Study of the stress–strain state of spongy bone around an implant under occlusal load

2020 ◽  
Vol 25 (5) ◽  
pp. 1172-1181
Author(s):  
Natela Zirakashvili
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Theory Of Elasticity ◽  
Boundary Element Methods ◽  
Porous System ◽  
Spongy Bone ◽  
Stress Strain ◽  
Jaw Bone ◽  
Stress Strain State ◽  
Occlusal Load

The article studies the stress–strain state of the spongy bone of an implanted jaw. A spongy bone can be considered as a multiporous area with its fissures and pores as the most visible components of a double-porous system. The work studies the stress–strain state of the spongy jaw-bone near the implant, which is under occlusal load. A mathematical model of the problem is the contact problem of the theory of elasticity between the implant and the jaw-bone. The problem is solved by using the boundary element methods, which are based on the solutions of Flamant (BEMF) and Boussinesq’s (BEMB) problems. The cases of various lengths of an implant diameter are considered. Stress contours (isolines) in the jaw-bone are drawn and the results obtained by BEMF and BEMB for the different-diameter implants are compared.

scholarly journals Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere

2019 ◽  
pp. 51-66
Author(s):  
Alexander O. Faddeev ◽  
Svetlana A. Pavlova ◽  
Tatiana M. Nevdakh
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Uniform Grid ◽  
Shear Stresses ◽  
Stress Strain ◽  
Gravitation Field ◽  
Vertical Movements ◽  
Stress Strain State ◽  
The Earth ◽  
Viscous Shear

Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment. Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed. Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.

scholarly journals A BEM-based mathematical model of the human cornea stress-strain state

2019 ◽  
Author(s):  
N. A. Babailov ◽  
A. E. Bogachev ◽  
S. A. Korotkih ◽  
O. A. Nefedova ◽  
L. F. Spevak
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Human Cornea ◽  
Stress Strain ◽  
Stress Strain State

scholarly journals Stress-strain state of ship hull structures restored using polymer coating

2021 ◽  
pp. 12-17
Author(s):  
С.И. Корягин ◽  
О.В. Шарков ◽  
Н.Л. Великанов
Keyword(s):  
Mathematical Model ◽  
Polymer Coating ◽  
Strain State ◽  
Metal Layer ◽  
Adhesive Layer ◽  
Metal Structure ◽  
Polymer Coatings ◽  
Calculation Algorithm ◽  
Stress Strain ◽  
Stress Strain State

Применение полимерных покрытий для ремонта корпусных конструкций выдвигает как актуальную задачу определения прочностных характеристик конструкций с покрытиями. Наличие отверстий, сквозной коррозии, являющихся концентраторами напряжений, делает эти места наиболее опасными, с точки зрения потери прочности, герметичности. Чаще всего разрушение происходит по адгезионному слою. Представлена математическая модель, учитывающая сосредоточенные усилия на концах адгезионного слоя композиционной конструкции типа «металл-покрытие». Проведены расчеты нормальных и касательных напряжений. Наибольшие значения напряжений в полимерном покрытии получены на кромке отверстия в слое металла. В результате анализа установлено, что увеличение перекрытия полимерным покрытием контура отверстия и удаленность от контура отверстия приводят к существенному уменьшению величин напряжений. Разработанная математическая модель и алгоритм вычислений позволяют расчетным путем определить напряженно-деформированное состояние металлической конструкции с отверстием и полимерным покрытием. The use of polymer coatings for the repair of hull structures puts forward as an urgent task to determine the strength characteristics of structures with coatings. The presence of holes, through corrosion, which are stress concentrators, makes these places the most dangerous, in terms of loss of strength, tightness. Most often, the destruction occurs along the adhesive layer. A mathematical model is presented that takes into account the concentrated forces at the ends of the adhesive layer of a composite structure of the "metal-coating" type. Calculations of normal and tangential stresses are performed. The highest stress values in the polymer coating are obtained at the edge of the hole in the metal layer. As a result of the analysis, it was found that an increase in the overlap of the polymer coating of the hole contour and the distance from the hole contour lead to a significant decrease in stress values. The developed mathematical model and calculation algorithm allow calculating the stress-strain state of a metal structure with a hole and a polymer coating.

scholarly journals Mathematical model of the stress-strain state of a rod with an inhomogeneous layered structure

2021 ◽  
Vol 82 (4) ◽  
pp. 14-22
Author(s):  
S. M. Akhmetov ◽  
◽  
M. T. Userbayev ◽  
Zh. U. Iklasova ◽  
A. B. Bolatova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Layered Structure ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State ◽  
Current State ◽  
Tension And Compression ◽  
The Difference ◽  
State Of Research ◽  
Wooden Structures

