Examples Of Numerical Analysis Research Articles

A two‐way coupling 2D‐3D hybrid finite element numerical model using overlapping method for tsunami simulation

AbstractThis paper describes a 2D‐3D hybrid model for tsunami simulations that uses an overlapping method based on an arbitrary grid. A 2D model is used to simulate wave propagation from the source area to the offshore area, and a 3D model is then used to simulate the free surface flow around structures in coastal areas. An overlapping method that satisfies the conservation and compatibility conditions is developed to couple the two models. The shallow water equations are applied for the 2D model, and the Navier‐Stokes equations and continuity equations are applied for the flow field of the 3D model. The Allen‐Cahn equation is applied for the interface‐capturing method of the 3D model. The stabilized finite element method is applied for the spatial discretization and the Crank‐Nicolson method is used for the temporal discretization of the governing equations. The model is verified and validated through several numerical analysis examples.

Aplicación de las teorías de Klein-Gordon y de Bogoliubov-deGennes a Niquelatos

In the present work we show the generalities of the classical field theory (CFT), we study its extension to the quantum field theory (QFT), where as an example of numerical analysis and combination with the field theory technique, we solve a system Klein-Gordon type (KGS) in two space-time dimensions (1+1) studying its stability through the spectral parameter λ(k), principle of convergence due to the parameters of the numerical network and the solution for the field ф (x;t), obtaining novel results. Also, we briefly study the technique of creation and destruction ladder operators from the perspective of the quantum harmonic oscillator, to define some properties and extensions to the problem in canonical quantization. Finally, we apply the topics studied to a problem of unconventional superconductivity in Nickelates compounds by solving the system of Bogoliubov-deGennes (BdG) Equations in the mean expansion of the field, obtaining the superconducting energy band.

متسلسلات هار النسبية لتقريب معادلات الحالة المتجانسة وغير المتجانسة

In this paper, we give a new approximate solution method to homogeneous and non-homogeneous state equations using rationalized Haar functions. Integration operational matrix of rationalized Haar functions are used to convert the computation of homogeneous and non homogeneous state equations to a simple system of algebraic equations. By using the method (based on Matlab programming) on numerical analysis examples, we show that our method has high degree of accuracy.

Mode tracking method based on information entropy prejudging mode swapping

Mode tracking based on correlation is a common method to achieve reasonable mode ordering in characteristic mode analysis (CMA). However, it is time-consuming to traverse the correlation calculation with all frequency points. For this reason, it is proposed to use information entropy in determining the frequency points of mode swapping in advance, which effectively improves the computational efficiency of CMA. Meanwhile, it is pointed out that for higher-order modes or electrically large structures, pseudo-degenerate modes are prone to appear, which results in mode swapping. In a large frequency range, the reactance property of a mode can be reversed, causing a change in the physical meaning of the mode. Therefore, CMA is best performed in the frequency range adapted to the structure size. Numerical analysis examples show the feasibility of this mode tracking method and confirm the rationality of mode performance analysis.

Axially Symmetric Vibration of a Complete Conic Shell

We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with vertex. The procedure of construction of systems of basis functions for the approximation of displacements of the shell is based on the account of the formal structure of the fundamental system of integrals of the original equations established as a result of the asymptotic integration of a singularly perturbed system of equations with regular singular point. We present examples of numerical analyses of specific conic shells illustrating the efficiency of the proposed algorithm for the solution of the problem.

Analysis of the engineering mathematical model of the physical properties of a three-layer hydroacoustic screen with anisotropic components

A numerical-analytical technique for analyzing the physical effects of the formation of fields of hydroacoustic waves in the area in front of a flat three-layer hydroacoustic screen and in the space behind the screen at normal incidence of a stationary hydroacoustic wave on it is presented. The engineering model of the screen uses the assumption that its components are made of anisotropic functional-gradient materials with exponential inhomogeneity in thickness, and thin, absolutely flexible, inextensible coatings can be applied to the outer and contact surfaces of the layers. The technique is based on the analytical integration of the equations of wave deformation of the screen components and obtaining complex amplitude characteristics for the reflected and generated hydroacoustic waves behind the screen when solving a system of algebraic equations with a functional matrix, which follows from the boundary conditions for the investigated problem. Parametric descriptions for the characteristics of the investigated physical fields are obtained and examples of numerical analysis of the considered engineering model are presented.

