Initial Stress-strain State Research Articles

НЕЛИНЕЙНАЯ ДЕФОРМАЦИОННАЯ МОДЕЛЬ СП 63.13330 В СТАДИЙНОЙ ПОСТАНОВКЕ

Normative documents in the field of reinforcement of reinforced concrete structures and the design of prefabricated monolithic structures fairly prescribe consideration of the initial stressstrain state of structures before reinforcement. The calculation can be performed using a normalized nonlinear deformed model according to SP 63.13330. At the same time, it does not explicitly provide for a calculation in several stages. The aim of the study is to develop a calculation method based on a normalized nonlinear deformation model in a staged formulation with minimal differences from the provisions of SP 63.13330. To achieve the goal, the following tasks are set: development of a calculation method, implementation of the method in the form of a universal program and verification of the developed program. The article presents a universal nonlinear deformation model in a staged formulation, which allows, within the framework of certain ratios, to calculate the strength and crack resistance of structural sections at an unlimited number of work stages, taking into account reinforcement, prestressing, initial stresses and cyclic loading (unloading and reloading). The method is implemented as a program in the Python programming language and verified on full-scale and numerical (finite element method) experiments. If we assume the initial stresses and deformations to be zero and calculate in one stage, then the proposed model is reduced to the SP 63.13330 model. For this reason, changing the norms according to the proposed method will not affect the current algorithms for calculating structures in one stage, however, it will significantly increase the scope of the model for calculating prefabricated monolithic, steel-reinforced concrete and reinforced structures. In addition, the accuracy of calculations of prestressed structures will increase, and it will be possible to calculate the cyclic loading of the section.

Коэффициенты электромагнитных связанностей композита "пьезоэлектрик / феррит" с учетом реальной структуры и начальных напряжений

New improved analytical solutions are obtained for tensors of effective pyro– electro–magneto–elastic properties of a piezoactive composite at initial stress-strain state (resulting from initial loading) that account for real two-point correlation functions of an irregular quasi-periodic random structure. The calculations of effective coefficients of electromagnetic and magnetoelectric coupling of the transversal isotropic unidirectional fibrous composite "PZT-4/ferrite" with an axisymmetric tensor of initial strain of the composite are presented. An increase in the absolute values of the effective coefficients is observed at negative (compressive) values of the initial strain tensor components of the composite.

Pavement Analysis with the Consideration of Unbound Granular Material Nonlinearity

Accurate pavement design and evaluation requires the execution of response analysis. Pavement materials’ behavior does not necessarily conform to the assumptions of the multi-linear elastic theory usually adopted during pavement analysis. In particular, the unbound granular materials located in the base and sub-base layers behave in a nonlinear elastic manner, which can be captured through advanced constitutive modeling of their resilient modulus. The finite element method enables us to code constitutive models and quantify potential variations in pavement responses because of different mechanistic assumptions. In this study, variations in response are investigated for a typical structure of a flexible pavement considering the nonlinear anisotropic behavior of the unbound materials together with their initial stress–strain state. To demonstrate the impact of their behavior on the outcome of pavement analysis, variable asphalt concrete layer thicknesses and moduli are assumed, such that they cover a large spectrum of roadways. It was found that pavement responses can be calculated up to 3.5 times higher than those retrieved from the conventional linear analysis. This comparison means that the alterative mechanistic modeling of the unbound granular materials can be proved to be more conservative (i.e., leading to higher strains) in terms of pavement design and analysis. From a practical perspective, this study alerts pavement scientists and engineers engaged in pavement design to a more reliable performance prediction, which is needed to bridge the gap between advanced modeling and routine analysis.

Analysis of mechanical behavior and electromechanical properties of REBCO-coated conductor tapes under combined bending-tension loads using numerical methods

