scholarly journals On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

2015 ◽  
Vol 9 (1) ◽  
pp. 27-32
Author(s):  
Andriy Styahar ◽  
Yarema Savula
Keyword(s):  
Domain Decomposition ◽  
Strain State ◽  
The Body ◽  
Decomposition Algorithm ◽  
Thin Inclusion ◽  
Stress Strain ◽  
Linear Elasticity Theory ◽  
Stress Strain State ◽  
Domain Decomposition Algorithm ◽  
Well Posed

Abstract We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.

scholarly journals Physically nonlinear deformation of a thin interphase inclusion under antiplane problem conditions

2019 ◽  
pp. 42-54
Author(s):  
Yosyf Piskozub ◽  
Heorgiy Sulym ◽  
Liubov Piskozub
Keyword(s):  
Nonlinear Deformation ◽  
Strain State ◽  
Variable Coefficients ◽  
The Body ◽  
Thin Inclusion ◽  
Stress Strain ◽  
Limit Values ◽  
Stress Strain State ◽  
Physically Nonlinear Deformation ◽  
Antiplane Problem

The longitudinal shear problem of the bimaterial with thin physically nonlinear inclusion at the interface matrix materials is considered. The solution of the formulated problem is constructed by the method of the conjugation of limit values of analytical functions with the use of the jump function method. A model of thin inclusion with arbitrary nonlinear strain characteristics is constructed. The solution of the problem is reduced to a system of singular integral equations with variable coefficients. A convergent iteration method for solving such a system for different types of physically nonlinear deformation is proposed. An incremental calculation method for calculating stress-strain state under multistep (including cyclic) quasi-static loading is developed. Numerical calculations of the body stress-strain state for various values of the parameters of the nonlinearity of the inclusion material are carried out. Their influence on the mode of deformation of the matrix under loading by a balanced system of concentrated forces is investigated.

scholarly journals INVESTIGATION OF LOCAL UNLOADING OF AN ELEMENT IN A FINITE ELEMENT CONTINUUM

2021 ◽  
pp. 86-96
Author(s):  
A.Yu. Burtsev ◽  
◽  
V.V. Glagolev ◽  
A.A. Markin ◽  
◽  
...  
Keyword(s):  
Finite Element ◽  
Failure Criterion ◽  
Strain State ◽  
Plastic Region ◽  
Elastoplastic Problem ◽  
The Body ◽  
Stress Strain ◽  
Adjacent Element ◽  
Stress Strain State ◽  
Ansys Workbench

The subcritical elastoplastic deformation and the fracturing of an element of a finite element continuum in the Ansys Workbench complex are considered. When solving the elastoplastic problem of the subcritical deformation, a finite element with the failure criterion reached is selected. In a pre-fracture state of the element, the nodal forces provided by the interaction with an adjacent element are determined using the Ansys Workbench internal procedure. The following step is the consideration of the varying stress-strain state of the body during the element destruction. The elastoplastic problem is solved in the conditions of simple unloading of the body surface adjacent to the destructible element while maintaining the external load corresponding to the destruction initiation. When implementing the local unloading, a possibility of the new plastic region formation and the partial unloading are studied. As a result, the stress-strain state of the body at the beginning of local unloading is not the same as that at the end of the process. The proposed approach differs from the “element killing” procedure when the element stiffness after the failure criterion reached is assumed to be close to zero. The paper provides solutions to the problems of deformation of elastic and elastoplastic plates with a side cut taking into account their element destruction.

scholarly journals COMPUTATIONAL-EXPERIMENTAL STUDY OF CONTACT INTERACTION OF BODIES WITH NEARLY FORM SURFACES

2021 ◽  
pp. 23-32
Author(s):  
Andrey Grabovskiy ◽  
Mykola А. Tkachuk ◽  
Natalia Domina ◽  
Ganna Tkachuk ◽  
Olha Ishchenko ◽  
...  
Keyword(s):  
Contact Pressure ◽  
Contact Interaction ◽  
Strain State ◽  
The Body ◽  
Contact Pressure Distribution ◽  
Interaction Method ◽  
Stress Strain ◽  
Stress Strain State ◽  
Flat Shape ◽  
Keywords Stress