A stochastic process discretization method combing active learning Kriging model for efficient time-variant reliability analysis

Time-variant reliability analysis (TRA) has attracted tremendous interest for evaluating product reliability in full life cycle. Discretization of stochastic process is considered one of the simplest ways to transform a time-variant problem into a time-invariant problem that becomes easier to handle. Its adoption in time-variant problem, nevertheless, requires overcoming two main issues on (1) the low efficiency of small discrete time interval, and (2) the low accuracy of large discrete time interval. To tackle these two challenges, we propose a Kriging-assisted time-variant reliability analysis method based upon stochastic process discretization (namely, K-TRPD for short). First, a complex time-variant reliability problem is converted into conventional time-invariant problem through discretization of stochastic process. Second, the most probable point (MPP) trajectory is approximated through a Kriging model over the entire time period concerned, whose input is identified from the discrete time points by an active learning approach; and the output is obtained by the first order reliability method (FORM) at the identified time points. Finally, the constructed Kriging model is utilized for time-invariant reliability analysis at each discrete time point, and the time-variant reliability is obtained by using the time-invariant reliability analysis results for analyzing the multivariate normal distribution function. In this study, three numerical analysis examples and one engineering design example are presented to demonstrate the effectiveness of the proposed method.

Nonstationary Nonlinear Problems of Heat Conduction for a Half Space

We propose a method for the determination of temperature fields in a half space with regard for the thermal radiation, temperature dependence of the thermal characteristics, densities of the surface and volume heat sources in the case of nonuniform distribution of the initial temperature. By using the Kirchhoff transformation, Green function, and linear splines, the corresponding problems of heat conduction are reduced to the solution of a recurrent system of nonlinear algebraic equations. We also present examples of numerical analyses.

Experiments and Numerical Simulations of the Annealing Temperature Influence on the Residual Stresses Level in S700MC Steel Welded Elements.

The article presents the results of research on the influence of temperature and time changes of the annealing process on the values and distribution of stresses in the simulated heat-affected zone of S700MC steel welded joints. For this purpose, tests were carried out on a thermal cycle simulator, as well as heating the prepared samples in accordance with the recorded welding thermal cycles, and then annealing at temperatures from 200 to 550 °C. The stresses values in the tested samples before and after the annealing process were measured by using X-ray diffraction (XRD). The performed tests were verified with the results of numerical analyses using the finite element method (FEM) performed in the VisualWeld (SYSWELD) environment as, on the one hand, the verification of the obtained results, and, on the other hand, the source of data for the development of a methodology for conducting analyses of heat treatment processes of S700MC steel welded structures. Also presented are three examples of numerical analyses for Gas Metal Arc (GMAW), laser and hybrid welding and then the annealing process of the obtained joints at selected temperatures. The main purpose of the work was to broaden the knowledge on the influence of annealing parameters on the values and distribution of stresses in welded joints, but also to signal the possibility of using modern software in engineering practice.

Computational Analysis of Axial Compressor Stages Characteristics

Published data on flat grid purges allow to evaluate the efficiency of blade devices with different kinematic scheme of stages and design parameters. The corresponding computer program ODOS-GP04 and examples of numerical analysis of the efficiency of flat grids and spatial blade devices of axial stages with different combinations of design parameters was provided. Further development of the ODOS-GP04 program is described below, which makes it possible to perform an estimated calculation of the gas-dynamic characteristics of the stages designed using this program. Analysis of the calculated characteristics of a number of typical stages allows to draw a conclusion about the influence of the main design parameters. This article is primarily addressed to people who are developing their knowledge of the gas dynamics of axial compressors. Some results of calculations do not correspond to the published experimental data. The authors expect that this may attract the attention of specialists working in the field of gas dynamics of axial compressors.

