Numerical Analysis Method Research Articles

INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS: NUMERICAL SIMULATION AND EXPERIMENT

The influence of injection distance on the porosity of Ni-based amorphous coatings (AMCs) prepared with a high-velocity air fuel (HVAF) process is discussed based on a numerical analysis and experimental methods. A computational fluid dynamics model was established to demonstrate the gas flow field and behavior of particles in flight at different spraying distances during HVAF spraying. When analyzing the changes in the particle velocity and temperature, the spraying distance is less than 30 µm. The velocity and temperature changes of small particles have a significant impact, and the optimal spray distance (350 mm) for obtaining a low porosity coating is predicted. The calculation was validated experimentally by producing a Ni-based AMC with a low porosity (1.87 %) that was manufactured using the predicted HVAF optimal spraying distance.

Fracture prediction and application in carbonate reservoirs based on the rescaled range analysis- finite difference numerical analysis methods

For carbonate reservoirs, the study of fractures is crucial. In this paper, the identification and prediction of fractures in carbonate reservoirs are carried out by applying R/S-FD numerical analysis method by using core, thin section and imaging logging data. The analysis concludes that the AC, CAL, DEN, and GR curves are very sensitive to the response of fracture development segments as calculated by the rescaled range analysis (R/S) analysis method, but some fractures are still misidentified. After finite difference (FD) calculation on the basis of R/S calculation, high-angle structural fractures can be accurately identified, and the R/S-FD fracture identification results of different curves can be verified with the results of core and imaging logging, and the fracture identification accuracy can reach 71.69%. The number of fracture development segments is positively correlated with the cumulative oil production, the number of producing layers and the cumulative thickness of producing layers, and the wells with more fracture development segments have higher cumulative oil production, more producing layers and larger cumulative thickness of producing layers. This method improves the accuracy of fracture identification in carbonate reservoirs, which is of great significance for oil and gas exploration.

Influence of Interior Column on the Behaviour of Quasi-Rectangular Tunnel

The growing population in major cities around the world requires significant development of transportation infrastructure, especially underground system. It requires the construction of more subway lines, and larger tunnel cross-sections. In underground construction, a cross-sectional shape which is a combination of circular and rectangular tunnels is an advanced trend. This shape incorporates the advantages of both forms. There are two terminologies used to classify these shapes, including sub-rectangular and quasi-rectangular tunnels. While the sub-rectangular tunnel lacks an interior column, the quasi-rectangular tunnel includes an interior column located at the center of tunnel. Recent studies focus on separately investigating the behavior of sub-rectangular and quasi-rectangular tunnels using various methods such as numerical methods, analytical methods, and experimental methods. The present study conducted a numerical comparison of these two types of tunnels. The results indicated that the presence of an interior column help to increase the stability of the lining structure. The internal forces within the quasi-rectangular tunnel with an interior column are smaller than those of the sub-rectangular tunnel and quasi-rectangular tunnel without an interior column.

Theoretical study of extreme ultraviolet pellicles with nanometer thicknesses

Extreme ultraviolet (EUV) pellicles are required for EUV defectivity management in high volume manufacturing (HVM). Theoretical analysis of EUV pellicles of nanometer thickness is helpful for these fabrications. In this paper, for maximum transverse deflection, an analytical–numerical method is contrasted against the finite element method (FEM) due to the ratio of thickness and width length of EUV pellicles. The difference was increased at a thickness of micron unit. Single- and multiple-variable methods of linear regression in deep learning were used to overcome the ANSYS limitation based on FEM, such as the meshing of more than 10 μm thickness, and shear loading, an error in FEM resulting from the impact on the stiffness matrix caused by variations in the length-to-thickness ratio increases in the beam element, respectively.

Nonlinear Deformation of Cylinders from Materials with Different Behavior in Tension and Compression

A new numerical-analytical method for solving physically nonlinear deformation problems of axisymmetrically loaded cylinders made of materials with different behavior in tension and compression has been developed. To linearize the problem, the uninterrupted parameter continuation method was used. For the variational formulation of the linearized problem, a functional in the Lagrange form, defined on the kinematically possible displacement rates, is constructed. To find the main unknowns of the problem of physically nonlinear cylinder deformation, the Cauchy problem for the system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta-Merson method with automatic step selection. The initial conditions were established by solving the problem of linear elastic deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta-Merson’s scheme are found from the solution of the variational problem for the functional in the Lagrange form. Variational problems are solved using the Ritz method. The test problem for the nonlinear elastic deformation of a thin cylindrical shell is solved. Coincidence of the spatial solution with the shell solution was obtained. Physically nonlinear deformation of a thick-walled cylinder was studied. It is shown that failure to take into account the different behavior of the material under tension and compression leads to significant errors in the calculations of stress-strain state parameters.

