Account Physical Nonlinearity Research Articles

Boundary value problems of integrodifferential equations under boundary conditions taking into account physical nonlinearity

When solving integrodifferential equations under boundary conditions, taking into account physical nonlinearity, a broad class of boundary-value problems of oscillations arises associated with various boundary conditions at the edges of a flat element. When taking into account non-stationary external influences, the main parameters is the frequency of natural vibrations of a flat component, taking into account temperature, prestressing, and other factors. The study of such problems, taking into account complicating factors, reduces to solving rather complex problems. The difficulty of solving these problems is due to both the type of equations and the variety. We analyze the results of previous works on the boundary problems of vibrations of plane elements. Possible boundary conditions at the edges of a flat element and the necessary initial conditions for solving particular problems of self-oscillation and forced vibrations, and other problems are considered. The set of equations, boundaries, and initial conditions make it possible to formulate and solve various boundary value problems of vibrations for a flat element. The oscillation equations for a flat element in the form of a plate given in this paper contain viscoelastic operators that describe the viscous behavior of the materials of a flat component. In studying oscillations and wave processes, it is advisable to take the kernels of viscoelastic operators regularly, since only such operators describe instantaneous elasticity and then viscous flow.

METHOD OF ASSESSMENT OF STRESSDEFORMED CONDITION OF STRUCTURAL STRUCTURES ON THE BASIS OF SUBSYSTEMS METHOD

he article considers a method for dynamic analysis of the interaction of the system "ground part  base  soil". The analysis of experimental data of the building, after action of seismic loading is used. The technique allows to solve dynamic problems taking into account physical nonlinearity. The problem of solving a dynamic problem in time by the method of subsystems is smoothed out. A practical example of calculating the reinforced concrete frame of a building in Odessa, taking into account the joint work of the foundationpilebuilding.

Vibrations of high-rise buildings under seismic impact taking into account physical nonlinearity

Analytical description of vibration loads of the complex construction structure is considered as a system of masses connected by means of viscoelastic springs. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle is used. A mathematical model of the problem under consideration has been developed, which boils down to the solution of a system of nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis. The results are shown as graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

TORSIONAL VIBRATIONS OF A CIRCULAR ELASTIC ROD TAKING INTO ACOUNT PHYSICAL NONLINEARITY

. In this work, on the basis of the equations of torsional vibrations of a circular rod derived by the author, taking into account physical nonlinearity, the problem of torsional vibrations of a rod is numerically solved. A comparative analysis of the results obtained for nonlinear and linear cases is carried out. To solve the problem, a numerical finite difference method is applied. The approximation of the oscillation equation and boundary conditions leads to a system of algebraic equations, the solution of which is not mathematically difficult. On the basis of the obtained numerical data of the problem, graphs of the dependences of the torsional displacement and stresses on time were constructed. The main conclusions made on the basis of the constructed graphs of displacement and stresses are presented.

Stress-strain state of concrete filled steel tubular columns of annular cross-section taking into account physical nonlinearity

The article presents the derivation of the resolving equations for calculating concrete filled steel tubular columns with an annular cross-section under central compression, taking into account physical nonlinearity. The solution is performed numerically by the finite difference method. The deformation theory of plasticity of concrete by G.A. Geniev is used as the law of deformation

Modified method of variable elasticity parameters for solving problems of dynamics of rod systems taking into account physical and geometric nonlinearities

The article describes an algorithm for calculating vibrations of rod systems by the finite element method, based on an iterative process that allows taking into account physical and geometric nonlinearity. The iterative process, which takes into account physical nonlinearity, is based on the introduction of the cubic dependence of stresses on deformations into the calculation and the comparison of the secant elastic modulus at each step of the iteration. When calculating the stiffness matrix, an additional term (matrix) is introduced that takes into account geometric nonlinearity. A comparative analysis of the results of the calculation with a linear dependence between stresses and deformations and the calculation with a cubic dependence of stresses on deformations is given.