A new design strategy for seismic safety in super earthquakes of continuous girder bridges

Abstract In recent years, devastating earthquakes have occurred all over the world, and the huge seismic damage of lifeline engineering structures would cause great personnel casualties and property loss. In order to guarantee the seismic safety of lifeline engineering structures, usually two seismic hazard levels, for instance Design Earthquake and Maximum Considered Earthquake are considered in most seismic design codes. However, several disastrous earthquakes have proved that seismic safety evaluation may underestimate seismic risks, which would result in serious damage of lifeline engineering structures. Therefore, another higher level of seismic hazard named Super Earthquake is proposed to be considered in this paper for very important lifeline engineering structures. To improve the seismic performance and meet seismic requirements of Super Earthquake, a new design strategy for seismic safety is proposed at first based on deep learning. In the proposed strategy, rigid blocks are combined with common seismic isolation bearings and expansion bearings and two new kinds of bearings are developed. Taking two continuous girder bridges as numerical analysis examples, the proposed strategy is compared with two other seismic design strategies adopted in current seismic codes and parametric analyses are conducted. It’s shown that the proposed strategy can combine the ductility capacities of piers and the functions of seismic isolation bearings and reduce all the concerned structural seismic responses in Super Earthquakes effectively.

Seismic wave input method for three-dimensional soil-structure dynamic interaction analysis based on the substructure of artificial boundaries

The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the finite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave field on the nodes of the substructure composed of elements that contain artificial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artificial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplified by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verified by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.

Different fidelity computational models in aeroelastic design of aircraft and WT models

Abstract Using of different fidelity computational models and relations between them in the multidisciplinary design system is considered. A structural design procedure and optimization methods for aeroelastic design of aircraft and wind tunnel models are discussed. An application of the topology-based optimization together with the two-level structural sizing method is considered. Main stages of the approach to synthesis of structural layouts of aircraft components are described. Some numerical examples of analysis and aero-structural optimization of aircraft wings are considered to demonstrate the proposed methods and algorithms. The accuracy, reliability and efficiency of using of the considered structural models at design studies are discussed.

Simulation of ferroelastic phase formation using phase-field model

In order to predict the formation of ferroelastic phases in crystal grains of La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF), which is a common material used for solid oxide fuel cells (SOFCs), we propose an analysis method based on a phase-field model. The phase-field model equipped with the elastic energy is introduced to realize the ferroelastic phase formation in a crystal grain. The finite element method (FEM) is employed to solve the phase transformation, and strain distributions are also calculated by FEM. On the basis of the developed analysis method, some numerical examples of analysis are performed to reproduce the deformation-induced nucleation and growth of ferroelastic phases of LSCF. Various microstructures are obtained from the simulations in accordance with the initial microstructure and their tendencies are discussed. These microstructures are reproduced by the proposed analysis method based on finite element method, which enables us to evaluate the deformation field in terms of changes of shape and stress.

EFFORT OF STEEL PIPE JACKING IN TERMS OF IMPERFECTION PIPES AND HETEROGENEITY OF GROUND

Purpose. The article presents problem of the influence of local inhomogeneities of ground on the internal forces in the steel pipe. Methodology. The authors presented the differences in the distributions of earth pressures for the pipes. One of the most common methods is the microtunneling technology. The examples of numerical analysis by finite element method (FEM) have been calculated. Findings. The results of numerical analysis are presented for selected ground conditions and the distribution of internal forces in the flexible section of the steel pipe is also shown. Originality and Practical value. The obtained results clearly show the influence of flexural rigidity of the pipe on the internal forces, the influence of flexural rigidity and the soil stiffness on the size of the bending moments in the steel of pipe jacking. They depend on the interaction of soil – steel pipe.