The stress-strain state (SSS) of a rod with an inhomogeneous layered structure is considered. On the basis of a brief review and analysis of the current state of research of rod systems, the relevance of the study of the SSS of layered-heterogeneous wooden structures is substantiated, taking into account the presence of different resistance of layers to tension and compression. On this basis, the authors solve the problem of determining the SSS of layered-heterogeneous wooden rods in creep conditions, where factors such as humidity and temperature, as well as the difference in the resistance of wood layers to stretching and compression are taken into account. When solving the problem, the mechanical-sorption creep of wood is also taken into account.

scholarly journals DETERMINATION OF STRESS-STRAIN STATE OF A THREE-LAYER BEAM WITH APPLICATION OF CONTACT LAYER METHOD

Vestnik MGSU ◽  
2016 ◽  
pp. 17-26 ◽  
Author(s):  
Vladimir Igorevich Andreev ◽  
Robert Alekseevich Turusov ◽  
Nikita Yur’evich Tsybin
Keyword(s):  
Experimental Data ◽  
Edge Effect ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Contact Layer ◽  
Theory Of Elasticity ◽  
Stress Strain ◽  
Tangential Stresses ◽  
Stress Strain State ◽  
Layer Method

The article deals with the solution for the stress-strain state of a multilayer composite beam with rectangular cross-section, which is bended by normally distributed load. The intermolecular interaction between layers is accomplished by the contact layer, in which the substances of adhesive and substrate are mixed. We consider the contact layer as a transversal anisotropic medium with such parameters that it can be represented as a set of short elastic rods, which are not connected to each other. For simplicity, we assume that the rods are normally oriented to the contact surface. The contact layer method allows us to solve the problem of determining the concentration of tangential stresses arising at the boundaries between the layers and the corner points, their changes, as well as to determine the physical properties of the contact layer basing on experimental data. Resolving the equations obtained in this article can be used for the solution of many problems of the theory of layered substances. These equations were derived from the fundamental laws of the theory of elasticity and generally accepted hypotheses of the theory of plates for the general case of the bending problem of a multilayer beam with any number of layers. The article deals with the example of the numerical solution of the problem of bending of a three-layer beam. On the basis of this solution the curves were obtained, which reflect the stress-strain state of one of the layers. All these curves have a narrow area of the edge effect. The edge effect is associated with a large gradient tangential stresses in the contact layer. The experimental data suggest that in this zone the destruction of the samples occurs. This fact allows us to say that the equations obtained in this article can be used to construct a theory of the strength layered beams under bending.

scholarly journals Visualization of the Stress-Strain State of Shell Structures Using Virtual and Augmented Reality Technologies

2020 ◽  
pp. paper13-1-paper13-12
Author(s):  
Alexey Semenov ◽  
Iurii Zgoda
Keyword(s):  
Mathematical Model ◽  
Thin Shell ◽  
Strain State ◽  
Interactive Visualization ◽  
Analysis Data ◽  
Shell Structures ◽  
Stress Strain ◽  
Heat Maps ◽  
Visualization Module ◽  
Stress Strain State

The paper describes a mathematical model of changes in the geometry of thin-shell structures for visualization of the analysis data on their stress-strain state (SSS). Based on this mathematical model, a visualization module for shell SSS visualization using VR and AR technologies was developed. The interactive visualization environment Unity 2019.3 and C# programming language were used. The interactive visualization module makes a 3D image of a shell structure and visualizes the SSS either through heat maps over the shell or through the changes in the shell geometry on the basis of the shell type, its geometric characteristics, and SSS analysis data (transferred to the visualization module by means of a JSON file). While working on the visualization module, the authors developed a system of components that makes it possible to visualize any 3D surface with coordinate axes (including numbers with a pitch determined automatically), visualize heat maps with a graduated scale, visualize a mesh over the graph to improve the perception of the surface deformations. The middle surface can also be deformed on the basis of SSS analysis data. This solution increases the efficiency of the work of specialists in civil engineering and architecture and can be used when training specialists in courses on thin-shell structures and procedural geometry.

scholarly journals MATHEMATICAL MODEL OF THE SOIL STRESS-STRAIN STATE IN THE PROCESS OF ITS INTERACTION WITH THE WORKING BODIES OF THE DIGGING MACHINE

2019 ◽  
Vol 9 (2) ◽  
pp. 157-163
Author(s):  
Ольга Дорняк ◽  
Olga Dornyak ◽  
Михаил Драпалюк ◽  
Mikhail Drapalyuk ◽  
Игорь Казаков ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State ◽  
Soil Stress ◽  
Working Bodies
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