Vol 19, No 4 (2023)
- Year: 2023
- Articles: 7
- URL: https://journals.rudn.ru/structural-mechanics/issue/view/1708
- DOI: https://doi.org/10.22363/1815-5235-2023-19-4
Full Issue
Analytical and numerical methods of analysis of structures
Torsion problem: stress statement and solution by the boundary element method
Abstract
The formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the approximate solution is the Prandtl stress function values, and the determination of stresses is brought down to numerical differentiation. The boundary integral equation of the second kind is obtained to formulate the problem with respect to stresses. The procedure for solving the problem by the boundary elements method is described, the system of solving equations is compiled. Solutions of test problems on torsion of rods with rectangular and channel cross-sections are presented. Comparison of the calculation results with known analytical solutions illustrates the reliability and permissible engineering accuracy of the obtained solutions.
339-348
Elastic-plastic analysis of shells by variational method on the basis of high-degree polynomials
Abstract
The purpose of the research is to develop a variational method for calculation of three-dimensional structures based on approximating functions with finite carriers of an arbitrary degree of approximation. In the early papers of the authors, the method was presented in a linear formulation, and the possibility of calculating both three-dimensional compound structures and thin shells was shown. This paper proposes an algorithm for strength calculation of thick and thin shells with elastic-plastic deformations. The geometry of shells is described in a curvilinear orthogonal coordinate system, e.g., in cylindrical, spherical, or conical ones. The calculation method uses the basic equations of small elastic-plastic deformations for the curvilinear coordinate system. The calculation algorithm was based on a model of material with linear strengthening. To obtain a resolving system of nonlinear equations, the Lagrange variational principle is used. The problem is solved by means of iteration. The first iteration corresponds to a linear problem. At each iteration, after solving the system of equations, the intensities of deformations at each point of integration are calculated. These intensities of deformations are substituted into the matrices of elasticity at the following iterations. The process of iteration is characterized by recalculation of the elasticity matrix at each iteration in each integration point. The researche have shown a stable convergence of the process of iteration. A testing solution of elastic-plastic deformation problems of a thick pipe and a thin shell was carried out. The calculation results were in good agreement with the results obtained both by classical formulas for elastic plastic deformation and with the results of calculations in the Ansys Mechanical program.
349-361
Dynamics of structures and buildings
The formula for the first natural frequency and the frequency spectrum of a spatial regular truss
Abstract
A scheme of a statically determinate spatial truss is proposed. The gable cover of the structure is formed by isosceles rod triangles with supports in the form of racks on the sides. A formula is derived for the lower boundary of the structure’s first natural frequency under the assumption that its mass is concentrated in the nodes. To calculate the stiffness of the truss according to the Maxwell - Mohr formula, the forces in the rods are found by cutting out the nodes in an analytical form. The lower limit of the fundamental frequency is calculated using the Dunkerley partial frequency method. A series of solutions obtained for trusses with a different number of panels is generalized to an arbitrary order of a regular truss by induction using Maple symbolic mathematics operators. Comparison of the analytical solution with the numerical value of the first frequency of the spectrum shows good agreement between the results. The spectra of a series of regular trusses of various orders are analyzed. Two spectral constants of the problem are found, one of which is the highest frequency of truss vibrations, which does not depend on their order.
362-371
Strengthening of damping properties after initial plastic deformation: static and dynamic tests
Abstract
The effect of the initial plastic deformation on the damping properties of low-carbon steel is experimentally studied, which corresponds to a change in the deformation diagram. The deformation diagram also refers to hysteresis loops that expand after the initial plastic deformation, called “plastic execution” in the work. When constructing hysteresis loops and recording damped oscillations, the amplitude values of loading cycles not exceeding 200 MPa are considered. Rods of rectangular box-shaped cross-section were used as samples. A description of static and dynamic laboratory installations that implement a pure bending scheme of the sample is given. Measurements are made by load cells with the fixation of counts in the computer memory with a frequency of 100 Hz. Cyclic symmetrical loads with a frequency of 2,62 Hz occur during oscillations in the sample. During the tests, the effect of a strong increase in hysteresis loops after the initial plastic deformation was reported to the sample was detected and quantitatively explored. The parameters of the loops are obtained depending on the value of the amplitude stress. The recorded graphs of decreasing amplitudes over time (up to 1000 periods) are in good agreement with the hysteresis loops obtained during static tests. The initial plastic deformation was also cyclic with deformation amplitudes 17% higher than the yield strength of the material. The effect of restoring the plastic deformation obtained by the sample after oscillations with stress amplitudes of 200 MPa was found. The oscillations cause the plastic deformation to be restored by more than 40%.
