Characteristics Of Stress-strain State Research Articles

МЕТОД ВИЗНАЧЕННЯ ХАРАКТЕРИСТИК НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ЛОНЖЕРОНА РЕГУЛЯРНОЇ ЧАСТИНИ ЛОПАТІ НЕСУЧОГО ГВИНТА ВЕРТОЛЬОТА ЗА ДОПОМОГОЮ СИСТЕМИ ANSYS

The helicopter main rotor blade is the basic product that determines the reliability and service life of the helicopter as a whole. The problem of predicting and ensuring the specified blade life is an urgent problem considered at the stage of its design. To determine the fatigue life of the blade it is necessary to know the characteristics of the stress-strain state. A method has been developed for determining the characteristics of the stress-strain state of the spar of the regular part of the rotor blade of a helicopter using the ANSYS system. Application of numerical methods of stress-strain state characteristics calculation allows to reduce considerably time and cost of blade design. The calculation results of regular part of the Mi-8 main rotor blade at the hover mode when it is loaded by aerodynamic and inertial load from the rotation, as well as the force of its own weight are presented in the work. Using the ANSYS system, a finite-element model of the regular part of the blade, consisting of a set of beam elements of variable cross-section, was developed, the calculation was carried out taking into account the geometric nonlinearity of the structure behavior and the analysis of the obtained results. To describe the response of materials to external influences, an elastically deformable isotropic body model is used with assignment of the appropriate elastic constants of the material. Analysis of calculation results includes determination of reactions at attachment points, values of maximum displacements of structural elements and stresses in weak sections. Diagrams of internal force factors (axial and shear forces and bending moment) along the blade span are plotted. With the help of these diagrams weak sections are determined and values of axial force and bending moment in these sections are calculated. Axial force reaches its maximum value Nx = 333689 N in the section along the axis of rib № 1. In this section, the bending moment reaches a maximum value of Mymax = 3078.3 N×m. At cross section r = 0.73 between axes of ribs No. 13 and No. 14, where shear force equals to zero, value of bending moment My = -1147,5 N×m. Thus, regular part of the blade is in combined stressed state - bending with tension. Static strength of the blade has been estimated using safety factor. To estimate a static strength equivalent von Mises stresses were considered as the maximum stresses. Safety factor of static strength of regular part of the blade in the weak section was 1,7. To estimate fatigue strength, distribution of the first principal stresses in the load-carrying elements was analyzed in terms of typical stress concentrators. The maximum level of the principal stresses in the considered sections was s1 = 138 MPa, which indicates that the blade material operates in the range of high cycle fatigue.

Improving the accuracy of the behaviour simulation of the material of the turbojet aircraft engine fan rotor blades in the event of a bird strike by using adapted finite element computational models

One of the most topical issues in aircraft building is checking the engines for bird strike resistance, i.e. their airworthiness following an in-flight bird strike. The most critical aircraft units are the turbojet engines. In this case, the turbofan blading is affected the first thing. Its deformation or failure can result in the failure of the entire engine. Numerical simulation of the process allows for a qualitative and quantitative assessment of the consequences of a bird strike on the blades. This enables to avoid full-scale experiments and design properly the units affected by such action. The paper deals with improving the accuracy of simulation modelling of the behaviour of the material of the fan rotor blades of a turbojet aircraft engine in the event of bird strike by using adapted finite-element computational models. Bird action is argumentatively replaced with a system of equivalent quasistatic loads. The most critical events of blade impact with medium and big-size birds were selected by analysing experimental data. The force impulses were compared to determine the strike locations and the sizes and masses of birds that are most dangerous from the viewpoint of disturbance of strength properties. Variant computational analyses deal with studying construction behaviour under static action of the joint load by centrifugal forces and loads that simulate bird action on the fan blading. The stress–strain state characteristics are used to assess the behaviour of the material and its strength properties. Simulation accuracy is confirmed by comparison with the results of bench tests.

