Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

напряженно-деформированное состояние

Biomechanical support for the physician’s decision when choosing a treatment option based on quantitative success criteria

Preoperative planning for the treatment of the consequences of diseases and injuries of the spino-pelvic complex surgical treatment is a mandatory procedure and should ensure the selection of implants, modes and techniques for their installation, as well as the reconstruction of the optimal biomechanics of the operated segment. For each individual patient, the surgeon chooses a treatment variant based on his qualitative and quantitative individual parameters.

Biomechanical Assessment of the Bone Ingrowth Effect During Cementless Endoprosthesis Osteointegration

Finite elementmodel of porous titaniuminserts for cementless endoprosthesis was reconstructed usingX-ray tomography. The stress distribution is calculated for a model with open-cell foam and composite bone / titanium. The results explain the mechanism of the porous structure destruction and positive influence of the osteointegration effect on the strength properties. Numerical calculations are confirmed by experimental data of the porous samples during compression testing.

Numerical analysis of renal artery pathologies

 Mathematical modeling based on experimental data (ultrasonic imaging, angiography, 3D reconstruction via spiral computed tomography) was performed. Anatomically precise model of renal artery was created. Basic principles of blood flow dynamics with stressstrain state of artery walls were studied for normal, pathologic renal arteries and arteries with hemostasis of intraorganic branches. 

Investigation of Harmonic Waves in the Viscoelastic Layer

The paper deals with the study of harmonic waves in the viscoelastic layer. The properties of the material are described by the constitutive equations in the integral form. The fractional exponential function of Rabotnov is chosen as a kernel of integral operator. Two cases are considered: symmetric stress-strain state (SSS) and asymmetric SSS. The properties of modes which change in time harmonically are investigated for the purpose of studying of the free vibrations. Dispersion equations for both cases are derived.

Numerical Study of Stress-Strain State of a Thin Anisotropic Rectangular Plate

Static bending of a thin rectangular anisotropic plate is considered in the framework of Kirchhoff hypotheses. At each point of the plate there is one plane of elastic symmetry parallel to the middle plane of the plate. It is assumed that the type of boundary conditions does not change along each of the straight sides. By applying of a modified method of spline collocation the twodimensional boundary value problem for the determination of deflection is reduced to a boundary value problem for the system of ordinary differential equations, which is solved numerically.

Some Aspects of Applying Finite Element Method to Contact Problems Using ABAQUS System

In this paper the selection of preferred computational scheme for numerical research of a contact interaction between a rigid indentor andanelastic-plastichalf-spaceusing ABAQUS system is фdescribed. Furthermore, the critical values of the load applied to indentor which don’t cause plastic deformation in the material and subsequently don’t effect the process of a surface hardening are determined. Some peculiarities of the forming of near-surface plastic region by static loading are investigated.

Stability of Vertical Mountain Developments in Elastic Viscous-Plastic Files with Porous Structure

The mathematical model of the basic intense-deformed condition of the vertical mountain development, considering elastic-viscousplastic properties of a file, and also porous structure of a material is constructed. Within the limits of the exact three-dimensional stability equations stability of the basic condition of vertical development in files of rocks with the compressed time is investigated. The estimation of influence on size of critical pressure of parametres of hills is given.  

Repair Technology Basis of Turbine Disks by Using StressStrain State Parameters

Stress-strain state of power steam turbine disks under operation conditions including both contouran dtighten loadings is considered. Full-size elastic-plastic stress-strain state analysis of turbine disk for different variants of considering key geometries is represented. As a result of numerical calculations three critical zones of turbine disk are defined. Proposed design modifications and repair technology to existing in-service power steam turbine disks by removing of damaged material volume are analyzedand substantiate donastress state parameters basis.