Simulation of the stress-strain state of shells under internal pressure using the mixed finite element method, taking into account physical nonlinearity

In this article, the finite element method (FEM) is used to model the stress-strain state (SSS) of shells experiencing internal pressure with elastic-plastic state being taken into account. Main geometric equations determining the location of an arbitrary point at load step are given. Mixed functionality used in implementation of FEM which allows to determine stresses and displacements simultaneously is obtained based on equality of possible and actual work of external and internal forces. Examples of stress-strain state of rotation shells with spherical and elliptical bottoms under internal pressure are provided. Static check of resultant external forces arising from applied pressure and resultant internal forces arising from stresses equality to zero is performed. Achieved results show correctness of the developed algorithm with elastic-plastic properties of the material being taken into account, ensuring that main requirements for the mathematical model are secured, namely adequacy, versatility and cost-effectiveness. Costs of resources computing are reduced by adopting a number of hypotheses and determination of stresses and strains at once ensuring cost-effectiveness and simplicity. Using developed scheme of the mixed functionality application in implementation of FEM the mathematical model acquires one of its main properties - “Potentiality”.

МОДЕЛИРОВАНИЕ УСТОЙЧИВОСТИ БУРИЛЬНЫХ КОЛОНН НА СТАДИИ ПРОЕКТИРОВАНИЯ – ГАРАНТИЯ НАДЕЖНОСТИ ИХ РАБОТЫ

In the address of the Head of state Kassym-Jomart Tokayev to the people of Kazakhstan, announced on September 1, 2020, a number of tasks related to improving the productivity of industrial production, including the oil industry, with the broad introduction of modern IT technologies. This is evidenced by the instruction of the President sent in his Message to the Western regions of the country on issues of investment attraction for construction in the future, petrochemical complexes and creating new production runs of high value added [1]. This requires in the near future expand the set of activities for finding and developing new oil and gas fields, and in line with this, a substantial increase in drilling operations, the introduction of effective methods of deep drilling. In this regard, it is very important to ensure the reliability of drilling systems (DS) at the design stage. This, in turn, allows you to solve several tasks simultaneously: based on the use of modeling methods and digital technologies, predict the performance and working properties of DS elements in advance, before they are created, and thereby significantly reduce the risks of large capital expenditures, human and time resources, which would have acquired an irreversible process already at the stage of operation; create digital technology platforms that can become the driving force of the digital ecosystem of the industry [1], in our case, drilling and exploitation of oil and gas fields, thus complementing the electronic database with information about problem situations and effective methods of their solution (elimination). In this paper, which is a continuation of the results of the authors ' research published in [2], we consider special cases of modeling the stability and vibration of drill strings (DStr) taking into account the geometric nonlinearity of deformation. Such cases are buckling often occur with increasing depth of drilling, i.e., length, DStr, where the system becomes quite like a long stretchedcompressed tubular rods under longitudinal and transverse loads. In order to study (predict) the reliability of DS in such situations, the dynamic stability of a geometrically nonlinear DStr under variable loads is investigated, and a method for applying the finite element method to study the dynamic stability of DStr under geometric nonlinearity of their deformation is proposed. To study these phenomena under DStr loading conditions, the authors of this article consider the dynamic stability of a weighed column, taking into account its physical nonlinearity under compressive loads of time variables. Based on the analysis of the obtained theoretical dependencies, the DStr deflections are compared for both physically linear and nonlinear problems. It is established that taking into account physical nonlinearity leads to an oscillatory process with a limited amplitude, and that the presence of nonlinearity for the selected parameters leads to an oscillatory process of the column. In General, the graphical dependencies that characterize the DStr stability parameters obtained on the basis of mathematical modeling methods demonstrate the ability to predict and control the Parameters of this process at the design stage, which allows us to estimate the most optimal zones (limits, ranges) that ensure the efficiency and reliability of the DS operation by varying their values in advance.

ИССЛЕДОВАНИЕ УСИЛИЙ В ВЕРТИКАЛЬНЫХ ШПОНОЧНЫХ СТЫКАХ КРУПНОПАНЕЛЬНОГО ЗДАНИЯ В ПРОЦЕССЕ ВОЗВЕДЕНИЯ

Recently, the world has seen a tendency of reinforced concrete housing construction industrialization. Russia has gained extensive experience in large-panel housing construction, which helps to find optimal structural solutions, but new solutions lead to the need for additional study. Modern software systems allow you to build volumetric models of a building, taking into account physical non-linearity, which helps to take into account the actual distribution of efforts between the elements. At the same time, to build the correct model of a large-panel building, the flexibility of joints between them is required. The flexibility is calculated by online tests the results of which are used to build the future model of a building in the process of its designing. The calculation model of a building gives an approximate estimate of structural behavior and the degree of its accuracy depends on the correct selection of the initial premises. This article estimates the numerical model of a large-panel building by comparing it with the results of direct observations of shear movements in the vertical joints of the most loaded walls of a building under construction. The observations were carried out on a 26-story large-panel building with a cross structural system with self-supporting external longitudinal walls. Vertical joints are monolithic reinforced concrete with the use of dowels with cable loop transverse reinforcement. In addition, estimation of forces at the joints is also given. In general, we may conclude that the calculation model of a large-panel building is applied correctly using elastic-flexible connections with limiting ultimate forces for vertical joints modeling. The modeling part of the study is performed using a finite element model taking into account the magnitude of the joints flexibility and the actual stiffness of the building structural elements. The results of the study can be used in modeling, calculation and design of large-panel buildings, and they provide new scientific knowledge about the operation of buildings of this type.