Calculation of Lateral Stability of Tank Trucks and its Relationship with Filling Rate

To investigate a theoretical algorithm model of the lateral stability of tank trucks and its relationship with the liquid filling rate, the shifting of the liquid centroid during non-full loading is considered. The deformation of the suspension and tires under load is assumed to exhibit a linear relationship. Using the principle of moment balance, a calculation model for the maximum stable roll angle and rollover critical acceleration of tank trucks based on the “liquid–tank–vehicle” tri-coupling is established, and the relationship between the maximum stable roll angle and rollover critical acceleration of tank trucks is analyzed and compared. Based on the result and a specific tank truck model, the effects of the liquid filling rate on the maximum stable roll angle, rollover critical acceleration, and tank tilt angle of tank trucks are investigated using numerical analysis methods. A comparison with the lateral stability of ordinary trucks loaded with solid goods is performed to further examine the effect of the liquid filling rate on the lateral stability of tank trucks. The results show that the maximum stable roll angle and rollover critical acceleration are consistent indicators for evaluating the lateral stability of tank trucks; the lateral stability of tank trucks decreases owing to the shift in the liquid centroid inside the tank; as the liquid filling rate increases, the lateral stability of the tank trucks deteriorates slightly.

Research on the dynamic behavior of flexible drilling tools in ultrashort-radius radial horizontal wells

A flexible drilling tool is a special drilling tool for ultrashort-radius radial horizontal wells. This tool is composed of many parts and has the characteristics of a multibody system. In this paper, a numerical method for the dynamic analysis of flexible drilling tools is proposed. The flexible drill tool is discretized into spatial beam elements, while the multilayer contact of the flexible drilling tool is represented by the multilayer dynamic gap element, and the dynamic model of the multibody system for the flexible drilling tool’s multilayer contact is established, considering the interaction force between the drill bit and the rock. The nonlinear dynamic equation is solved using the Newmark method and Newton–Raphson method. An analysis of the dynamic behavior of a flexible drilling tool is conducted. The results indicate that the flexible drilling tool experiences vortex formation due to the interaction between the flexible drilling pipe and the guide pipe, leading to increased friction and wear. This situation hinders safe drilling operations with flexible drilling tools. The collision force of the flexible drilling tool near the bottom of the hole is more severe than that of the other tool types, which may lead to failure of the connection.

Applying Laplace Transformation on Epidemiological Models as Caputo Derivatives

This paper delves into the application of fractional calculus, with a focus on Caputo derivatives, in epidemiological models using ordinary differential equations. It highlights the critical role Caputo derivatives play in modeling intricate systems with memory effects and assesses various epidemiological models, including SIR variants, demonstrating how Caputo derivatives capture fractional-order dynamics and memory phenomena found in real epidemics. The study showcases the utility of Laplace transformations for analyzing systems described by ordinary differential equations with Caputo derivatives. This approach facilitates both analytical and numerical methods for system analysis and parameter estimation. Additionally, the paper introduces a tabular representation for epidemiological models, enabling a visual and analytical exploration of variable relationships and dynamics. This matrix-based framework permits the application of linear algebra techniques to assess stability and equilibrium points, yielding valuable insights into long-term behavior and control strategies. In summary, this research underscores the significance of Caputo derivatives, Laplace transformations, and matrix representation in epidemiological modeling. We assume that by using this type of methodology we can get analytic solutions by hand when considering a function as constant in certain cases and it will not be necessary to search for numerical methods.

Моделирование транспортных потоков методом системной динамики

The article discusses the application of the system dynamics methodology for simulation of controlled traffic flows. In the classical formulation, system dynamics models represent a system of finite-difference equations, which is an approximation of the Cauchy problem by the Euler method. The implementation of finite-difference equations in system dynamics by J. Forrester is carried out by the DYNAMO specialized graphical tools. It is proposed that the Cauchy problem be implemented using structural diagrams in which a one-to-one correspondence of specific structural links to system dynamics paradigms is established. As a result of the research, it was shown that an aperiodic link with a typical nonlinear “saturation” function identifies with a sufficient accuracy the basic paradigms of system dynamics, such as rates, levels and delays. It is shown that the resulting system of ordinary differential equations, when imposing control conditions, has discontinuities of the first kind in derivatives and requires integration methods with a variable step and variable order for effective solution. The proposed approach to modeling traffic flows, in contrast to the classical one, allows the use of modern modeling tools with a graphical language of structural diagrams and a library of methods for numerical analysis of complex dynamic processes. The implementation of a specific test scenario for modeling traffic flows was carried out in the SimInTech software package. The efficiency metrics of integration methods are obtained. A comparative analysis of the effectiveness of integration methods in solving this problem was carried out. It is shown that the most effective in solving problems of the considered class are the explicit adaptive integration methods ARK21, AM61 with a variable step from the SimInTech library, which are much more effective than the explicit Euler method in classical system dynamics.