  In many constructions, their elements are in contact with nominally matching (congruent) surfaces. In reality, this contact is disturbed due to deviations in the shape of these surfaces from the nominal. To study the effect of this perturbation on the distribution of contact pressure, the analysis of the stress-strain state of the body system of punched sheet-die is carried out. The middle element of this system deviates from the nominally flat shape. This causes a change in the contact pressure distribution. The proportionality between the clamping force and the level of contact pressure is also lost. The reliability and accuracy of the results obtained by numerical calculation have been experimentally confirmed. Keywords: stress-strain state; contact pressure; contact interaction; method of variational inequalities; Kalker variational principle; finite element method

scholarly journals Stress-strain state of a combined toroidal baromembrane apparatus

2021 ◽  
Vol 21 (2) ◽  
pp. 123-132
Author(s):  
S. I. Lazarev ◽  
О. V. Lomakina ◽  
V. Е. Bulanov ◽  
I. V. Khorokhorina
Keyword(s):  
Strain State ◽  
Liquid Waste ◽  
The Body ◽  
Transmembrane Pressure ◽  
Toroidal Shell ◽  
Outer Diameter ◽  
Stress Strain ◽  
Load Bearing ◽  
Stress Strain State ◽  
Membrane Apparatus

Introduction. Currently, the purification of wastewater and technological solutions by membrane methods is considered a promising way to neutralize liquid waste. Therefore, the task of developing an engineering method for calculating baromembrane devices is a challenge. Studies on methods involving calculation of design and process variables, membrane equipment design, research of technological features of membrane devices, selection of design schemes, as well as methods of strength and rigidity analysis, are investigated.Materials and Methods. Basic elements of the body of the combined membrane apparatus are considered, a design scheme is proposed, and a method for calculating the strength and rigidity of the main load-bearing element, the cover, is described.  Results. The methods determine the required dimensions of shells and plates for the development of a combined membrane apparatus, and evaluate the strength properties of the devices of this class. The construction elements of the apparatus (primarily, the load-bearing covers) must meet not only the requirements of efficiency and quality of separation and cleaning of solutions, but also the conditions for safe operation. Therefore, the design of the device covers should be based on the optimal design dimensions (thicknesses of round plates, toroidal shells, and support rings). To test the method, the stress-strain state of the membrane apparatus structure was calculated for strength and rigidity. As an example, we consider one cover presented in the form of an open toroidal shell. The evaluation of the application of this technique, taking into account the fact that the shell is mated with a round plate in the inner diameter, and with a ring in the outer diameter, has provided the determination of the required parameters.Discussion and Conclusions. The obtained method of analytical description of the mechanical impact on the elements of the combined apparatus and the example of calculating the toroidal shell and plate, enables to evaluate the stressstrain state of the structure for strength and rigidity. The results of the calculation of covers made of various materials at different pressures are presented. Loading the combined apparatus with transmembrane pressure made it possible to determine the required dimensions of the shells and plates for its design and development. 

The stress-strain state at the junction of a jacket shell to the body of a vessel

1971 ◽  
Vol 7 (3) ◽  
pp. 205-207
Author(s):  
V. D. Babanskii ◽  
V. F. Kurylev ◽  
S. M. Kutepov
Keyword(s):  
Strain State ◽  
The Body ◽  
Stress Strain ◽  
Stress Strain State

scholarly journals Peculiarities of the stress-strain state of the “excavation – geo-environment” and “embankment – geo-environment” systems in the process of erecting them (part II)

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Mikhail Krasnov ◽  
Nikolay Gorshkov ◽  
Yuan Jingwen ◽  
Svetlana Jdanova
Keyword(s):  
Finite Elements ◽  
Strain State ◽  
Common Ground ◽  
Displacement Vector ◽  
Limit State ◽  
The Body ◽  
Volume Deformation ◽  
Stress Strain ◽  
Stress Strain State ◽  
The Stability

