Elements In Engineering Structures Research Articles

A pre-failure narrow concrete cracks dataset for engineering structures damage classification and segmentation

Monitoring of structures’ condition plays a fundamental role in providing safety for users and extending the structures’ lifespan. The monitoring is conducted through on-site inspections by engineers thus this process is time-consuming, labor-intensive and prone to subjective engineering opinions. Detecting damage using machine learning algorithms on images can support engineers’ work, especially for early damages which are difficult to see with the human eye. This article is focused on the concrete crack detection problem in engineering structural elements. Despite the availability of several concrete crack detection datasets, no dataset allows semantic segmentation of cracks narrower than 0.3 mm (the crack width limit for typical engineering structures elements and environmental conditions according to EC 1992-1-1) and the ability for crack classification is limited. The provided open dataset represents only cracks below the crack width limit of 0.3mm, which do not yet indicate concrete elements failure. It is dedicated for early crack classification and segmentation, so that damage protection can be taken at an early stage to prevent structural element damages.

Stability of Individual Phases in the Elastic Matrix of a Composite

A methodology for analytical stability assessment of individual compressed flexible phases of discretely heterogeneous composite elements of engineering structures is proposed to ensure their reliable safe operation and minimise the consequences of emergencies. Based on the energy balance equation for the proportional forces of a normal resistance of the medium to the phase displacement, expressions are obtained for determining the critical force, taking into account the possible initial curvature (non-rectilinearity) of a single phase in the elastic medium of the matrix for three possible cases of stability loss. The approbation of the results of the study on the example of deformation features of reinforcing bars in a compressed reinforced concrete column is presented.

A BRIEF OVERVIEW OF STATIONARY TWO-DIMENSIONAL THERMOELASTIC STATE MODELS IN HOMOGENEOUS AND PIECEWISE-HOMOGENEOUS BODIES WITH CRACKS

Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for the body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. Findings. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity factors at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. The influence of thermophysical and mechanical properties of inclusion on the SIF sat the crack types was investigated. The dependences of the stress intensity factor which characterizes the distribution of the intensity of stresses at the vertices of a crack have been built, as well as its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhoods of crack vertices depending on the geometrical and mechanical factors. As a result, this allows to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region due to the action of constant temperature as well as due to local heating by a heat flux were obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by the appropriate selection of composite components with appropriate mechanical characteristics.

MODELING THE INFLUENCE OF THE SHAPE OF THE LOCAL HEAT FLOW INTENSITY DISTRIBUTION ON THE SURFACE OF A SEMI-INFINITE BODY ON THE STRESS STATE IN THE VICINITY OF A SUBSURFACE CRACK

Purpose. A mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. Heat flux due to frictional heating on the local area of the body causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the crack placement. Methodology. The methods for studying the two-dimensional thermoelastic state of a body with cracks as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. Findings. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle orientation of the crack as well as forms of the intensity distribution of the local heat flux. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. Originality. The scientific novelty lies in the fact that the solutions to two-dimensional problems of heat conduction and thermoelasticity for a half-plane containing a crack due to local heating by a heat flux were obtained. This would make it possible to obtain a comparative analysis of the intensity of thermal stresses around the top of the crack, depending on the form of distribution of the intensity of the heat flow on the surface of the body. Practical value. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with the crack that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.

