• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.323-340
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• 1997

In this study we prove the mesh-independence principle via Steffensen's method. This principle asserts that when Steffensen's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation then the behavior of th discretized process is asymptoti-cally the same as that for the original iteration. Local and semilo-cal convergencve results as well as an error analysis for Steffensen's method are also provided.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.139-159
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• 2000

In this manuscript we study perturbed Newton-like methods for the solution of nonlinear operator equations in a Banach space and their discretized versions in connection with the mesh independence principle. This principle asserts that the behavior of the discretized process is asymptotically the same as that for the original iteration and consequently, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved by others using Newton's method for certain classes of boundary value problems and even more generally by considering a Lipschitz uniform discretization. In some of our earlierpapers we extend these results to include Newton-like methods under more general conditions. However, all previous results assume that the iterates can be computed exactly. This is mot true in general. That in why we use perturbed Newton-like methods and even more general conditions. Our results, on the one hand, extend, and on the other hand, make more practical and applicable all previous results.

• Wind and Structures
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• 제24권3호
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• pp.223-247
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• 2017

By using numerical simulation, vast and detailed information and observation of the physics of flow over a train model can be obtained. However, the accuracy of the numerical results is questionable as it is affected by grid convergence error. This paper describes a systematic method of computational grid refinement for the Unsteady Reynolds Navier-Stokes (URANS) of flow around a generic model of trains using the OpenFOAM software. The sensitivity of the computed flow field on different mesh resolutions is investigated in this paper. This involves solutions on three different grid refinements, namely fine, medium, and coarse grids to investigate the effect of grid dependency. The level of grid independence is evaluated using a form of Richardson extrapolation and Grid Convergence Index (GCI). This is done by comparing the GCI results of various parameters between different levels of mesh resolutions. In this study, monotonic convergence criteria were achieved, indicating that the grid convergence error was progressively reduced. The fine grid resolution's GCI value was less than 1%. The results from a simulation of the finest grid resolution, which includes pressure coefficient, drag coefficient and flow visualization, are presented and compared to previous available data.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Computers and Concrete
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• 제15권4호
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• pp.515-545
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• 2015

The paper presents results of FE simulations of the strain-rate sensitive concrete behaviour under dynamic loading at the macroscopic level. To take the loading velocity effect into account, viscosity, stress modifications and inertial effects were included into a rate-independent elasto-plastic formulation. In addition, a decrease of the material stiffness was considered for a very high loading velocity to simulate fragmentation. In order to ensure the mesh-independence and to properly reproduce strain localization in the entire range of loading velocities, a constitutive formulation was enhanced by a characteristic length of micro-structure using a non-local theory. Numerical results were compared with corresponding laboratory tests and available analytical formulae.

• Computers and Concrete
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• 제4권5호
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• pp.377-402
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• 2007

The paper presents quasi-static plane strain FE-simulations of strain localization in reinforced concrete beams without stirrups. The material was modeled with two different isotropic continuum crack models: an elasto-plastic and a damage one. In case of elasto-plasticity, linear Drucker-Prager criterion with a non-associated flow rule was defined in the compressive regime and a Rankine criterion with an associated flow rule was adopted in the tensile regime. In the case of a damage model, the degradation of the material due to micro-cracking was described with a single scalar damage parameter. To ensure the mesh-independence and to capture size effects, both criteria were enhanced in a softening regime by nonlocal terms. Thus, a characteristic length of micro-structure was included. The effect of a characteristic length, reinforcement ratio, bond-slip stiffness, fracture energy and beam size on strain localization was investigated. The numerical results with reinforced concrete beams were quantitatively compared with corresponding laboratory tests by Walraven (1978).

• International Journal of Naval Architecture and Ocean Engineering
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• 제12권1호
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• pp.102-115
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• 2020

In this study, the SST k - ω turbulence model and the sliding mesh technology based on RANS method have been adopted to simulate the exciting force and hydrodynamic of a pump-jet propulsor in different oblique inflow angle (0°, 10°, 20°, 30°) and different advance ratio (J = 0.95, J = 1.18, J = 1.58).The fully structured grid and full channel model have been adopted to improved computational accuracy. The classical skewed marine propeller E779A with different advance ratio was carried out to verify the accuracy of the numerical simulation method. The grid independence was verified. The time-domain data of pump-jet propulsor exciting force including bearing force and fluctuating pressure in different working conditions was monitored, and then which was converted to frequency domain data by fast Fourier transform (FFT). The variation laws of bearing force and fluctuating pressure in different advance ratio and different oblique flow angle has been presented. The influence of the peak of pulsation pressure in different oblique flow angle and different advance ratio has been presented. The results show that the exciting force increases with the increase of the advance ratio, the closer which is to the rotor domain and the closer to the blades tip, the greater the variation of the pulsating pressure. At the same time, the exciting force decrease with the oblique flow angle increases. And the vertical and transverse forces will change more obviously, which is the main cause of the exciting force. In addition, the pressure distribution and the velocity distribution of rotor blades tip in different oblique flow angles has been investigated.

• Structural Engineering and Mechanics
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• 제88권5호
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• pp.451-462
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• 2023

Lumped Damage Mechanics (LDM) is a theory proposed in the late eighties, which assumes that structural collapse may be analyzed as a two-phase phenomenon. In the first (pre-localization) stage, energy dissipation is a continuous process and it may be modelled by means of the classic versions of the theory of plasticity or Continuum Damage Mechanics (CDM). The second, post-localization, phase can be modelled assuming that energy dissipation is lumped in zones of zero volume: inelastic hinges, hinge lines or localization surfaces. This paper proposes a new LDM formulation for cracking in concrete structures in tension. It also describes its numerical implementation in conventional finite element programs. The results of three numerical simulations of experimental tests reported in the literature are presented. They correspond to plain and fiber-reinforced concrete specimens. A fourth simulation describes also the experimental results of a new test using the digital image correlation technique. These numerical simulations are also compared with the ones obtained using conventional Cohesive Fracture Mechanics (CFM). It is then shown that LDM conserves the advantages of both, CDM and CFM, while overcoming their drawbacks.

• 한국농공학회논문집
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• 제59권6호
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• pp.61-71
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• 2017

The tracer gas method has an advantage that can estimate total and local ventilation rate by tracing air flow. However, the field measurement using tracer gas has disadvantages such as danger, inefficiency, and high cost. Therefore, the aim of this study was to evaluate ventilation rate in pig house by using the thermal distribution data rather than tracer gas. Especially, LMA (Local Mean Age), which is an index based on the age of air theory, was used to evaluate the ventilation rate in pig house. Firstly, the field experiment was conducted to measure micro-climate inside pig house, such as the air temperature, $CO_2$ concentration and wind velocity. And then, LMA was calculated based on the decay of $CO_2$ concentration and air temperature, respectively. This study compared between LMA determined by $CO_2$ concentration and air temperature; the average error and root mean square error were 3.76 s and 5.34 s. From these results, it was determined that thermal distribution data could be used for estimation of LMA. Finally, CFD (Computational fluid dynamic) model was validated using LMA and wind velocity. The mesh size was designed to be 0.1 m based on the grid independence test, and the Standard $k-{\omega}$ model was eventually chosen as the proper turbulence model. The developed CFD model was highly appropriate for evaluating the ventilation rate in pig house.