INVESTIGATION OF STRESS-STRAIN STATE OF TRANSVERSELY ISOTROPIC PLATES UNDER BENDING USING EQUATION OF STATICS {1,2} –APPROXIMATION

The study examined the construction of the fundamental solution for the equations of statics {1,2} – approximation for transversely isotropic plates under bending with the action of concentrated force. Equations {1,2} -approximation were obtained by the decomposition method in the thickness coordinate using the Legendre polynomials. These equations take into account all the components of the stress tensor, including the transverse shear and normal stresses. Since the classical theory of Kirchhoff-Love doesn’t take account of these stresses, the study on the basis of refined theories of stress-strain state of transversely isotropic plates under the action of concentrated force effects is an important scientific and technical problem. The fundamental solution of obtained equations results using a two-dimensional Fourier integral transform and inverse treatment techniques, built with the help of a special G-function. This method allows reducing the system of resolving differential equations for statics of flat plates and shells to a system of algebraic equations. After that, the inverse Fourier transform restores the fundamental solution. The work was carried out numerical studies that demonstrate patterns of behavior of components of the stress-strain state, depending on the elastic constants of transversely isotropic material. The results play a decisive role in the study of boundary value problems in the mechanics of thin-walled elements of constructions, including under the influence of concentrated and local diverse forces

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure

DEFORMATION ANALYSIS OF LAYERED REINFORCED CONCRETE - FOAM CONCRETE FLOOR SLABS

This article presents a theoretical study of a stress-strain state of layered reinforced concrete - foam concrete floor slabs (hereinafter called as the LRFCS), with the use of a deformation analysis. Compressive and tensile diagrams of the foam concrete, a tensile diagram of the reinforced concrete and compressive and tensile diagrams of the reinforcement rod are used for the estimation of the stress-strain state of the calculated cross-section of the LRFCS. It should be noted that this article presents the deformation method of loading by the scheme of pure bending for the LRFCS. This deformation method of loading is determined by six shapes of the stress-strain state. These shapes of the stress-strain state are represented by the corresponding distribution diagrams of the relative deformations and the distribution diagrams of internal stresses in the calculated cross-section of the floor slab. Also, this article presents the corresponding equilibrium equations of internal efforts and moments, which act in the calculated cross-section of the floor slab for all shapes of its stress-strain state. Consequently, the mentioned recommendations and mathematical dependencies allow to evaluate the stress-strain state of the LRFCS from its initial loading to its destruction

Using optical fibers (OF) to control the stress-strain state of steel structures subject to fatigue failure

The article presents the results related to developing and practical testing the method of monitoring the stress strain state of steel structures of mine hoisting machines. Certain positive properties of optical fibers make it possible to use them for measuring the stress-strain state of steel structures. An optical fiber of the ITU-T G.652.D standard is used as a sensor. The analysis and review of the current state of development of fiber-optic conductors is performed. The proposed method of non-destructive testing the stress-strain state of metal structures is capable of providing continuous measurements in real time. The proposed method is universal and suitable for monitoring the stress-strain state of any metal structures subject to fatigue failure

Influence of installation elastic bending on stress-strain state of pipeline aboveground passages in mountains

The experiment-calculated methods of diagnosing stress-strain state of the pipeline aboveground beam passages are shown. By the example of pipeline aboveground passage in the Carpathians the influence of installation elastic bending on its stress-strain state was studied

Improving the method of controlling the stress-strain state of steel structures of electromechanical systems

The article presents the results of improving the method of controlling the stress-strain state of steel structures of mine hoisting machines, which can be attributed to electromechanical systems. The method of controlling the stress-strain state of steel structures of electromechanical systems subjected to fatigue failure is based on the use of mechanical properties of an optical fiber (OF) and the effect of photoelasticity arising from its deformation. The optical fiber is used as a sensor and allows to controlthe stress-strain state of metal structures in real time

Многовариантные исследования напряженно-деформированного состояния рамы ветроэнергетической установки большой мощности

Наведені результати досліджень напружено-деформованого стану зварної рами вітроенергетичної установки. Досліджено вплив зовнішніх навантажень на напружено-деформований стан зварних швів. Результати є складовими спеціалізованої бази даних.Results of investigation of stress-strain state of a wind energy conversion plant frame are given. Influence of external loading on stress-strain state of welded joints is investigated. The results are components of a specialized database

Simulation of stress-strain state drum mine winders

В работе проведено теоретическое исследование влияния геометрических и жесткостных характеристик барабана шахтной подъемной машины на расчетные нагрузки и напряженно‐деформированное состояние, с учетом ослабления натяжения навитых витков каната.Conducted theoretical research of the influence of geometric and stiffness characteristics of the hoisting machine drum on design loads and stress‐strain state, taking into account the release of tension rope

On stress/strain state in a rotating disk

In the framework of mechanics of continuum bodies, the problem of stress/strain state in a high-speed rotating disk of constant thickness has been considered. The material of the disk is assumed to be homogeneous, elastic/perfectly-plastic. In the plastic zone, the stresses and plastic strains are related by some associated law similar to the one employed in deformation theory of plasticity. The general algorithm of the solution covers any smooth plasticity function. At some steps of the algorithm, it is possible to get analytical expressions, particularly, for the quadratic Mises yield criterion. For the given model, the notion of control parameters (external and internal) has been introduced. The allowable boundaries of external parameters have been defined as well. For some states of the disk, the coherent values of external parameters have been obtained. The results are represented graphically to show various states of the disk. The usage of piecewise plasticity functions has been briefly discussed. The results obtained can be used in preliminary engineering design and related numerical codes.info:eu-repo/semantics/publishedVersio