INVESTIGATION OF STABILITY OF NONLINEAR NORMAL MODES OF DISSIPATIVE SYSTEM OSCILLATIONS UNDER INFLUENCE OF MAGNETIC FIELD

In the paper the dynamics of the vibrating system consisting of two pendulums connected by elastic coupling and located in a magnetic field is studied. A case is considered when masses of the pendulums differ significantly. Under the influence of various external factors, such as magnetic forces and loads, which are present in engineering systems, the analysis of vibration regimes in non-linear systems becomes more complex. Here the nonlinear normal connected vibration mode in a system under consideration is analyzed. We have investigated the influence of changes in system parameters on the vibra- tion mode for both small and large initial angles of the pendulum deflection. Both the analytical method, namely, the method of many scales, and nu- merical simulations based on the fourth order Runge – Kutta method are used to analyze the vibration regimes. The initial conditions used to calculate this mode were determined analytically. The simulation includes construction of phase diagrams, trajectories in configuration space, and spectra, which allows us to evaluate the system dynamics, including both regular and complex regimes of vibrations. To study the stability of the vibration mode, a numerical-analytical method associated with the Lyapunov stability criterion is used. The stability of the mode is determined by assessing orthogonal deviations with respect to the corresponding modal trajectories in the configuration space. Regions of instability on planes and in the space of the system parameters are obtained.

SIMULATION OF DYNAMIC PROCESSES IN A p - i - n DIODE BY THE METHODS OF PERTURBATION THEORY

In the paper a mathematical model of the dynamic process of the electron-hole plasma formation in the active region ( i - region) of a semiconductor p - i - n - diode in the direct bias mode with a harmonic signal fed on the diode is developed. The basis of the model is a nonlinear nonstationary sin- gularly perturbed boundary value problem for a system of continuity equations of electron-hole currents and Poisson's equation. The algorithm for searching the charge carrier concentration distributions and the potential distribution is based on the asymptotic method of boundary functions and the Fourier method. In the course of the research, a technique for decomposing a nonlinear problem based on the development of perturbation theory me- thods was proposed. The initial nonlinear problem is reduced to a recurrent sequence of linear stationary boundary value problems, solved by classical and partially original analytical-numerical methods. The identification of the boundary functions in the solution of the problem provides, in particular, in contrast to the classical approximation of ambipolar diffusion, an adequate description of the electric field strength behavior in the active region of p - i - n - diodes. The obtained research results shed light on the peculiarities of the formation of the impedance characteristics of p - i - n - structures. The results of the work reveal more deeply the nature of the physical processes in the studied technical system and are aimed at improving the methodology for modeling and designing control semiconductor devices.

Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Effects of varying heat transfer rates for borehole heat exchangers in layered subsurface with groundwater flow

The existence of groundwater flow adds a convective heat component to shallow geothermal heat pump systems, significantly improving heat transfer efficiency. Numerous analytical and numerical methods have been proposed to assess the impact of groundwater flow on ground heat exchangers. However, numerical simulations often require significant resources and time, while conventional analytical solutions overlook the time and depth-varying heat transfer rates, leading to inaccurate temperature predictions. This study proposes a computationally efficient semi-analytical solution by extending the line source solution and coupling it with a thermal resistance model. This approach addresses variations in heat transfer rate over time and depth, overcoming the limitations of conventional analytical solutions. Compared with a three-dimensional numerical model constructed in COMSOL Multiphysics, the average absolute percentage error (MAPE) of borehole wall temperatures for a U-shaped borehole heat exchanger (BHE) is approximately 1 %, across a wide range of water flow velocities and thermal conductivity ratios between two contacting geological layers. A significant advantage of the proposed solution is its computational efficiency. The proposed solution can complete long-term simulations with over 9,000 time steps in about 10 min, as opposed to numerical models that typically require several hours. The excellent computational efficiency and substantial accuracy make the proposed solution a simple and effective tool for the design and optimization of BHEs in engineering applications.

Seepage Behavior of Underwater Tunnels in Stratum with Inclined Surface: Insights from Numerical Analysis

This paper is to investigate the seepage behavior of underwater tunnel with inclined boundary at the contact between water body and underwater stratum. Extensive finite element analyses using COMSOL are performed considering various magnitudes of inclination degree of underwater soil surface. The rationality of the numerical analysis method is demonstrated via comparing with analytical solutions. It is found that the inclined boundary has a significant impact on the seepage field of underwater tunnel. The hydraulic head distribution, streamline evolution, velocity and other aspects are comprehensively analyzed, and relevant conclusions are drawn. The streamlines in waters are not vertically downward, but presents a certain acute angle distribution with the stratum direction. And the interface angle toward the depth is larger. Streamlines will also become denser. The streamline flows into the tunnel from all directions. And the attenuation speed of water head in the lower part of tunnel is less than that in the upper part. Thereby serving the optimal design and construction of practical projects.