Numerical algorithm for solving of nonlinear problems of structural mechanics based on the continuation method in combination with the dynamic relaxation method

A numerical algorithm of strength and stability analysis of nonlinear deformable bar systems and thin-walled spatial structures is proposed. A numerical technique is based on the continuation method and the dynamic relaxation method. When using the method of dynamic relaxation the state of static equilibrium of structures is defined after the damped oscillations by integrating over leading parameter. The solution of the initial equation system describing the motion of the mechanical system is reduced to the solution of Cauchy problem for systems of ordinary differential equations. At an each step in the leading parameter the vector of nodal displacements and the time parameter are defined. Several examples of numerical analysis for bar, shell and plate are given.

Kinematic Analysis of 4-UPU Parallel Mechanism Based on Influence Coefficient

Mechanism kinematic influence coefficient deeply reflects the essence of the kinematics and dynamics mechanism, analysis of the problems of many institutions can use the influence coefficient of clear and clearly expressed. In this paper, with less degree of freedom parallel mechanism as the research object, through the virtual mechanism method to derive one or two order influence coefficient matrix, based on the analysis of the mechanism and influence of speed and acceleration coefficient matrix. Finally, the precision of the method for solving the kinematics is proved by examples of numerical analysis.

Minimum weight design of sinusoidal corrugated web beam using differential evolution algorithm

Due to their many advantages, corrugated steel plates are widely used in various applications including bridges. Starting with airplane design, these corrugated steel plates have been used in civil engineering applications such as buildings and bridges, and many studies on corrugated steel plates are being conducted. However, most of these studies focused on the strength of girders through analysis and experiment of corrugated steel plates and studies on the optimization of corrugated steel plates are still insufficient. The present study developed the weight optimum design using the differential evolution and investigated the effects of parameters. The optimization program was verified with differential evolution through the numerical analysis examples of simple beams and fixed beams. For this verification, the optimization program using the genetic algorithm that has been studied was compared with the weight optimum graph of the optimization program of differential evolution proposed in this study. As a result, the graphs of these two optimization programs increased similarly. The change rate was 3.57% or lower in the example of uniformly load for fixed beam, 1.60% or lower in the example of concentrated load for fixed beam, and 1.44% or lower in the example of uniformly load for simple beam. Furthermore, in the graph of changing design variables, the changing web thickness showed a similar trend as the increasing trend of the optimum sectional area.

Reinforced concrete tank walls and bridge abutments: Early-age behaviour, analytic approaches and numerical models

The problem of early age cracking is still underestimated in concrete structures in which limited possibility of deformation under thermal-moisture effects may generate dangerous stresses. Thermal-shrinkage cracking of externally-restrained concrete members is frequently observed in wall members supported on previously cast foundation, such as tank walls, bridge abutments or retaining walls.The article discusses early-age behaviour of reinforced concrete tank walls and bridge abutments. The character of thermal and shrinkage stresses along with typical cracking patterns are presented. Several examples of real structures in which early age cracking was observed are also shown in the article. Finally, available analytic and numerical models to predict thermal-shrinkage stress development and cracking risk in early age concrete in such structures are discussed. An example of numerical analysis is presented to show the advantage of the numerical approach of analysis.

A time‐marching collocation method based on quintic Hermite polynomials and adjustable acceleration and jerk constraints

SUMMARYThis paper introduces a time‐marching algorithm for linear systems based on quintic Hermite polynomial displacement interpolation. This fully implicit, single‐step collocation method enforces acceleration and jerk constraints at a point in time that is selected by the user. The collocation point, then, is the parameter that determines accuracy, stability, and high‐frequency damping behavior. Numerical experiments indicate that the method converges at a rate of four, even for problems involving harmonic external forcing and viscous damping. Significantly, the convergence rate also does not deteriorate when algorithmic damping is employed. Period error is extremely small, on the order of a few percent at moderate frequencies even with algorithmic damping. The undamped algorithm is shown to have the highest accuracy and to be symplectic, but it is also conditionally stable and nondissipative—the exact stability limits are calculated. A wide range of parameter settings provide an unconditionally stable algorithm, which preserves low modes while rapidly dissipating high modes. Three finite element analysis numerical examples demonstrate the capabilities of the algorithm on one‐dimensional linear dynamic problems. This article is a US Government work and is in the public domain in the USA.