• Title, Summary, Keyword: numerical methods

### A Novel Numerical Method for Considering Friction During Pre-stressing Construction of Cable-Supported Structures

• Zhao, Zhongwei;Liang, Bing;Yan, Renzhang
• International journal of steel structures
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• v.18 no.5
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• pp.1699-1709
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• 2018
• Suspen-dome structures are extensively used due to their superiority over traditional structures. The friction between cable and joints may severely influence the distribution of cable force, especially during the pre-stressing construction period. An accurate and efficient numerical method has not yet been developed that can be used for estimating the influence of friction on cable force distribution. Thus, this study proposes an efficient friction element to simulate friction between cable and joint. A flowchart for estimating the value of friction force is introduced. These novel numerical methods were adopted to estimate the influence of friction on cable force distribution. The accuracy and efficiency of these numerical methods were validated through numerical tests.

### SOME RECENT TOPICS IN COMPUTATIONAL MATHEMATICS - FINITE ELEMENT METHODS

• Park, Eun-Jae
• Korean Journal of Mathematics
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• v.13 no.2
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• pp.127-137
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• 2005
• The objective of numerical analysis is to devise and analyze efficient algorithms or numerical methods for equations arising in mathematical modeling for science and engineering. In this article, we present some recent topics in computational mathematics, specially in the finite element method and overview the development of the mixed finite element method in the context of second order elliptic and parabolic problems. Multiscale methods such as MsFEM, HMM, and VMsM are included.

### Numerical methods for the dynamic analysis of masonry structures

• Structural Engineering and Mechanics
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• v.22 no.1
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• pp.107-130
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• 2006
• The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.

### Comparison of Numerical Orbit Integration between Runge-Kutta and Adams-Bashforth-Moulton using GLObal NAvigation Satellite System Broadcast Ephemeris

• Son, Eunseong;Lim, Deok Won;Ahn, Jongsun;Shin, Miri;Chun, Sebum
• Journal of Positioning, Navigation, and Timing
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• v.8 no.4
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• pp.201-208
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• 2019
• Numerical integration is necessary for satellite orbit determination and its prediction. The numerical integration algorithm can be divided into single-step and multi-step method. There are lots of single-step and multi-step methods. However, the Runge-Kutta method in single-step and the Adams method in multi-step are generally used in global navigation satellite system (GNSS) satellite orbit. In this study, 4th and 8th order Runge-Kutta methods and various order of Adams-Bashforth-Moulton methods were used for GLObal NAvigation Satellite System (GLONASS) orbit integration using its broadcast ephemeris and these methods were compared with international GNSS service (IGS) final products for 7days. As a result, the RMSE of Runge-Kutta methods were 3.13m and 4th and 8th order Runge-Kutta results were very close and also 3rd to 9th order Adams-Bashforth-Moulton results. About result of computation time, this study showed that 4th order Runge-Kutta was the fastest. However, in case of 8th order Runge-Kutta, it was faster than 14th order Adams-Bashforth-Moulton but slower than 13th order Adams-Bashforth-Moulton in this study.

### The Application of welding numerical simulation on two typical welded structures in railway vehicles

• Ya-na, Li;Cheng-tao, Li;Bin, Yuan;Su-ming, Xie
• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.145-155
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• 2012
• The thin-plate structure and the box-beam structure are two typical welded structures in railway vehicles. Because of their structure complexity, bigger size and multi-seams, welding residual distortion which occur in welding process bring unfavorable effect on the quality of welding products manufacturing and service. As a result, welding distortion forecasting and control become an important and urgent research topic in railway vehicles. In this paper, three different numerical methods are presented corresponding to three typical types of welded structures of railway vehicles and welding deformation are simulated. Consistence of numerical results and experimental data proves the correctness of models and feasibility of simulation methods.

### Research on Numerical Calculation of Normal Modes in Nonlinear Vibrating Systems (비선형 진동계 정규모드의 수치적 계산 연구)

• Lee, Kyoung-Hyun;Han, Hyung-Suk;Park, Sungho;Jeon, Soohong
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.795-805
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• 2016
• Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

### NUMERICAL METHODS FOR CAVITATING FLOW

• SHIN Byeong Rog
• 한국전산유체공학회:학술대회논문집
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• pp.1-9
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• 2001
• In this paper, some numerical methods recently developed for gas-liquid two-phase flows are reviewed. And then, a preconditioning method to solve cavitating flow by the author is introduced. This method employs a finite-difference Runge-Kutta method combined with MUSCL TVD scheme, and a homogeneous equilibrium cavitation model. So that it permits to treat simply the whole gas-liquid two-phase flow field including wave propagation, large density changes and incompressible flow characteristic at low Mach number. Finally, numerical results such as detailed observations of the unsteady cavity flows, a sheet cavitation break-off phenomena and some data related to performance characteristics of hydrofoils are shown.

### Combination of Element-Free Galerkin Method and Infinite Elements (무요소법과 무한요소의 결합에 관한 연구)

• 이상호;김태연
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.76-83
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• 2001
• In this study, a new method coupling of Element-Free Galerkin(EFG) method and Infinite Elements(IE) method is presented for extending application of the EFG method to engineering problems in unbounded domain. EFG method and IE method are briefly reviewed, and then the coupling procedure of the two methods is proposed. Numerical Algorithm by way of EFG-lE coupling technique is also developed. Numerical results illustrate the performance of the proposed technique. The accuracy of numerical solutions by the developed algorithm is guaranteed in comparing those of the other methods.

### Influence of Submerged Breakwater in front of Rubble Mound Breakwater (경사식 방파제의 전면에 설치된 수중방파제의 영향에 관한 연구)

• Min, Hyun-Seong;Cho, Yong-Sik
• 한국방재학회:학술대회논문집
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• pp.217-220
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• 2008
• The reflection coefficients and the run-up heights affected by submerged structures are studied by using the numerical and the laboratory experimental methods. The three-point method is chosen to calculate the reflection coefficients in both the experimental and the numerical methods. The results of numerical simulations are shown a good agreement with laboratory measurements. The reflection coefficients increase and the run-up heights decrease when the rubble mound breakwater is defended by low-crested structures.

### A New Time Stepping Method for Solving One Dimensional Burgers' Equations

• Piao, Xiang Fan;Kim, Sang-Dong;Kim, Phil-Su;Kim, Do-Hyung
• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.327-346
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• 2012
• In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.