Papers by Keyword: Analytical Method

Abstract: The problem of bending of a beam of variable stiffness resting on a continuous homogeneous elastic Winkler-type foundation is considered. The exact solution of the corresponding bending differential equation is found for the case when the beam stiffness is an arbitrary continuous function. Based on the exact solution, an analytical method for beam calculation is developed. This method produces accurate results and is computationally efficient. It is implemented in a computer program and demonstrated by the calculation of a truncated wedge-shaped beam. The calculation results are provided in numerical and graphical formats.

Abstract: The problem of axisymmetric bending of a ring plate, which is under the influence of a constant uniformly distributed transverse load and rests on a non-uniform elastic Winkler foundation, is considered. The inhomogeneity of the elastic foundation is given by a power function with an arbitrary non-negative power exponent . In analytical form, the fundamental functions and a partial solution of the corresponding differential equation are found. These functions are dimensionless and are represented by absolutely and uniformly convergent power series. In turn, formulas for the parameters of the stress-strain state of the plate are expressed through the specified functions. In fact, the calculation of the plate is reduced to the procedure of numerical implementation of explicit analytical formulas. The practical application of the obtained solutions is demonstrated using the example of a concrete slab with both fixed contours, resting on a cubic-variable elastic foundation

Abstract: The enhancement of interdiffusion coefficients in bulk Ti-Mo alloy system by the SPS/FAST process was investigated at 1000°C for 8hrs and at 1200°C for 4hrs. During annealing, the current density of the SPS was maintained at an RMS of 188 A/cm² for the sample annealed at 1000°C and 177 A/cm² for the sample annealed at 1200°C and the average heating rate was 200 K/min. The elemental concentration of Ti and Mo across the interdiffusion region was measured using electron probe microanalyzer (EPMA) and the resulting concentration vs distance profiles applied in evaluating the interdiffusion coefficients using the Den-Broeder and the analytical methods. The interdiffusion coefficients calculated using the two methods were then compared in order to ensure accuracy and reliability. Possible enhancement of the diffusion process in SPS was established by comparing interdiffusion coefficients obtained from SPS annealing to those obtained from the literature for the same alloy and annealing temperature but for which no electric current was flowing through the sample. The results showed that interdiffusion coefficients evaluated using the Den-Broeder method were closely similar to those evaluated using the analytical method. The results also showed that the interdiffusion coefficients measured in the presence of an electric current were significantly higher than those obtained from traditional annealing methods. This enhancement can be attributed to increased vacancy concentration and defect mobility facilitated by the electric current while flowing through the Ti-Mo sample.

Abstract: The thermal model of a permanent magnet motor (PMM) is investigated in this study using the lumped parameter thermal approach to calculate temperature variation at steady-state and transient conditions. The temperature variation of the motor components over time under various loads is investigated. The proposed thermal model was constructed with the MATLAB code. The thermal characteristics of the motor are examined using the simulation results. The optimization and sensitivity analysis are done using the response surface method (RSM) by design expert software. It can be seen that increasing the load and time increases the temperature of all parts in the machine. Also, point multiplication with 0.998 desirability is presented, which has the best efficiency with the lowest temperature.

Abstract: An analytical method for calculating the bending of ring plates resting on a non-homogeneous elastic Winkler foundation has been developed for the case when the bedding factor and load are given by any continuous functions. The method is based on the exact solution of the corresponding differential equation. Calculation formulas for the parameters of the stress-strain state of the plate are given in closed form. An example illustrates the practical application of the developed method. The case is considered when the bedding factor changes according to the parabolic law, and the load is given by the sine law. Calculation results are presented in numerical and graphic formats. For comparison, the calculation results obtained by the finite element method are also provided.

Abstract: Calculation formulas are given in the analytical form, which allow to study the bending of beams on a non-homogeneous solid Winkler elastic foundation. An example demonstrates the practical application of the developed method. The case is considered when the bed coefficient changes according to a parabolic law, and the variable distributed load acting on the beam is given by a linear law. The results of the calculation by the author's method are presented in numerical and graphical formats. For comparison, the calculation results obtained by the finite element method are also provided.

Abstract: The paper proposes an analytical method for calculating a long cylindrical shell supported by two identical side elements and loaded with vertical load. The case when the shell is hinged on curvilinear edges is considered, and recommendations for taking into account other boundary conditions are given. No restrictions are imposed on the shape and dimensions of the cross-section of the side element. The proposed algorithm assumes the possibility of implementing two approaches - calculation according to the general semimoment theory and calculation with simplifying hypotheses for flat shells of medium length. In the presented work, the first approach is considered. Mathematically, the problem is reduced to a system of four linear equations. By solving this system, it is possible to determine the forces and displacements due to the action of additional boundary forces, and by adding them with the corresponding components of the momentless stress state, one can obtain the total forces and displacements in the cylindrical shell.

Abstract: This study aims to review variation pattern of moisture content ratio of grains in deep-bed drying process, guide the drying technology design, realize real-time tracking and regulation in drying process, improve the quality of drying process and reduce energy consumption. Based on the moisture diffusion model in thin layer drying process, the principle of mass conservation of deep drying process, state function and irreversible thermodynamics analytic method, we have established and solved basic equations of deep-bed drying of grains, obtained the moisture content ratio of grains and analysis formula of drying velocity distribution in processes of concurrent flow drying, counter flow drying, cross-flow drying and standing drying and resolved the sustained decreasing drying process of grains in the concurrent flow drying and extreme point of drying rate in the counter-flow drying. Under the same conditions of temperature, humidity and air output, the drying velocity in counter-flow drying significantly higher than that in the concurrent flow drying. It means the energy utilization effects in counter-flow drying is better than that in the concurrent flow drying. Drying characteristics of grains in cross-flow drying and standing flow drying are the same, while drying rates in inlet-air side and outlet-air side vary widely. It means that when the layer thickness is 0.5m and the moisture content is over 20%, the drying rate in outlet-air side is nearly zero and the drying uniformity is bad. Tests on 5HP-3.5 recirculation drier shows that maximum deviation between analytic value and measured value in deep drying process is 0.69% and the range scope is -0.27%-0.69%. From the drying characteristics of grains, deviations mainly come from instrument detection deviations. The analytic method has important significance for realizing real-time tracking and regulation in drying process, guiding drying technology design, reducing energy consumption, increasing drying rate and drying machine capacity.

Abstract: The present article describes the analysis of electromagnetic field in an induction MHD-stirrer for liquid metals with the account of transverse di-mensions of the inductor and bath with melt. The parameters of the equivalent circuit of a MHD-stirrer and its electromagnetic characteristics have been defined.

Abstract: The numerical analysis model and analytic formula, concerning flexural-tensile composite modulus of steel deck paving materials, were established with five-point loading composite beams, in order to explore the modulus value of steel deck paving materials. Regarding the three typical asphalt pavement material such as SMA10, GA10 and EA10, the composite modulus of paving material was calculated by analyzing stepwise loading data, and a universal flexural-tensile composite modulus range is proposed: SMA10 is 500 ~ 550MPa, GA10 is 500 ~ 600MPa, EA10 is 650 ~ 700MPa. The results show good agreement between the modulus of the numerical analysis method and analytical formula method. The proposed analytical formulas can calculate the flexural-tensile composite modulus more easily according to the actual load conditions, and the modulus value played a significant role in guiding the design and mechanical analysis of steel deck pavement system.