Rare-earth barium copper oxide (REBCO) high-temperature superconducting-coated conductor (CC) tapes are potential conductors for high-field magnets. In an operating high-field magnet, REBCO CC tapes are bent into coils and simultaneously subjected to hoop electromagnetic forces. Under these combined bending-tension loads, the critical current () of the REBCO CC tapes is at risk of irreversible degradation. Therefore, investigating the mechanical behavior and electromechanical properties of REBCO CC tapes under combined bending-tension loads is necessary. In this study, the mechanical behavior of REBCO CC tapes was analyzed using a finite element model (FEM). First, in the fabrication-cooling process of REBCO CC tapes, the thermal residual stress/strain accumulated in the constituent layers was analyzed. Then, considering the thermal residual stress/strain as the initial stress–strain state, the mechanical behavior of REBCO CC tapes under various mechanical loads, such as axial tension, bending, and combined bending-tension at 77 K, was analyzed. Furthermore, a phenomenological model of the internal strain in the REBCO films dependence of was developed for analyzing the electromechanical properties of REBCO CC tapes under combined bending-tension loads at 77 K. Calculated results showed that the compressive thermal residual strain in REBCO films at 77 K was −0.25%, and the internal strain in the REBCO films corresponding to the irreversible degradation of was 0.45% under axial tension loads, which was verified by experimental results. Under bending and combined bending-tension loads, the distribution of the internal strain in the REBCO films along the width direction was non-uniform owing to the Poisson effect, and the onset of the irreversible degradation of occurred at the outer edge of the REBCO films. The phenomenological model was experimentally verified to be effective in degradation behavior prediction under combined bending-tension loads, and model predictions based on the FEM results indicated that the electromechanical properties were significantly influenced by the bending modes (tensile bending or compressive bending) of the REBCO CC tapes.

Dynamic behavior of a compressed reinforced concrete column with regard to the loading prehistory

In recent years, numerous studies of the resistance of structural systems and their substructures to progressive collapse in case of failure of a load-bearing element have been conducted all over the world. Aspects of resistance to progressive collapse of reinforced concrete frames that have not been investigated to date include the consideration of changes in the mechanical and deformational characteristics of the material over time. Therefore, in this study, the analytical solution of the problem of longitudinal bending of a compressed reinforced concrete element under dynamic loading taking into account the initial stress-strain state from the preceding long-term loading based on the viscoelastic model is constructed. Numerical solution of the problem by the Runge-Kutta method is considered. It was found that the calculation results for different integration steps turned out to be similar. However, the calculation results for the integration step of 0.005 s differed by 22.3% from the calculation results for the step of 0.001 s. The difference in the calculation results for integration steps of 0.001 and 0.002 s did not exceed 1.3%.

MODELLING AND ANALYSIS OF INITIAL STRESS STATE IN A THIN-WALL CYLINDER WITH VARIABLE CHARACTERISTICS

A linearized model of prestressed elastic body vibrations is described in terms of the nonsymmetric Piola stress tensor, and a weak statement of the original problem is given. With the help of the Lagrange variational principle, we construct a statement of the problem of steady axisymmetric oscillations of a thin-walled (shell-like) cylinder with variable material properties in the presence of an inhomogeneous prestress field. The motion equations, essential and natural boundary conditions are formulated. Integral characteristics are introduced that average the change in prestresses and material properties over the shell thickness. On the basis of the model presented, the problem on steady-state vibrations of a functionally graded prestressed cylindrical shell is numerically investigated via the shooting method; the influence of the laws of change in material modules and prestress components on dynamic characteristics (e.g., amplitude-frequency characteristics, natural vibration frequencies) is analyzed, a comparative analysis of the solutions is carried out depending on the thin-walled parameter. For the considered cylindrical shell with axial inhomogeneity, based on the acoustic sounding data, we study the inverse problem of restoring two laws of prestress inhomogeneity characterizing the nonuniform initial stress-strain state of tension or inflation. As additional information, we consider the measurement data of the displacement components on the cylinder's surface, given in a set of points at a certain frequency of steady-state oscillations; in such a case, the material characteristics are considered to be known and may depend on the axial coordinate, which makes it possible to set an arbitrary functional gradient along the axis of the cylinder. The mode of probing loading is determined by specifying the traction type and oscillation frequency. Explicit formulas for the desired laws of prestress inhomogeneity are obtained, and computational experiments are carried out to restore them. A high accuracy of reconstruction is revealed far from the ends of the cylinder when probing at a frequency in the vicinity of the first resonance.

A modelling technique to investigate the effects of quasi-static loads on guided-wave based structural health monitoring systems

Guided wave-based methods for damage detection have been widely investigated as techniques to identify damages and their dimensions in structures. Most of the research activities presented in literature have been performed focusing on simple case studies in a laboratory environment, whereas Structural Health Monitoring systems should be investigated under operational loading conditions. When subjected to an operational load, propagation mechanisms can change, suffering from the interaction between propagating signal and scattered waves due to an initial stress-strain state, and so leading to errors in damage sites estimation. In this work, a numerical model, based on Finite Element approach, is proposed to investigate the effects of an initial stress-strain state, induced by a quasi-static load, on guided-wave propagation mechanisms. The case study consists of a real structure, a blended winglet of a general aviation aircraft. The methodology was assessed with reference to different scenarios.

