卷 21, 编号 2 (2025)
- 年: 2025
- 文章: 8
- URL: https://journals.rcsi.science/1815-5235/issue/view/22012
- DOI: https://doi.org/10.22363/1815-5235-2025-21-2
完整期次
Analysis and design of building structures
Finite Element for the Analysis of Reinforced Concrete Beams with Non-Uniform Steel Fiber Reinforcement
摘要
A method has been developed for calculating and constructing a physically nonlinear finite element of a multilayer reinforcement beam, which allows to calculate the values of displacements, strains and stresses in a characteristic layer. To establish the actual stress-strain state of bent heterogeneous fiber reinforced concrete elements, an experimental study of a steel-fiber-concrete beam with non-uniform fiber reinforcement along the cross-section height (from 0.5 to 2.0%) was carried out. Strains and displacements of the beam at characteristic points are determined, and normal tensile and compressive stresses are obtained. The experimental data obtained were used to verify the finite element of the multilayer reinforcement beam. The developed finite element of the beam was based on the modified theory of calculation of multilayer beams proposed by P.M. Varvak. The multilayer beam model takes into account the curvature of the cross section under the action of shear stresses by including the generalized component of shear strain in the functional of the total potential energy. In addition to the experimental data, nonlinear analysis of a multilayer beam was performed in the Ansys software package. The discrepancy between the calculation results using the developed finite element and the experimental data ranged from 6 to 11%, and from 11 to 15% with the calculation results obtained in Ansys. The developed finite element is integrated into the PRINCE computing complex, and as part of this program it can be used to calculate heterogeneous fiber-reinforced elements.
83-95
Analysis of Water Seepage into Vacuum Anchor Subjected to Pull-Out Load
摘要
When constructing offshore facilities, their reliable fixation to the bottom surface is required. Many solutions for fixing to the bottom surface (weights and anchors) have been developed in the world. To solve this problem, it is proposed to use a vacuum anchor design. Conceptual diagrams of vacuum anchors installed in soft soils are presented. The purpose of the study is to substantiate the operability of vacuum anchors taking into account the influence of infiltration processes. To achieve this goal, mathematical techniques, search and analysis of Russian and international sources with data comparison were used. The position of the water seepage lines in permeable soil is determined by the electrohydrodynamic analogy method. Water seepage into the anchor subjected to a pull-out load was calculated; the seepage discharge of water was determined depending on the depth of the water body at the installation site, the thickness of the permeable soil layer and its permeability coefficient, and the geometric parameters of the vacuum anchors. The technology of driving vacuum anchors into soft bottom soil is described, the conditions of driving the anchor into the bottom soil and the conditions of it pulling out from the soil are calculated. It is established that vacuum anchors used for soft bottom soils have a significant retaining capacity with relatively small dimensions. At the same time, the thickness of the permeable layer of the bottom soil, exceeding five embedment lengths of the vacuum anchor into the bottom soil, practically does not affect the value of water seepage inside the vacuum anchor when subjected to a pull-out load. A reduction in costs is predicted when introducing vacuum anchors into the practice of marine construction.
96-107
Analytical and numerical methods of analysis of structures
Natural Frequency Spectrum and Fundamental Frequency Formula for Plane Periodic Lattice Truss
摘要
The goal is to determine the free vibration natural frequency spectrum for a plane statically determinate truss with a cross-shaped lattice. The truss members are elastic and have the same stiffness. Both truss supports are pinned; the truss is externally statically indeterminate. A model, in which the mass of the structure is uniformly distributed over its nodes, and their vibrations occur vertically, is considered. The Maxwell-Mohr method is used to determine the stiffness of the truss. The member forces included in the formula are calculated by the method of joints using the standard operators of Maple mathematical software in symbolic form. The eigenvalues of the matrix for trusses with different numbers of panels are determined using the Maple system operators. Spectral constants are found in the overall picture of the frequency distribution constructed for trusses of different orders. A formula for the relationship between the first frequency and the number of panels is derived from the analysis of the series of analytical solutions for trusses of different orders. A simplified version of the Dunkerley method is used for the solution, which gives a more accurate approximation in a simple form. The relationship between the truss deflection under distributed load and the number of panels was found. Spectral constants were found in the frequency spectrum.
