper provides the analysis of the effect of friction and loading parameters on the size of these zones. Hysteretic behaviour of the stress and displacement discontinuities in these domains is observed.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

2021 ◽  
Vol 316 ◽  
pp. 936-941
Author(s):  
Natalya Ya. Golovina
Keyword(s):  
Mathematical Models ◽  
Strain Curve ◽  
Variational Model ◽  
Linear Deformation ◽  
Plastic Materials ◽  
Non Linear ◽  
Linear Sections ◽  
Elastic Plastic Materials ◽  
Deformation Section ◽  
St3sp Steel

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

scholarly journals Deformation of rockfill in bodies of rockfill dams

2019 ◽  
pp. 5-5
Author(s):  
Mikhail Sainov
Keyword(s):  
Reinforced Concrete ◽  
Deformation Modulus ◽  
Deformation Model ◽  
Observation Data ◽  
Linear Deformation ◽  
Laboratory Test Results ◽  
Wide Range ◽  
Deformation Properties ◽  
Non Linear ◽  
The Impact

Introduction. The main factor determining the stress-strain state (SSS) of rockfill dam with reinforced concrete faces is deformability of the dam body material, mostly rockfill. However, the deformation properties of rockfill have not been sufficiently studied yet for the time being due to technical complexity of the matter, Materials and methods. To determine the deformation parameters of rockfill, scientific and technical information on the results of rockfill laboratory tests in stabilometers were collected and analyzed, as well as field data on deformations in the existing rockfill dams. After that, the values of rockfill linear deformation modulus obtained in the laboratory and in the field were compared. The laboratory test results were processed and analyzed to determine the parameters of the non-linear rockfill deformation model. Results. Analyses of the field observation data demonstrates that the deformation of the rockfill in the existing dams varies in a wide range: its linear deformation modulus may vary from 30 to 500 МPа. It was found out that the results of the most rockfill tests conducted in the laboratory, as a rule, approximately correspond to the lower limit of the rockfill deformation modulus variation range in the bodies of the existing dams. This can be explained by the discrepancy in density and particle sizes of model and natural soils. Only recently, results of rockfill experimental tests were obtained which were comparable with the results of the field measurements. They demonstrate that depending on the stress state the rockfill linear deformation modulus may reach 700 МPа. The processing of the results of those experiments made it possible to determine the parameters on the non-linear model describing the deformation of rockfill in the dam body. Conclusions. The obtained data allows for enhancement of the validity of rockfill dams SSS analyses, as well as for studying of the impact of the non-linear character of the rockfill deformation on the SSS of reinforced concrete faces of rockfill dams.

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

scholarly journals Analysis and settlement evaluation of an end-bearing granular pile with non-linear deformation modulus

2018 ◽  
Vol 40 (3) ◽  
pp. 188-201 ◽  
Author(s):  
Jitendra Kumar Sharma ◽  
Pooja Gupta
Keyword(s):  
Influence Factor ◽  
Ground Improvement ◽  
Deformation Modulus ◽  
Relative Length ◽  
Stone Columns ◽  
Linear Deformation ◽  
Dense Sand ◽  
Granular Pile ◽  
Non Linear ◽  
Granular Piles

AbstractGround improvement with granular piles increases the load-carrying capacity, reduces the settlement of foundations built on the reinforced ground and is also a good alternative to concrete pile. Granular piles or stone columns are composed of granular material, such as crushed stone or coarse dense sand. An analytical approach based on the continuum approach is presented for the non-linear behaviour of the granular pile. The formulation for pile element displacement is done considering the non-homogeneity of the granular pile as it reflects the true behaviour and also accounts for the changes in the state of the granular pile due to installation, stiffening and improvement effects. The present study shows that the settlement influence factor for an end-bearing granular pile decreases with increase in the relative stiffness of the bearing stratum. The settlement influence factor decreases with increase in linear and non-linear non-homogeneity parameters for all values of relative length. For a shorter pile, the rate of decrease of the settlement influence factor is greater in comparison to that for a longer pile. Shear stress at the soil–granular pile interface reduces in the upper compressible portion of the granular pile and increases in the lower stiffer portion of the granular pile due to the non-homogeneity of an end-bearing granular pile.

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