Birger method of variable parameters for the problems of flexible plates

The paper describes the application of the Birger method of variable parameters as applied to solving problems of flexible plates taking into account physical nonlinearity. The load-deflection curves for various values of the geometric and physical-geometric parameters are given. The limiting values of the physic-geometric parameter are calculated at which the calculation should be carried out with one or two non-linearities.

CALCULATION OF THE STRENGTH OF RUBBER-CORD MEMBRANES IN REAL OPERATING CONDITIONS

The article analyzes the existing methods of calculating the strength and torsional vibrations of rubber-cord shells of elastic couplings. The refined estimation of these calculated dependences taking into account physical nonlinearity and thermal fields of elastic shells is made.

Computer Modelling of RC Beams Reinforced with High Strength Rebars and Steel Plate

Abstract The use of computers provides the opportunity to analyse and design complex structures, taking into account the geometric and physical nonlinearity of construction materials. In the article the study of stress-strain state of mixed steel-concrete beams, were presented. The results of this study showed that the method of calculation according to designe codes gave satisfactorily results of calculated strength compared with experiments. However, these methodes do not provide complete information of structural performance at all levels of load. For a more complete study of the stress-strain state and the physical nature of the processes occurring in steel-concrete structures reinforced with a mixed reinforcement, the calculation method using “Lira” software complex is proposed. The method of calculation is based on the finite element method. The calculation is made taking into account physical nonlinearity and real diagrams of σ-ε of materials using the nonlinear deformation law №14 of “Lira” software complex. The proposed method of calculation allows to determine the values of bearing capacity, the development of deformations and the beginning of crack formation, as well as stresses at all load levels.

The effect of cracks on the bearing capacity of reinforced concrete slabs

Cracks occur in reinforced concrete slabs for two reasons - due to increased operational loads and due to manufacturing and installation defects. When cracks are detected, the question arises about the residual bearing capacity of the slab and the need of its strengthening. To solve this problem by calculation, it is necessary to take into account physical nonlinearity. An algorithm for the calculation by the finite element method is proposed. The main feature of the algorithm is the use of multilayered finite elements, which allows modeling the cracks by specifying the corresponding material characteristics of those layers which the crack passes through. A method for determining the bearing capacity of a slab with cracks after its reinforcement with composite fabrics is also considered. An example of the study of the stress-strain state of a reinforced concrete slab with cracks by the proposed method is given. The implementation of the algorithm in the PRINS program is described and the possibility of using this program for solving practical problems is discussed.

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

To the approximation of rectangular and complex cross-sections of reinforced concrete structures under the action torsion with bending

Special analytical method for determining tangential tension stresses in reinforced concrete structures operating in conditions of complex resistance –torsion with bending is proposed in this paper. Its peculiarity consists in the approximation of rectangular and any complicated cross-sections of reinforced concrete structures with the help of their division into squares with the circles inscribed there in, connected together into a single monolithic figure. The dependence of tangential torsion stresses becomes valid on the distance to the centre of the circle under consideration within each j-th circle. The further the circle from the centre of the rectangle is located, the greater its moment of inertia becomes and the maximum stresses are reached in the middle of the rectangle the long sides. Such model makes it possible to remove the question of the necessity using of special tables also for their calculation in the elastic stage. Also it makes possible to separate the stress-strain state in a whole set of circular sections from the additional field associated with the deformation of the rectangular section. The authors corrected and significantly supplemented the dependencies for taking into account the deplanation of a rectangular cross-section rod. Attention is focused on the physical essence of longitudinal displacements caused by deplanation, an analogy with elementary movements caused by shearing forces is carried out. In the study, the classification of spatial cracks for reinforced concrete rod structures under the action torsion with bending was generalized; while the process of spatial cracks formation of the first, second, and third types is tied to the proposed method for determining tangential stresses (angular deformations) for complex cross-sections. The proposed dependencies allow us to search for the values of the model design parameters at of the stress-strain state stages of the reinforced concrete rod structure, including in the plastic and in the limiting stages. The components of the torsion stress (angular deformations) are again synthesized and separated by the proposed method for the convenience of analysis in principal stresses tensors (main strains). Transformational transitions from a cylindrical to a Cartesian coordinate system and the attraction of local coordinate systems made it possible to simplify the equations as much as possible. Moreover, the equations are constructed in such a way that the resolving system does not turn into a decaying system. The physical interpretation of the solution obtained, with respect to the problem of crack resistance, is that it allows us to search for the minimum generalized load that corresponds to the formation of the first, second or third spatial crack types and the coordinates of their formation point. As a result, the effectiveness of the proposed method is shown with approximating rectangular and complex cross sections of reinforced concrete structures under the action torsion with bending and taking into account physical nonlinearity, deplanation of cross-sections, pre stressing in longitudinal and transverse reinforcement and the influence of local stress fields.