GEODETIC SUPPLY FOR THE CONSTRUCTION OF ENGINEERING STRUCTURES

The construction of engineering structures when transferring the project to the area is impossible without geodetic work. The composition and sequence of engineering and geodetic works depend on the features of the design and construction of facilities and the type of structure. The purpose of the article is to consider geodetic works in the construction of engineering structures. The issues of performing engineering and geodetic works during the construction of structural elements of the bridge are considered. During the construction process, it is necessary to ensure full compliance with the design documentation and high accuracy of work performance. These requirements can be achieved by using high-precision geodetic works with constant monitoring of the installation work. At all stages of the bridge construction, geodetic works accompany the transfer to the terrain of the bridge axis, the resistance axis, perform a detailed breakdown during the construction of resistances and the installation of purlins. Also, the construction of individual parts of the building is constantly monitored, the dimensions and shape of the mounting elements are checked. When building large structures, it is necessary to have information about the points of the geodetic base of the bridge crossing, an extract from the catalog of coordinates and elevations of the geodetic base. The breakdown is carried out by tying to the points of the geodetic reference network, which has coordinates in the absolute or conditional system. Modern construction requires the use of new technologies and methods for performing geodetic work related to the introduction of electronic devices and programs for automated information processing into geodetic practice. Currently, a large number of geodetic instruments and new technologies in geodesy have been created, which differ from traditional ones. To carry out survey work, geodetic instruments, such as electronic total station and levels, were used. The electronic total station measures distances, angles and processes data directly in the process of field work, has an internal memory where it can store all the data obtained as a result of measurements. The digital level has a device for automatic registration of measurements along the rail and a processor for subsequent processing of all leveling results. During measurements, the device measures the distance to the rail and the elevation between points. This eliminates two main types of errors: observation errors when taking a reading and error in distance measurements. During the construction of supports, a temporary rapper is installed on each of them, which is tied to permanent rappers by leveling moves. The removal of marks on the supports is carried out by methods of geometric or trigonometric leveling. The coordinates of the rappers were received and entered into the local plan. Marks for serifs of the device with a retroreflective effect were pasted on the bridge supports. The data of coordinates and heights were entered into the total station memory. Geodetic work carried out during the construction of the span structure ensures the accuracy of its assembly in accordance with the project. After the installation is completed, the assembly results and deviations from the project are monitored. The construction of structural elements of engineering structures must comply with building codes and geometric parameters of the facility design.

Effect of Uniaxial Fatigue Aging and Fabric Orientation on Low Impact Velocity Response of Glass Fibers/Elium Acrylic Composite Laminates.

Impact resistance is one of the most critical features of composite structures, and therefore, its examination for a new material has a fundamental importance. This paper is devoted to the characterization of the fully recyclable thermoplastic ELIUM acrylic resin reinforced by glass fabric woven, which belongs to a new category of materials requiring advanced testing before their application in responsible elements of engineering structures. Its high strength, low weight as well as low production cost give excellent opportunities for its wide application in the automotive industry as a replacement of the thermoset-based laminates. The study presents an experimental work concerning the effect of damage due to low and high cyclic fatigue aging of two groups of specimens, first with the woven fabric orientations of [0°/90°]4 and secondly with [45°/45°]4, on the low impact velocity properties. The impact resistance was measured in terms of load peak, absorbed energy, penetration threshold and damage analysis. The low velocity impact results indicate that the uniaxial cyclic loading (fatigue aging) of the material leads to the reduction of impact resistance, especially at the high impact energy levels. Scanning Electron Microscopy (SEM) and Computed Tomography (CT) scan observations reveal that the damage area grows with the increase of both strain amplitude and impact energy.

On ways to increase protection of special structures from impact action

The technique of research of dynamic processes of elements of engineering constructions of special purpose from explosive action of projectiles is developed. Elastically reinforced beams with hinged ends were chosen for the physical model of elements of engineering structures. It is assumed that the elastic properties of the latter satisfy the nonlinear technical law of elasticity. A mathematical model of the process of a series of impact actions of projectiles at different points of the element of the protective structure is constructed. The latter is a boundary value problem for a partial differential equation. Its peculiarity is that the external dynamic action is a discrete function of linear and time variables. To determine the dynamic effect of a series of impacts on the object under study, and thus the level of protection of the structure, the basic ideas of perturbation theory methods are extended to new classes of systems. This allowed to obtain an analytical dependence of the deformation of the elastically reinforced element on the basic physical and mechanical characteristics of the material of the protective element, its reinforcement and the characteristics of the external action of the projectiles. It is shown that the most dangerous cases, given the security of the structure, are those when the impact is repeated at equal intervals, in addition, the point of impact is closer to the middle of the protective element. The obtained theoretical results can be the basis for selection at the stage of designing the main physical and mechanical characteristics of the elements of engineering structures and their reinforcement in order to reliably protect personnel and equipment from the maximum possible impact on it of the shock series of projectiles. The reliability of the obtained results is confirmed by: a) generalization of widely tested methods to new classes of dynamical systems; b) obtaining in the limit case the consequences known in scientific sources concerning the linearly elastic characteristics of the elements of protective structures; c) their consistency with the essence of the physical process itself, which is considered in the work.