Excavations and embankments are the most common ground transport structures, operational reliability and durability of which is determined by the stability of their sides and slopes. The first article deals with the features of stress-strain state and changes in stability of ground transport structures (excavations) based on modeling according to the certified program of finite element method GenIDE32. At modeling the layer-by-layer excavation of homogeneous soil from excavations with finite geometrical sizes was carried out. In the excavation edge array, in the field of displacement vector ui, appeared are poorly studied phenomena in the form of «rotation circles» or short vortices. These phenomena, discovered in model experiments (Yu.I. Soloviev, 1956), require detailed research in the future. Graphic results of the calculations performed allow one to see the appearance and development of zones of «plasticity» or limit state in the form of zones of «shift-compression», «compression-shift» and «stretching». Shift-compression zones and vice versa are shown as shaded finite elements at an angle crosswise, while stretch zones are shown as shaded vertically, horizontally and vertically, and horizontally finite elements. These zones, in the process of modeling, are drawn in the edges of the projections of a slide with vertical and horizontal cracks. The contours of the landslide prisms show themselves well when the average relative volume deformation values of ε are displayed on the screen. The display of this value in two colors defines the landslide contours in this figure. Sliding lines with the minimum value of the stability coefficient kst min pass near the borders, where values of this parameter are equal to zero. In this figure, in the upper part of the array, you can see the places where vertical cracks are formed. The analysis also uses graphs of stress-strain state trajectories in the space of stress tensor invariants σij and relative deformations εij in significant nodes and finite elements, located, including, in places of sliding lines with kst min. They make it possible to see from the volume and shape deformation graphs where the system with the calculated condition is located, for example, from the condition at which the body of the landslide was formed.

scholarly journals Research of stress-strain state and stability of a rokfill dam under seismic actions

Vestnik MGSU ◽  
2015 ◽  
pp. 157-166
Author(s):  
Vyacheslav Valentinovich Orekhov
Keyword(s):  
Strain State ◽  
Initial Conditions ◽  
The Body ◽  
Cohesionless Soil ◽  
Soil Base ◽  
Stress Strain ◽  
Stress Strain State ◽  
Soil Skeleton ◽  
Water Saturated ◽  
Seismic Impacts

One of the main factors determining the safety of earth sea and river hydraulic structures erected on water-saturated grounds is the process of consolidation, manifested under the action of static and seismic loads. A feature of cohesionless soils located in the structure itself or in its base, is their potential ability to liquefaction under seismic impacts. This paper describes the method of calculating the saturated soil’s environments under seismic actions based on the numerical solution of differential equations of the theory of consolidation by finite element method. The results of the static problem solving for the phased construction of the installation are used as the initial conditions. In order to describe the deformability of soil materials mathematical model formed by the theory of plastic flow with hardening is used. The parameters of this model are determined by the results of triaxial testing of soils. As an example, we study the interaction of a sea rockfill dam with a sandy base under seismic impacts, determined by the synthetic accelerograms. The results of calculations of the stress-strain state of the two sections of the dam (shallow and deep) are presented, and assessment is made of the possibility of liquefaction of sandy soil base. It is shown that the pore pressure that occurs in water-saturated cohesionless soil base and the body of the dam under seismic impacts, unloads the soil skeleton, which leads to a decrease in local shear safety factors. And, in the less dense soil base of the shallow section of the dam, the soil skeleton is unloaded to a greater extent, which negatively affects its overall safety factor.

scholarly journals DETERMINATION OF STRESS-STRAIN STATE OF THE BODY SURFACE OR ITS AREA IN CASE OF PERFECT PLASTICITY AT GIVEN STRESS AND DISPLACEMENT VECTORS

2020 ◽  
Vol 2 ◽  
pp. 201-209
Author(s):  
Anvar I. Chanyshev ◽  
Ilgizar M. Abdulin ◽  
Olga A. Lukyashko
Keyword(s):  
Body Surface ◽  
Strain State ◽  
Rapid Assessment ◽  
Strain Tensor ◽  
The Body ◽  
Plastic State ◽  
Cauchy Stress ◽  
Stress Strain ◽  
Stress Strain State ◽  
Displacement Vectors

Ideally plastic state of material under conditions of Mises plasticity, proportionality of stress and strain deviators (deformation theory of plasticity) and elastic volume change is considered. Given the Cauchy stress and displacement vectors specified on the body surface (with indicated state) or its area, all six components of the stress tensor, all six components of the strain tensor, and also three components of the rotation vector are restored on this surface. This method for determining the stress-strain state can be related to the methods of rapid assessment of the structure state (body surface), since differential equations inside the body are not involved.

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