Нелинейное деформирование и устойчивость композитной цилиндрической оболочки при комбинированном нагружении изгибающим моментом и краевой поперечной силой

Currently, polymer composite materials are widely used in the modern aircraft structures. Their application significantly reduces the weight of the structure, while maintaining its strength and stiffness characteristics. A large number of works have been published on the study of the strength of such structures, but the issues of strength and stability during their nonlinear deformation remain unresolved. There is a small number of works on the study of strength and stability of thin-walled shells made of polymer composite materials. The latter is especially necessary for thin-walled aircraft fuselage structures, where the loss of composite skin stability is unacceptable. The problem of determining the influence of the stacking order of monolayers in a skin on the strength and stability of composite material shells under nonlinear deformation remains unsolved. Methods for calculating the strength and stability of thin-walled composite structures, regarding the nonlinearity of the initial stress-strain state, are not well developed. Therefore, the development of reliable and efficient methods for calculating shells made of composite materials is an urgent task. The article describes solving the problem of strength and stability of cylindrical composite shells under arbitrary loading using finite element methods and Newton-Kantorovich linearization. Critical loads have been determined in the course of solving a geometrically nonlinear problem using the Sylvester criterion. The stability of a circular cylindrical shell made of a polymer composite material has been studied under combined loading by a bending moment and a transverse force. The influence of the nonlinearity of deformation, methods of stacking monolayers on the shell critical loads has been determined.

Исследование влияния порядка укладки монослоев на устойчивость композитной цилиндрической оболочки

The stability of a circular cylindrical shell made of a polymer composite material has been investigated under various types of loading: torsional and bending moments, edge compressive and transverse forces, and external pressure. The research results are obtained on the basis of a technique that implements the finite element method for solving the problems of strength and stability of reinforced cylindrical shells made of the polymer composite material, taking into account the momentness and nonlinearity of their initial subcritical stress-strain state. The effect of stacking monolayers and the deforming nonlinearity on the critical loads of shell buckling has been determined.

Исследование нелинейного деформирования и устойчивости композитного отсека фюзеляжа самолета при поперечном изгибе

Currently, there is a lack of studies on the strength and stability of reinforced composite shells, taking into account the momentness and nonlinearity of the initial stress-strain state. Most of the known solutions to the shells stability problems are obtained by analytical and numerical methods, as a rule, in the linear approximation, i.e. in the classical formulation. A developed technique is proposed implementing the finite element method for solving the problems of strength and stability of discrete-reinforced cylindrical shells made of the composite material, taking into account the momentness and nonlinearity of their subcritical stress-strain state. The transverse bending stability of the reinforced aircraft fuselage compartment made of composite material has been investigated. The effect of deformation nonlinearity, stiffness of stringer set, shell thickness on critical loads of the shell instability has been determined.

On characteristic identification for prestressed human skin

In the paper, we present a model of skin in the form of viscoelastic layer-like structure that is inhomogeneous in thickness and consists in turn of three layers: subcutaneous fat, dermis and epidermis. We also assume the presence of an inhomogeneous uniaxial prestress in the skin layer arisen as a result of relaxation after the skin lifting (tightening) surgery procedure. We formulate the problem on the basis of the general problem statement on steady-state vibrations of an inhomogeneous body, taking into account the initial stress-strain state. Using the correspondence principle, the elastic moduli in the problem statement are replaced by complex analogs corresponding to the model of a standard viscoelastic body. The inverse problem is to determine the mechanical characteristics (complex analogs of the Lame parameters) and prestress using the data on the acoustic response for a periodic probing non-invasive effect on the layer surface. By using the Fourier transform in the longitudinal coordinate, we reduce the original problem to solving a number of simpler problems in transforms. Based on the combination of different loading modes, we present a two-stage scheme for identifying mechanical properties and prestress. Within this scheme, at the first stage, complex analogs of the Lame parameters are successively determined using the iterative approach and the Tikhonov regularization method. At the second stage, by using the functions found at the first stage, prestresses are determined using the proposed projection technique. We illustrate the approach developed to the considered skin integument problem by performing computational experiments showing the efficiency of the techniques proposed in the ranges corresponding to the real values of the sought-for parameters. Additionally, we provide some recommendations on the choice of frequency ranges for the best identification at each stage.