The Influence of a Reinforced Beam on the Safety of Engineering Structures

Abstract The Reinforcement with carbon tapes is the next step to increase the safety of using elements of engineering structures. The conducted tests illustrate the strength capabilities of aluminum beams reinforced with a CFRP tape. The aim of the conducted tests is to compare the bending strength of aluminum beams before and after the reinforcement. On the basis of the numerical analysis, the displacements and stresses in the modeled beams were also compared. Moreover, the possible applications of the reinforced aluminum beam in engineering structures are presented in this article

Metrological control of electrolytic sensors for measuring angular deviations: application in monitoring displacements of engineering structures

The work evaluates the metrological reliability of electrolytic sensors (electrolevels) used to determine angular deviations of elements of engineering structures. The motivation for the work resulted from its strategic application to control the stability of civil engineering structures, notably with application in geotechnics (e.g.: different types of dams of interest in engineering). The methodology used is based on the metrological consistency associated with the quality control process of a set of electrolevels submitted, simultaneously, to a careful calibration process, with traceability ensured to a standard angular deviation pattern. Mounted on a rigid bar, but pivoted at one of its ends to allow angular displacements, the output of each electrolevel is compared with the previously calibrated standard, for different controlled conditions of angular deviation imposed on the bar articulated to a center of rotation. The result of the analysis of typical calibration data for nine electrolevels allowed to show that the expression of the uncertainties associated with the calibration measurements performed constitutes an essential foundation to ensure the metrological reliability of the electrolevels, having allowed to validate a method of discard of electrolevels not meeting the allowable tolerance for a specific engineering application. Among the conclusions of the work, it was possible to qualify the statistical treatment of the levels of uncertainty as a sufficiently robust strategy to validate the electrolevels as a reliable instrument for angular displacement measurements, with a level of confidence appropriate to its application in civil engineering.

Mathematical modeling of thermoelastic state in a tree-component piecewise-homogeneous plate containing a crack

Purpose. A two-dimensional mathematical model of the problem of thermoelasticity for three-component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks. Graphic dependences of stress intensity factors (SIFs) at the tops of the crack have been built. This would make it possible to obtain the critical values of constant temperature in the two joined dissimilar elastic half-planes containing an inclusion and a crack in order to prevent crack growth, which would not allow the local destruction of the body. Methodology. Based on the method of the function of a complex variable we have studied the two-dimensional thermoelastic state for body with crack as stress concentrators. As result, the problem of thermoelasticity was reduced to a system of two singular integral equations (SIE) of the first and second kind, a numerical solution of which was found by the method of mechanical quadratures. The two-dimensional mathematical model of the thermoelastic state has been built in order to determine the stress intensity coefficients at the top of the crack and inclusion. The systems of singular integral equations of the first and second kinds of the specified problem on closed (contour of inclusion) and open (crack) contours are constructed. Numerical solution of the integral equations in the case of constant temperature in the two joined dissimilar elastic half-planes containing the crack and an inclusion was obtained by the mechanical quadrature method. Influence of thermophysical and mechanical properties of an inclusion on the SIF sat the crack types was investigated. Graphic dependences of the stress intensity factors which characterize distribution of the intensity of stresses at the vertices of a crack have been built, as well as on its elastic and thermoelastic characteristics of inclusion. This would make it possible to analyze the intensity of stresses in the neighborhood of a crack vertices depending on the geometrical and mechanical factors. As a result, this allow to determine the critical values of temperature in the three-component plate containing a crack in order to prevent the growth of the crack, as well as to prevent the local destruction of the body. It was found that that the appropriate selection of mechanical and thermophysical characteristics of the components of a three-component plate containing a crack can be useful to achieve an improvement in body strength in terms of the mechanics of destruction by reducing stress intensity factors at the crack’s vertices. Originality. The solutions of the new two-dimensional problem of thermoelasticity for a specified region (a two joined dissimilar elastic half-planes containing inclusion and a crack) due to the action of constant temperature is obtained. The studied model is the generalization of the previous models to determine the two-dimensional thermoelastic state in a piecewise-homogeneous plate weakened by internal cracks. Practical value. The practical application of this model is a more complete description of the stress-strain state in piecewise homogeneous structural elements with cracks operating under temperature loads. The results of numerical calculations obtained from the solution of systems of equations and presented in the form of graphs can be used in the design of rational modes of operation of structural elements. This takes into account the possibility of preventing the growth of cracks by appropriate selection of composite components with appropriate mechanical characteristics.