МНОГОУРОВНЕВОЕ МАСШТАБНОЕ КОМПЛЕКСНОЕ ИССЛЕДОВАНИЕ ДЕФОРМИРОВАНИЯ МЕТАЛЛИЧЕСКИХ МАТЕРИАЛОВ

The paper considers the theoretical and experimental questions connected with researches of elastic and plastic deformation of metal materials. The article shows that joint multilevel large-scale study performed by physics-mechanics and material engineers of the patterns connecting characteristics of stress-strain state with parameters of a structural condition of a metal material will allow to develop modern physical and mathematical models of a material. For this purpose in-depth study of the shift deformations forming plastic properties of a material and processes formation of defects and a new free surface is necessary. The paper presents the examples of such a research, and provides methods of analysis of structure and physical and mechanical characteristics at different structural levels of a polycrystalline metal material.

АНАЛИЗ НАПРЯЖЕННО – ДЕФОРМИРОВАННОГО СОСТОЯНИЯ ЗАКЛЕПОЧНОГО СОЕДИНЕНИЯ С ПОМОЩЬЮ CAE СИСТЕМЫ ABAQUS

The method for analyzing of stress-strain state characteristics of unloaded riveted joints performed with OST 1 11781-74 rivets has been developed using Coupled Euler-Lagrange finite element approach implemented in the CAD / CAE system Abaqus. A comparative analysis of the stress-strain state characteristics of the examined riveted joint’s finite element models using the Lagrangian and the Coupled Lagrangian-Eulerian finite element approaches has been conducted. A three- dimensional finite element model based on the CLE method has been proposed for further study of fatigue strength and durability of the loaded riveted joints.

Estimating the Seismic Load of Building Structures

Mathematical models are presented for calculating the stress–strain state (SSS) of structures under seismic impacts. The general mathematical formulation for determining the SSS is considered. For linear models, two methods are presented for calculating the SSS characteristics by decomposition of the eigenvectors: a method that integrates the time equations for given accelerograms of the base and a method that uses standard seismic spectra. In calculating seismic spectra, various methods for summing the tones of oscillations of structures are proposed to evaluate the structural response. In order to assess the forces and moments of interaction between a structure and the foundation supports and to test the calculation programs, mathematical models of structures are presented in the form of simple mechanical analogs: angular oscillators. These calculation methods take into account building code requirements and have been adapted to modern software packages that use the finite element method.

NUMERICAL STUDY OF STRESS-STRAIN STATE OF HUMAN FEET AFTER OPERATIONAL TREATMENT WITH BIOGLASS APPLICATION

The paper presents the results of a numerical study of the effect on stress-strain state of the elements of a person's leg after surgical treatment, replacement of damaged tissues with osteomyelitis with implants made of bioglass. The mathematical model of conducted research was based on the basic relations of continuum mechanics, in conjunction with numerical methods, in particular, by the finite element method. In the course of the study, three design groups were considered, the differences of which consisted in the size of bioglass implants, each group, in turn, consisted of four design schemes, two of which described an “intact” state and a “damaged” state, the other two the schemes described the human leg after surgical treatment of implant installation made of various types of bioglass -AC-5 and FAR-5, respectively. According to the results of the research, characteristics of stress-strain state were obtained and a comparative analysis was carried out.

Continuum mathematical modelling of pathological growth of blood vessels

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

Универсальный метод оценки прочности элементов верхнего строения железнодорожного пути на основе расчетной модели балки на упругом основании

Objective: To develop a universal method of track structure elements’ strength analysis, taking into account variable cross-section of elements and the form of foundation. To provide a graph-analytical model of analysis, as the basis of the method, for calculating stress-strain state characteristics of a beam on elastic foundation. Methods: Graph-analytical method was used to identify the characteristics of stress-strain state of a beam on elastic foundation. The method in question is an alternative one, compared to a routine theoretical calculation, the basis of which is a fundamental equation of a bending line and further from this equation, by means of successive integration method, any characteristic of stress-strain state of a beam on elastic foundation can be obtained. Results: A universal graph-analytical method was developed, taking into account factors, which cause deviation from a theoretical scheme of a beam bearing on elastic foundation, such as the possibility of calculating different elements of track structure bearing capacity, considering its variable cross-section (sole chairs, ferroconcrete sleepers, tongues, frogs, etc.), foundation form alternation, on which the calculated elements bear, as well as unequal elasticity of foundation. Practical importance: Application of such a universal method, which differs from an accepted idealized scheme of a beam bearing on elastic foundation, offers wide perspectives in stress-strain state assessment of not only new tracks, being designed, but also in the process of their current state. Application of the method in question makes it possible to avoid analytical lengthy mathematical calculations with any form of cross-section alternation along the length of a beam, with any form of foundation, as well as heavy expenditures, compared to other modern bearing capacity calculating methods, such as finite element method, finite difference method, and finite volume method.