108-117
Two-Field Prismatic Finite Element Under Elasto-Plastic Deformation
摘要
For elasto-plastic analysis of structures at a particular load step, a mixed finite element in the form of a prism with triangular bases was obtained. Displacement increments and stress increments were taken as nodal unknowns. The target quantities were approximated using linear functions. Two versions of physical equations were used to describe elasto-plastic deformation. The first version used the constitutive equations of the theory of plastic flow. In the second version, the physical equations were obtained based on the hypothesis of proportionality of the components of the deviators of deformation increments to the components of the deviators of stress increments. To obtain the stiffness matrix of the prismatic finite element, a nonlinear mixed functional was used, as a result of the minimization of which two systems of algebraic equations with respect to nodal unknowns were obtained. As a result of solving these systems, the stiffness matrix of the finite element was determined, using which the stiffness matrix of the analysed structure was formed. After determining the displacements at a load step, the values of the nodal stress increments were determined. A specific example shows the agreement of the calculation results using the two versions of the constitutive equations of elasto-plastic deformation.
118-127
Dynamic Loading of Bar Systems with a Finite Number of Degrees of Freedom
摘要
The study of the stability of systems with a finite number of degrees of freedom under the influence of dynamic loads is an important problem of structural mechanics. Such systems are widely used in mechanical systems in various fields: construction, mechanical engineering, aircraft construction, shipbuilding, instrument engineering, and biomechanics. In case of seismic impacts, it is necessary to check the building’s structural elements for dynamic stability. The issue of determining the critical state of systems with a finite number of degrees of freedom under dynamic loads is solved in this paper. The article presents a method for analyzing the dynamic stability of bar systems with one and two degrees of freedom. Bar systems with a finite number of degrees of freedom, which are subjected to a dynamic compressive load in the longitudinal direction, are considered. In the hinges, the bars are connected by elastic springs that counteract the instability of the system. To solve the problem, ordinary differential equations are composed. One equation is composed for a single-degree-of-freedom system and a system of two equations for a three-bar system (a two-degree-of-freedom system). The obtained equations allow to study the stability of a system with a finite number of degrees of freedom. Numerical method is used to solve the problem. Numerical integration of the equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the relationships between the deflection of the bar systems and the acting dynamic load are constructed. The change in the “ t 1 time” shows the value of the dynamic coefficient k д. The influence of the parameter of the rate of change of the compressive load and the initial imperfection on the criteria of dynamic stability of bar systems with one and two degrees of freedom is investigated.
128-137
Analysis of thin elastic shells
Systems of Approximating Functions when Using Variational Methods for Calculating Thin-Walled Building Structures
摘要
The question of the use of approximating functions in the calculation of thinwalled building structures is investigated and the requirements that they must satisfy are analyzed. A rule is formulated that allows one to distinguish between the principal boundary conditions and natural ones. It is shown that the approximating functions must satisfy the principal boundary conditions, while the natural boundary conditions are included in the equilibrium equations and are satisfied automatically when solving a boundary value problem. The accuracy of their fulfillment depends on the accuracy of the solution of the problem itself. An example shows what errors can result from the use of approximating functions that satisfy the specified boundary conditions, but do not satisfy the completeness conditions. Some systems of functions for which the completeness condition in the energy space has been proven are considered. Using the example of Legendre orthogonal polynomials, a technique is given for forming approximating functions that satisfy the specified boundary conditions and the completeness conditions of a system of functions. The efficiency of using the obtained approximating functions in solving boundary value problems using the Galerkin method is shown.
138-154
Torses with Two Curves in Intersecting Planes and with Parallel Axes
摘要
Methods for designing torse surfaces with two specified plane directrix curves in intersecting planes, which are projected onto the opposite sides of an arbitrary plane quadrilateral base, are studied and implemented. The other two sides of the base coincide with the two genertrix lines. The theoretical construction techniques are illustrated and visualized using computer graphics for four torse surfaces. Parabolas of the second and fourth orders and a hyperbola are chosen as the directrix curves. The geometric and strength studies on torse surfaces and shells that have been conducted by scientists over the past 10 years are briefly described. They show that interest in their study is not fading, but is moving towards computer modeling and comparative strength calculations using the finite element method. The directions in research of various torses, that are desirable to extend to the torse surfaces proposed for implementation, are illustrated.
155-166
Dynamics of structures and buildings
Variant Design of Girder-Slab Structure with Different Geometric Cells Under Flexural Vibrations
摘要
Girder-slab structures are widely used in industrial buildings, bridge decks, complex combined engineering structures and other objects of construction and mechanical engineering. An important task in their design is to find the most economical structural solution with the least amount of material while ensuring the necessary strength and rigidity. Therefore, the development of methods and algorithms for searching of the most rational and optimal design solutions is of great significance. The authors offer a technique of variant design of girder-slab structures with various cell shapes: rectangular, triangular, rhombic, trapezoidal and other, when analyzing vibrations. The technique is based on the principles of physicomechanical analogies and geometrical methods of structural mechanics. For a numerical example, a cantilever girder-slab structure on trapezoidal base is studied. The bars are of typical sections, the flooring is smooth steel. It is shown that cell geometry affects flexural vibrations of the girder-slab structure and material consumption.
167-178