Recent developments in hybrid aluminium metal matrix composites: A review

This work is done by reviewing the experiments and studies done by various researchers, organizations and institutions on development and mechanical characterization of the hybrid Aluminium metal matrix composites. Metal Matrix Composites or (MMCs) has developed an ever growing interest in recent times for future applications in the aerospace as well as the automotive industries due to their superior strength to weight ratio and higher temperature resistance. MMCs are created by adding a reinforcement material into a metal matrix. Aluminium based metal matrix composites are widely considered one of the best engineering structural elements because of the fact that the possess high strength, high stiffness, high thermal stability, wear resistance and many benefits fitting to its purpose and also varies with the nature and amount of reinforcements used. The work is carried out referring various research papers, publications and educational articles by various authors. The various reinforced aluminium metal matrix composites (AMMCs) reviewed and the development techniques, mechanical property enhancements are put to the analysis. Major reinforcements include silicon carbide, boron carbide, fly ash, tungsten etc while several researches focused on the development of sustainable products by non-conventional and hybrid reinforcements.

Technical Theory of Bending of Elastic Rectangular Plate Pivotally Supported on the Perimeter or Pinched Along Two Adjacent Sides

There is a need to improve methods for calculating elements of engineering structures and equipment for strength and stiffness, which directly affects the safety of nuclear power facilities. For the first time the theory of pure bending of rectangular plates pivotally supported at corner points is generalized to the case of their bending both when the plates are hinged around the perimeter and when a rectangular plate is pinched on two adjacent sides. It should be noted that the obtained system of equilibrium equations does not allow satisfying the equilibrium equations exactly, but only in the sense of the average integral value. However, the authors think this method of solving the deflection problem is much more mathematically and physically justified in comparison with the use of Kirchhoff hypotheses, which lead to contradictions when zero shear forces are assumed to be nonzero, only in order to obtain a deliberately equilibrium equation. The proposed approach allows us to evaluate the deflection of the plate in the case when the main vector of forces applied to the plate can be applied to its geometric center. The article indicates the conditions for the distribution of the transverse load under which it can be assumed that the main vector of forces can be applied to the geometric center of the plate. As examples, the problems of deflection of a rectangular plate under its own weight have been solved both when hinged around the perimeter and when pinched on two adjacent sides.

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

The DNA molecule is the most evolved and most complex molecule created by nature. The primary role of DNA in medicine is long-term storage of genetic information. Genetic modifying is one of the most critical challenges that scientists face. On the other hand, it is said that under the influence of acoustic, electromagnetic, and scalar waves, the genetic code of DNA can be read or rewritten. In this article, the most accurate and comprehensive dynamic model will be presented for DNA. Each of the two strands is modeled with an out of plane curved beam and then by doubling this two strands with springs, consider the hydrogen bond strength between this two strands. Beams are traditionally descriptions of mechanical engineering structural elements or building. However, any structure such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed similarly. Also, in this model, the mass of the nucleobases in the DNA structure, the effects of the fluid surrounding the DNA (nucleoplasm) and the effects of temperature changes are also considered. Finally, by deriving governing equations from Hamilton’s principle method and solving these equations with the generalized differential quadrature method (GDQM), the frequency and mode shape of the DNA is obtained for the first time. In the end, validation of the obtained results from solving the governing equations of mathematical model compared to the obtained results from the COMSOL software is confirmed. By the help of these results, a conceptual idea for controlling cancer with using the DNA resonance frequency is presented. This idea will be presented to stop the cancerous cell’s protein synthesis and modifying DNA sequence and genetic manipulation of the cell. On the other hand, by the presented DNA model and by obtaining DNA frequency, experimental studies of the effects of waves on DNA such as phantom effect or DNA teleportation can also be studied scientifically and precisely.