Torsional wave dispersion in a bi-layered hollow cylinder with inhomogeneous initial stresses caused by internal and external radial pressures

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

ANALYSIS OF THE CAPABILITIES OF THE LOGOS SOFTWARE PACKAGE FOR CALCULATING THE SEISMIC IMPACT ON A STRUCTURE

The possibilities of the LOGOS software package for calculating seismic vibrations of buried structures, considering the contact interaction with the ground and the gravity field, are investigated and expanded. To reduce computational costs, the LOGOS software package includes a method for modeling non-reflective boundary conditions that was developed earlier and implemented in the “Dynamics-2” software package, which allows reducing the size of the computational domain. The results of numerical simulation in the LOGOS of shear wave propagation in an elastic bounded subdomain of a continuous medium are presented, demonstrating the effectiveness of non-reflecting boundary conditions for a three-dimensional formulation. The dynamic relaxation technique used in the dynamic strength module of the LOGOS software package for calculating the initial static stresses from the action of the gravity field with the subsequent solution of the non-stationary problem is investigated. Numerical estimates of the expected accuracy of the dynamic solution are obtained, depending on the specified accuracy of the static calculation. Thus, the relative error in the change in kinetic energy when using the dynamic relaxation algorithm 10–4 gives a relative error of 10–3 in velocities and 10–2 in stresses, reducing the specified calculation error by 2 orders of magnitude reduces the relative error in calculating velocities by 3 times, stresses – by 5 times. The calculation of the initial stress-strain state of the building-ground system from the action of the gravity field is compared using the dynamic relaxation procedure and using the stationing procedure implemented in the “Dynamics-2” software package. In all problems in the three-dimensional formulation, 8-node hexahedra with one-point integration are used, in the two-dimensional formulation – equivalent 4-node finite elements, for the integration of the defining system of equations, an explicit “cross” scheme is used. Between the subdomains, variants of contact with gluing and contact with friction are implemented. The capabilities of LOGOS for conducting multiprocessor calculations allowed us to make estimates of the convergence of the problem under consideration based on a series of computational experiments.

Computer modeling of volumetric damageability in the mine roadway neighbourhood

The object of research is a rock massif with various cross-sectional shapes of roadway. The purpose of work: computer modeling of stress-strain state and volumetric damageability in the neighbourhood of a mine roadway. The undisturbed rock massif has an initial stress-strain state (under its own weight) before a mine roadway is formed. Therefore, to determine the stress-strain state of the rock massif with the mine roadway, we must first calculate the stress state of the rock massif without the roadway and then take it into account as a pre-stressed state for the rock massif therewith. Damageability assessment of the rock massif with a mine roadway was carried out based on the obtained distributions of stresses and strains. We calculated volumetric damageability through the model of a deformed solid body with dangerous volume. Dangerous volume is a limited area where stresses or strains exceed the predetermined threshold. Calculation of dangerous volumes and integral damageability was carried out in the finite element package ANSYS. The program was written in APDL. The ratios between the existing and limiting stresses was calculated for each finite element. The elements for which this ratio exceeds unity will form a dangerous volume for the whole model. As a result, we have an array of finite elements constituting the dangerous volume and its value. The developed method for assessing damageability in the mine roadway neighbourhood takes into account various cross-sectional shapes of the mine roadway and its depth. The relevance of studying possible destruction regions using the model of a deformed solid body with dangerous volume was substantiated.

SERVICE BEHAVIOUR OF THE SELF-STRESSED MEMBERS REINFORCED WITH FRP BARS

Fiber reinforced polymer (FRP) bars, as a structural reinforcement, are characterized by the number of advantages, such as: high strength-to-density ratio; absence of corrosion; resistance to the negative influence of the different aggressive mediums. Nevertheless, a wide practical application of such a bars finds an embarrassment because of the law modulus of elasticity (it varies from 30 GPa to 60 GPa), that leads to the development of the excessive crack opening as well as deflections under the loading. To enhance structural performance of the FRP reinforced concrete members, pretensioning of FRP bars can be considered as a good option. Opposite to the concrete members mechanical pretensioning, physico-chemical method of bars pretensioning based on the self-stressing concrete utilizing is considered. Influence of the controlled initial stress-strain state obtained during early age concrete expansion on the mechanical resistance of the self-stressed concrete members reinforced with both steel and FRP bars was studied.