Review of modern models of development of corrosion damage and research tendency of their influence to strength and reliability of elements of pipeline systems

The analysis of current research in the field of reliability analysis, corrosion damaged pipelines was made in this paper.The methods used to determine the life-time of pipelines have been divided into two groups: those in which the reliability analysis is based on the assessment of changes in physical and mechanical properties of the material, and those which are used the finite element method made a explicit modeling of damage on surface of pipelines, whereby the numerically defined characteristics of stress strain state and analyzes the strength and reliability.From the analysis of works was defined, appearance of corrosion defects on the surface of the pipeline leads to plastic deformation even at relatively small size of damage, and speed up the development of corrosion. This suggests that in the determination of residual life, it is necessary to use methods of accumulation is low cyclic fatigue.

Fundamental system of solutions of the axially symmetric problem of the theory of elasticity for a body with a plane sheet of volume moment dipoles and forces

UDC 539.3 We have constructed the fundamental system of solutions of the axially symmetric problem of the theory of elasticity for an unbounded body with a sheet of volume forces, normal to a chosen plane, and moment dipoles, which is a mathematical model of the internal boundary layer of a certain type. With the help of such layers, one succeeds in formulating some inverse problems of elasticity and, hence, the related problems of the control of stress-strain state on the corresponding surfaces. We have also formulated and solved the generalized Kelvin problem and, according to it, for the plane of distributed normal load, and established the law of distribution of the moment dipoles (sheet parameters), which provides the vertical displacements assigned for points of the plane, in particular, zero, by the corresponding tension. Based on the definition of zero- and first-order singular material surfaces of discontinuity of the field characteristics [9], we investigate a variant of such surface as a mathematical model of the plane sheet of (distributed according to certain laws, determined by two generating functions) volume moment dipoles and volume, normal to the plane of distribution, forces, which are represented via the Hankel integrals. These distributions correspond to the fundamental system of solutions of the equations of statics of an elastic body in a cylindrical coordinate system, according to which the radial displacement, volume strain, and normal stresses have jumps in passage across the sheet plane [6, 10], and the tangential stress contains a term concentrated only in this plane. According to the definition in [9], we consider such a plane (zero- and first-order material singular surface) as an internal boundary layer, which is a material carrier of certain properties, different from those predicted by the equations of the linear theory of elasticity, and enables one to model certain types of planar defects of the structure of a perfect elastic material. The constructed solutions for the displacement field and all the other field characteristics of stress-strain state in a cylindrical coordinate system are written in terns of the Hankel integrals and contain the generating functions of the distribution densities of volume moment dipoles and volume forces unknown beforehand. Their appropriate choice enables one to obtain the solutions of a certain class of axially symmetric problems of the mechanics of deformable solids. Note that the fundamental system of solutions of the equations of statics with a sheet of volume forces, tangent to the plane, and momentless dipoles in a cylindrical coordinate system was constructed in [3]. 1. Fundamental System of Solutions of the Second-Type Equations of Statics

Analyticity of the solution of a plane elastoplastic problem

Elastoplastic problems of the theory of ideal plasticity were studied numerically by the method of small parameter in the monographs [1–3], and strengthening elastoplastic problems were studied in the monograph [4], where a rather complete bibliography of studies in this direction is given. The conditions for the continuous dependence of the the stress-strain state characteristics on the boundary conditions and the material inhomogeneity are defined using the implicit function theorem in [5, 6].

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented