Papers by Keyword: Method

Abstract: A variant of the mathematical theory of deformation of multilayer nonlinearly elastic (according to Kauderer) plates of arbitrary constant thickness with non-symmetric structure in thickness has been constructed. The transverse load on the horizontal faces can be arbitrary static. The components of the stress-strain state (SSS) and the boundary conditions on the lateral surface are functions of three spatial coordinates. Spatial boundary value problems for multilayer plates are reduced to two-dimensional using three-dimensional equations of the theory of elasticity, the Reissner variational principle, and the expansion of the components of the SSS into infinite mathematical series by combinations of Legendre polynomials within each layer. This approach differs significantly from the approaches of other authors. The main dependencies, boundary conditions and systems of equilibrium differential equations with high-order partial derivatives with respect to the displacement components are derived. All dependencies and equations contain nonlinear terms. The new methodology for constructing a variant of the nonlinear theory makes it possible to accurately satisfy the boundary conditions on the horizontal faces of the plate and on the lateral surface, and to accurately satisfy the conditions of rigid conjugation of adjacent layers. The system of equilibrium equations has a high order. An analytical method for solving these systems is proposed and developed. The method is based on algebraic, differential and operator transformations of the initial systems. They are reduced to two convenient defining systems: one describes the vortex edge effect with a refinement of the SSS, and the other describes a refined internal SSS with a potential edge effect. The order of the systems of differential equations does not depend on the number of layers, but depends only on the number of retained terms in the mathematical seriess. The internal SSS is separated from the potential edge effect. By the method of order reduction, the determining systems are reduced to second-order differential equations. This significantly simplifies the solution of boundary value problems. General solutions for all components of the SSS were found through general solutions of second-order differential equations. For plates with non-symmetric structure, the equations of skew-symmetric and symmetric deformation are interconnected, unlike plates with a symmetric structure. Numerical results are presented for a two-layer linearly elastic plate under cylindrical bending.

Abstract: An optimized method for assessing the fire protection efficiency of intumescent coatings has been proposed, which can be applied during the development and research of new formulations of fire retardant compositions. To achieve this goal, a critical analysis of existing methods for evaluating the fire protection efficiency of intumescent fire retardant coatings has been conducted, both those approved by regulatory documents and those used by researchers for the fire protection agents effectiveness rapid assessments. Based on the analysis of the studied methods advantages and disadvantages, an optimized method for evaluating the intumescent fire-resistant coatings efficiency has been proposed to reduce the time for preparing and processing experimental results. The proposed optimized method involves the use of an electrical furnace with an insulated test chamber for heat accumulation as a source of thermal radiation, which allows obtaining temperatures on the reverse side of the metal plate exceeding 950 °C. As a criterion for fire protection efficiency, it is proposed to use the comparison of the time to reach the critical temperature (500 °C) on the outer side of metal plates protected by fire retardant coatings. The efficiency of fire protection of the metal plate has been investigated using the proposed method for three samples of intumescent fire protection agents: a coating based on epoxy oligomer, ammonium polyphosphate, aluminum hydroxide, and intercalated graphite, a coating on a styrene-acrylic basis of industrial production, and a well-known coating based on epoxy oligomer filled with monoammonium phosphate and intercalated graphite. The results of the experiment allowed a comparative assessment of the studied coatings fire protection efficiency. The use of the optimized method significantly simplifies the experiment and reduces the time spent on sample preparation and processing of its results.

Abstract: A new version of the mathematical theory of non-thin multilayer nonlinearly elastic Kauderer plates of symmetric structures has been constructed. The components of the stress-strain state (SSS) and boundary conditions on the side surface of the plate are considered functions of three spatial coordinates. The variant is based on the development of components of the SSS of the plate along the transverse coordinate with the help of combinations of Legendre polynomials within each layer. The three-dimensional physically nonlinear boundary value problem for a multilayer non-thin plate is reduced to a two-dimensional one using the three-dimensional equations of the theory of elasticity and Reissner's variational principle. The main dependencies are obtained. Derived systems of high-order differential equations of equilibrium with partial derivatives and boundary conditions containing nonlinear terms from the SSS. The conjugation conditions at the boundary of adjacent layers (rigid connection) are exactly fulfilled for displacements, transverse tangential and normal stresses. The boundary conditions for stresses on the horizontal faces of the plate are also exactly fulfilled. The system of high-order differential equations of equilibrium is transformed into two systems that independently describe skew-symmetric and symmetric deformation relative to the median plane of the plate. In turn, each of these systems is transformed into differential equations that describe vortex boundary effects and equations that describe an internal SSS with a potential boundary layer-type boundary effect. The solution of systems of high-order equations by the developed method is reduced to the solution of second-order differential equations (Poisson and Helmholtz equations). General solutions of the system of differential equilibrium equations are obtained. The validity and accuracy of the variant of the mathematical theory is confirmed by comparisons with exact solutions of bending problems for linearly elastic plates with different mechanical and geometrical parameters. The newly constructed variant of the theory and the developed method provide a real opportunity to solve boundary problems in a spatial formulation with high accuracy for multilayer platens under various loads and boundary conditions on the lateral surface.

Abstract: Methods for determining the actual limit of fire resistance of reinforced concrete building structures in case of fire are analyzed. On the basis of the offered methods the technique which gives the chance to receive data of temperature distributions on a surface of a fragment of a wall and in its section is created. The method of conducting a fire test to calculate the limit of fire resistance of a small fragment of the load-bearing wall and verify the reproducibility of experimental data is described. The distribution of temperatures over the entire area of the fire furnace, the studied fragment was checked and the obtained results were analyzed. According to the results of this work, the following was established: the aim of the work was to obtain the results of temperature distributions on the surface, in the points of integration in the cross sections of fragments of reinforced concrete walls for further calculation of their fire resistance limit and check reproducibility of experimental data. It is established that the temperature obtained as a result of the fire test corresponds to the standard temperature of the fire and this method of fire test to determine the temperature distributions of a small fragment of the load-bearing wall in fire conditions is acceptable for use. The error between the experimentally determined and theoretically calculated limit of fire resistance is not more than 3%.

Abstract: This research has been made a simple method for the detection of potassium iodate (KIO₃) in a kitchen salt using cassava starch (Manihot esculenta). The process of making this test kits using acid solvent as the reagent, KIO₃ solution, and indicator of cassava starch. The used cassava starch is in two conditions are dry starch for H₂SO₄ and wet starch for H₃PO₄. Based on the two solvents are then made a standard color series based on KIO₃ levels of 10, 20, 30, 40, and 50 ppm. Validation of this method has analyzed using Spectrophotometer UV-Vis. From the results of this analysis obtained calibration curve of each standard with both solvent. Coefficients determination for linearity using H₃PO₄ and H₂SO₄ solution is 0.9874 and 0.9656. From that results from the H₃PO₄ solution applied to the detection of potassium iodate (KIO₃) in a kitchen salt using cassava starch (Manihot esculenta) with a concentration in the range 30-40 ppm.

Abstract: The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a beam. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars”) that is very similar to this paper except that the geometry considered in that paper is a bar.

Abstract: The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a bar. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams”) that is very similar to this paper except that the geometry considered in that paper is a beam.

Abstract: The paper briefly describes the methods for testing soils by triaxial compression. Among the many mechanical characteristics of the soil, deformation and strength properties remain as the main and widely used ones, the determination of which is an important experimental task. In recent years, new test schemes, more advanced designs of instruments and equipment for the study of various soils have been proposed. Like any material, the soil has limited strength, and under certain external influences the soil massifs collapse, as a result of which their individual parts get unlimitedly large displacements. Triaxial soil compression is becoming more widespread in the production of engineering and geological studies to justify the construction projects of various engineering structures. Based on the results of this work, recommendations for the practical application of the obtained soil characteristics for the geotechnical geoinformational database of the city of Nur-Sultan are made.

Abstract: In this paper the mechanic of forming the parts is investigated by conducting the experiments, performed using the device for the implementation of the novel method based on flanging process.

Abstract: The main characteristics of metal long products quality include mechanical properties, depending on the microstructure state. The key indicator for evaluation the micro-structure of high carbon steel can be considered the 1st grain grade lamellar pearlite B_fp. For the currently used pearlite dispersion method, according to GOST 8233-56, it is characterized by the subjectivity of the view fields choice for the microstructure evaluation, that reduces the quality of the obtained results. The study purpose was to improve the method of high-carbon steel wire rod microstructure estimation, to reduce the error magnitude in determining the 1st grain grade lamellar pearlite. The experiments were carried out on samples of high-carbon steel wire rod with a carbon content of 0,58 – 0,77 %. The pearlite dispersion was evaluated in 27 view fields, located on mutually perpendicular diagonals of the sample cross section. The study results showed the possibility of reducing the error in determining the estimated value of the high-carbon steel wire rod microstructure pearlite dispersion. Microstructure evaluation in the five view fields should be carried out, taking into account the weight coefficients, determined by the ratio of the zones length, occupied by pearlite with a certain percentage of the 1st grade grain pearlite to the wire rod radius. The proposed method of the microstructure evaluation increases assessment accuracy, without complication of its implementation process.