A Numerical Method for the Stability Analysis of Linear Age-Structured Models with Nonlocal Diffusion

A Numerical Method for the Stability Analysis of Linear Age-Structured Models with Nonlocal Diffusion

Determining the stresses near crack tips in composite plates based on the Williams series and singular integral equations

The paper presents a numerical-analytical method developed to determine the stresses formed in composite plates near the tips of curved cracks by means of the Williams series. The coefficients of the terms of the Williams series and T-stresses have been calculated based on the derivatives of the displacement discontinuity of the crack edges. It has been shown that the calculations can be simplified implementing the Green's solutions by the Lekhnitskii method. The numerical algorithms based on Lobatto quadrature formulas have been used to solve the singular equations and determine both the coefficients the Williams power series and T-stresses. The proposed approach has been used to analyze rectilinear and curvilinear cracks in composite plates. In addition, the Green's solutions have been implemented to investigate the cracks located in a half-plane, near an elliptical hole, in rectangular plates, and in strip. One- and two-period problems have been considered for plates with cracks in the present calculations. The high accuracy of the performed calculations of the stresses near the crack tips in composite plates using elementary formulas contained by the Williams series has been confirmed on the test examples.

A Transit Tilt and Offset Errors Calibration Method for Improving Laser Tracker Measurement Accuracy Based on the Telecentric Measurement System

Laser trackers are instruments used to measure the three-dimensional coordinates of objects with high precision. It is necessary to study calibration methods to identify geometric errors of laser trackers so as to compensate for errors and improve measurement accuracy. Among the offsets, tilts, and eccentricity errors in the system, the transit tilt and offset errors play important roles and have an essential effect on the measurement accuracy, which need to be calibrated and compensated for. Current methods for detecting geometric errors between the transit and standing axes are complex and time-consuming. In this paper, a fast and novel calibration method is proposed, which can be easily operated with high precision. Two test rods are coaxially mounted on the ends of the transit axis to extend the hidden transit axis. Then, a telecentric measurement system is used to record the projection images of the test rods and identify the position of the transit axis. The transit offset and tilt errors were thus obtained by comparing the central axis positions of the two test rods before and after the standing axis rotated 180 degrees. Moreover, a numerical analysis method was proposed based on the least square circle fitting method to calibrate the installation eccentricity errors of the test rods. Experimental results verify that the measurement accuracy of the laser tracker can be improved after error compensation using the calibrated transit offset and tilt errors. The measurement error of the laser tracker can be reduced from 161 µm to about 73 µm after compensation at a distance of 5 m, while the error can be decreased from 143 µm to about 108 µm at a distance of 10 m.

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

SummaryThis study aims to analyze the buckling and post‐buckling behaviors of multilayer nanocomposite beams reinforced with graphene oxide powders (GOPs) at low concentrations. The GOPs are randomly oriented and evenly distributed throughout the composite layers, with their weight fraction varying in the thickness direction. The Halpin‐Tsai model is employed to estimate each layer's effective material properties. The nonlinear governing equations for the FG‐GOPRC beam are derived based on the first‐order shear deformation beam theory, and a nonlinear algebraic system is formulated using the principle of potential energy. In this research, a comprehensive parametric analysis is conducted to examine the influence of various factors on the buckling and post‐buckling behaviors of the composite beams. These factors include the distribution pattern and weight fraction of graphene platelets (GPLs) nanofillers, as well as the geometry, size, slenderness ratio, and boundary conditions of the beams. Through the analysis, the study highlights the significant strengthening effect of these factors on the buckling and post‐buckling performance of the composite beams. The findings from this investigation contribute to a deeper understanding of the behavior of multilayer nanocomposite beams reinforced with GOPs. This knowledge can be valuable in designing and optimizing of composite structures for enhanced buckling resistance and post‐buckling performance.

Numerical study of distributed-order Bessel fractional derivative with application to Euler–Poisson–Darboux equation

The present paper introduces the distributed-order (DO) Bessel fractional derivative for study of the Euler–Poisson–Darboux (EPD) equation including the spatial Riesz fractional derivative (RFD). For this purpose, we discretize the integral term of the DO fractional derivative and approximate the RFD derivative. We thereafter apply an implicit difference method (IDM) for numerical analysis and solvability of the reduced system from the IDM is discussed. The stability and convergent theorems are stated and the numerical tests are given to show efficiency of the proposed technique and to verify good agreement with the theoretical concepts.

Application of the finite analytic numerical method to a flow-dependent variational data assimilation

Application of the finite analytic numerical method to a flow-dependent variational data assimilation