Mathematical modeling of elastic state in a three-component plate containing a crack due to the action of unidirectional tension

Purpose. A two-dimensional mathematical model for the problem of elasticity theory in a three-component plate containing rectilinear crack due to the action of mechanical efforts is examined. As a consequence, the intensity of stresses in the vicinity of tops of the crack increases, which significantly affects strength of the body. This may lead to the growth of a crack and to the local destruction of a structure. Such a model represents to some extent a mechanism of destruction of the elements of engineering structures with cracks, we determined stress intensity factors (SIFs) at the tops of the crack, which are subsequently used to determine critical values of the tension. Therefore, the aim of present work is to determine the two-dimensional elastic state in plate containing an elastic two-component circular inclusion and crack under conditions of power load in the case of unidirectional tension of the plate perpendicular for the crack line. This makes it possible to determine the critical values of unidirectional tension in order to prevent crack growth, which will not allow the local destruction of the body. Methodology. The methods of studying two-dimensional elastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of elasticity theory is reduced to singular integral equations (SIE) of the first and second kind, the numerical solution by the method of mechanical quadratures was obtained. Findings. In this paper two-dimensional mathematical model in the form of the system of two singular integral equations on closed contour (boundary of inclusion) and unclosed contour (crack) are obtained; numerical solutions of these integral equations were received by the method of mechanical quadratures; stress intensity factors at the tops of a crack are identify and explored to detect the effects of mechanical character. Graphical dependencies of SIFs, which characterize distribution of the intensity of stresses at the tops of a crack as function of elastic properties of inclusion and also as function of the distance between crack and inclusion are obtained. This makes it possible to analyze the intensity of stresses in the vicinity of a crack's tops depending on the geometrical and mechanical factors, as well as to determine the limit of permissible values of unidirectional tension of the plate perpendicular to the crack line at which the crack begins to grow and the body being locally destroyed. It is shown that the proper selection of elastic characteristics of the components of three-component plate can help achieve an improvement in the strength of the body in terms of the mechanics of destruction by reducing SIFs at the crack's tops. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of elasticity for a specified region (plate containing an elastic two- component circular inclusion and a rectilinear crack) under the action of unidirectional tension of the plate perpendicular to the crack line are obtained. Practical value. Practical value of the present work lies in the possibility of a more complete accounting of actual stressed-strained state in the piecewise-homogeneous elements of a structure with cracks that work under conditions of different mechanical loads. The results of specific studies that are given in the form of graphs could be used when designing rational operational modes of structural elements. In this case, the possibility for preventing the growth of a crack through the appropriate selection of composite's components with the corresponding mechanical characteristics is obtained.

Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element

Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

Estimation of Near-Bottom Suspension-Carrying Flow around a Pipeline

In a model format, the force effect of a stratified ideal fluid flow on streamlined elements of engineering structures is investigated. Integral representations of wave drag and lift force are obtained. Numerical calculations are performed for the real marine medium. The conditions under which significant changes in hydrodynamic reactions to streamlined elements of technical structures occur are revealed.

On a model of indentation for a functionally graded strip

When different elements of engineering structures are manufactured, functionally graded coatings are applied to provide them with desired properties. The determination of the properties of the coatings after the coating process is an important stage in their development. Note that one of the most widely used techniques to identify the properties of new materials, including coatings, is the indentation method.

A Model of Indentation for a Functionally Graded Strip

When different elements of engineering structures are manufactured, functionally graded coatings are applied to provide them with desired properties. The determination of the properties of the coatings after the coating process is an important stage in their development. Note that one of the most widely used techniques to identify the properties of new materials, including coatings, is the indentation method [1–3].

Effect of fatigue crack propagation on natural frequencies of system in AISI 4140 Steel

In this study, we investigated the effect of fatigue crack propagation of the beams which have a vital importance in engineering applications, on the natural frequency of the system. Beams which have a wide range of applications, are used as fundamental structural elements in engineering structures. Therefore, early detection of any damages in these structures is of vital importance for the prevention of possible destructive damages. One of the widely used methods of early detection of damages is the vibration analysis of the structure. Hence, it is of vital importance to detect and monitor any changes in the natural frequencies of the structure. From this standpoint, in this study we experimentally investigated the effect of fatigue crack propagation on beams produced from 4140 steel, of the natural frequency of the beam. A crack was opened on the 8

Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux

Purpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. Heat flux due to frictional heating on the local area of the body, causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of a practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the period of cracks placement. Methodology. The methods for studying two-dimensional thermoelastic state of a body with crack as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. Findings. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle of orientation and on the relative position of cracks. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. Originality. The originality of our solution lies in the fact that the new two-dimensional problems of heat conduction and thermoelasticity for a half plane containing a periodic cracks due to local heating by a heat flux are obtained. Practical value. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.