372-385
Critical radius of pipe bending caused by the material destruction
Abstract
The authors investigate the possibility of intensification of pipe bending by creating a minimum curvature considering the thin-wall profile, which is on the limit of exhausting the material’s bearing capacity (destruction). They consider an annular shell (pipe) under the action of pure bending moment, assuming the hypothesis of planar cross-sections and regarding the effect of T. Karman. The deformation changes of geometrical parameters (profile ovalization, wall thinning) are found. The compressive (radial) and tensile (tangential) deformations are calculated with account of their continuity based on the condition of volume constancy. In accordance with the accepted assumptions of mathematical modeling, the dependence of the radial stress on the edge of the bending segment, known from the theory of sheet stamping, is taken, where the most convenient criterion for plasticity is the hypothesis of the energy of shape change of the Mohr’s theory, characterized by the intensity of deformations in the bent section of the pipe, which determines the destruction of the material. The criterion of plasticity, specific mechanical properties of the material obtained in tensile tests (yield and strength limits, relative elongation) and approximated by a step dependence are used for making a combined estimation of the influence of geometric parameters (thinness, ovalization of the profile, deformation thinning of the wall) on the realization of bending of minimum curvature, characterized by loss of wall stability with subsequent failure due to exhaustion of the bearing capacity of the material possessing specific plasticity. Summarizing the results of the minimum (corrugation) and critical (destruction) bending radii, makes it possible to establish the ultimate degree of bending intensification.
386-391
Construction materials and products
Physical features of the problems of liquid corrosion of reinforced concrete from the standpoint of the theory of heat and mass transfer
Abstract
The results of the study of non-isothermal mass-exchange processes occurring during liquid corrosion of iron-concrete are presented. The degree of development of this direction of research is shown: the classification of liquid corrosion of concrete is given, the effect of “free calcium hydroxide” on the stability of cement stone minerals is described, the relative change in the strength of concrete depending on the dimensionless concentration of calcium hydroxide is shown. For concrete and reinforced concrete structures subjected to liquid corrosion, the boundary value problem of non-isothermal mass transfer in the “cement concrete - liquid” system is formulated on the basis of a nonlinear differential equation of mass conductivity of a parabolic type with an arbitrary form of the initial concentration distribution function and combined boundary conditions of the first, second and third kind. A combined approach to solving the problem of non-isothermal unsteady mass transfer is proposed, based on the division of the life cycle of a building structure into “micro-processes”, followed by the separation of the thickness of the structure within the considered small time interval into concentration zones. Analytical solutions to the problem of unsteady mass transfer in the processes of liquid corrosion of concrete for each selected concentration zone have been obtained, allowing to calculate the concentrations of the target component in the solid phase, thereby predicting the dynamics and kinetics of destructive processes of cement concretes. Extensive numerical experiments have been carried out showing the effect of process parameters on the dynamics and kinetics of liquid corrosion of reinforced concrete.
392-409
Experimental researches
Experimental and analytical models of longitudinal deformation in pipe-concrete specimens with small cross-sections
Abstract
The results of experimental studies of deformation problems in pipeconcrete specimens with small cross sections are provided and analyzed. The stress-strain state of a steel pipe and a pipe filled with concrete is studied and compared. Experimental determination of the dependencies between axial load and deformations of pipe-concrete and steel bars, as well as evaluation of concrete’s and steel pipe’s contribution to the total load-bearing capacity of the composite section are provided. Tests were carried out for short pipe-concrete specimens with the pipe dimensions equal to 60x2, 76x3 and 102x3.5, as well as for hollow steel pipes with the corresponding dimensions. The diagrams of deformation were obtained basing on the experimental results. The deformation of the pipe-concrete element under central compression occurs in proportion to the deformation of a hollow steel element with the same diameter, that made it possible to evaluate the contribution of concrete to the work of the pipe-concrete cross-section, which turned out to be constant at each stage of deformation. A methodology has been proposed that enables to describe analytically the deformability of pipe-concrete elements under axial compression by means of the analytical model based on the experimental data.
410-418