Analysis of oscillations of framework at pulse influence taking into account physical non-linearity

The article illustrates the analysis of oscillations of a flat multi-storey framework as discrete dissipative systems (DDS) at pulse influence by the time analysis method (TAM). Brief theoretical prepositions of TAM, such as description of the equation of motion of the DDS and expressions of response parameters, are given. The design dynamic model of the structure represents the flat three-storey shear frame having three degrees of freedom. The calculation results are oscillograms of internal response characteristics and reaction parameters of the system on the time slice t ϵ [0;8] sec. The multi-cycle nature of deformation of racks and also the change of parameters of plastic zones of framework supporters in the process of non-linear oscillations are considered.

Introducing Physical Nonlinearity in the Design of Aluminum-Alloy Vehicle Components

The application of the finite-element method in the design of vehicle components consisting of physically nonlinear materials is possible by parabolic approximation of the actual deformation diagram. Taking account of physical nonlinearity permits satisfactory design of the load-bearing structures in vehicles.

Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress–strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to ordinary differential equations (ODEs). The theorem regarding convergence of this method is formulated for the class of similar-like problems. The convergence of the proposed iterational procedure used for obtaining a solution to contact problems of two plates is proved. In the studied case, the physical nonlinearity is introduced with the help of variable parameters associated with plate stiffness. The work is supplemented with a few numerical examples. Both Fourier and Morlet power spectra are employed to detect and analyse regular and chaotic vibrations of two interacting plates.

Static calculation of bearing construction elements taking into account physical nonlinearity

One of the most important characteristics of construction behavior is physical nonlinearity which appears in the course of deformation between strain and deformations. Its account complicates algorithm; therefore, many modern construction calculations are spent in an elastic stage that lead to the overestimated results, not corresponding to real work of the construction. In this connection, it is necessary to develop such models of construction, which fully enough and unequivocally confirm to investigated objects and processes of their deformation.

THE MODELING OF STRUCTURAL ENFORCEMENT BY COMPOSITE MATERIALS ON “LIRA-SAPR”

This paper provides detailed suggestions for process of modeling the structural reinforcement by composite materials on the software package "LIRA-SAPR". It provides the implementation of bearing capacity checks for reinforced elements on the program called "ESPRI". The article offers an algorithm for calculation the construction objects in case of the changing of design situation, taking into account the modeling of the composite structure reinforcement. It considers the modeling process of reinforcement of structures using classical methods, such as using of metal casing. In the article you can also find a numerical modeling example of the frame structure reinforcement, with the selection and verification of the composite material. It considered the process of modeling the bearing capacity increasing with using the classical methods, namely the increase of the metal hooping. The article investigates the example of a numerical simulation of the frame bearing capacity increasing with the selection and verification of the composite material. Using the finite element method a mathematical model of the frame structure was constructed. In the frame work it was taken into account the occurrence of the bearing capacity increasing by composite materials in some elements. It compared the kinematic characteristics and effort that have arisen within the frame design model with static analysis, also taking into account physical nonlinearity in the calculation and enhancing certain elements reinforced with composite material. Also in this paper we describe a method of modeling the bearing capacity increasing with using the metal hooping.The calculation of reinforced element is made on the program called ESPRI, followed by an analysis of the overall calculation model work on the software package "LIRA-SAPR". The result of the article is a comparison and analysis of the stress-strain state of the considered computational model for various problem formulations. The results could be used for wider application in the study of methods for increasing the bearing capacity of buildings and structures.