Forecast of potential rockburst hazard during the reconstruction of the Yugo-Zapadnaya mine at the Darasun deposit

Research aim is to study the geomechanical conditions of the Yugo-Zapadnaya mine at the Darasun gold ore deposit during the reconstruction of mining to forecast the rockburst hazard. Methodology. Laboratory tests of physical and mechanical properties of rocks were carried out. The initial stress-strain state of the rock mass was assessed by natural measurements and by solving the inverse geomechanical problem. The method of finite element analysis determined the technogenic stresses in the structural elements of the geotecnologies. Engineering calculations of critical depths of rockbursts were performed. Results and conclusions. By results of researches it is established, that the natural field of in-situ stresses in the deposit array of rocks is distributed discretely: high-stress, medium-stress and off-load zones are distinguished. The rocks have high strength and elastic properties and are prone to brittle fracture. The actual mining has reached critical depth of rockburst. Air headings and ceiling are in the most hazardous state. To increase the safety of mining, a set of measures has been proposed: unloading roof ceiling and corners with slots, giving the roof a hipped shape, replacing the ceiling with a concrete pillar. It is recommended to conduct operational geomechanical monitoring at the mine.

Концепция проведения крупномасштабных термомеханических экспериментов в ПИЛ в Нижнеканском массиве горных пород

Numerical simulation of thermomechanical processes in a deep underground radioactive waste repository requires information on the host rock and the engineered barriers properties at a scale of dozens of centimeters, meters and more. However, the extrapolation of the values obtained on small-scale samples in surface laboratories yields excessive uncertainties. The materials behavior is also influenced by conditions that cannot be reliably reproduced in a surface laboratory, such as water content or initial stress-strain state. Following experiments are planned to study the host rock and the engineered barriers behavior during heating under conditions similar to those expected in the repository, as well as to assess their large-scale thermomechanical properties. In the experiment focused on the excavation damaged zone thermal mechanics, the behavior of reinforced drift walls and vaults under heating will be studied. The experimental facility will involve two drifts with the same orientation as the planned repository ones. As a result, the spatial distribution of excavation damaged zone thermomechanical parameters and their evolution due to heating will be identified. The second experiment focuses on the host rock mass behavior under spatially nonuniform unsteady heating. The facility will feature two vertical boreholes with heaters. The experiment will be divided into several stages: study of the host rock initial state, estimation of the rock main thermomechanical properties, study of the temporal evolution of the stress field due to 3D temperature gradients and of the processes in the host rock occurring during its cooling and re-saturation with water. Following the completion of the separate-effect test program, an integrated experiment should be carried out to study the coupled processes with respect to their mutual influence. The obtained results will be used to refine the values of input parameters for numerical simulations and their uncertainty ranges, as well as to validate the computer codes.

Tension-Compression and Shear of Plane Test Specimens from Laminated Composites with the [90°]s Structure. Initial Stress-Strain State

Using the previously constructed equations of the theory of the plane multi-layer beams with a thin-layer structure in thickness, based on a discrete-structural model, a linear problem on the formation of the initial (subcritical) stress-strain state in test specimens of a unidirectional laminated composites with the [90°]s structure was given in shear tensile-compression tests. A numerical method was developed for solving the formulated problem, based on the reduction of the original problem to a system of integro-algebraic equations and the construction of their solution by the method of finite sums. The properties of the constructed equations are investigated and numerical experiments are carried out on the basis of the developed method. It is shown that in the test specimens of the laminated composite of the considered structure at their tension (compression) in the direction across the fibers and in shear, predominantly normal tensile (compression) stresses are formed, which are constant along the length and width of the specimen, and the tangential stresses in these directions are variable.

Естественное напряженно-деформированное состояние нижних горизонтов шахты Юго-Западная Дарасунского рудного поля

Естественное напряженно-деформированное состояние нижних горизонтов шахты Юго-Западная Дарасунского рудного поля

Determining Coalbed Methane Content Structure

The study provides experimental evidence of scientific ideas that are important for developing the phenomenological basis of the theory of phase transformations in the ‘coal – methane’ system accompanying the formation of gas-dynamic processes in coal beds when their initial stress-strain state and temperature background are disturbed during mining. Residual gas content of coal was determined versus the time after its recovery from coal beds and the weighted mean particle size; the effect of the pore structure of natural coals on the gas-dynamic activity of coal beds was estimated. It was shown that the major part of volatile compounds (mostly methane) is dissolved in the bulk of carbon layers.