• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.695-708
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• 2024

In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.629-645
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• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Wind and Structures
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• v.5 no.2_3_4
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• pp.317-328
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• 2002

A numerical investigation on the turbulent flows over a three-dimensional steep hill is presented. The numerical model developed for the present work is based on the finite volume method and the SIMPLE algorithm with a non-staggered grid system. Standard $k-{\varepsilon}$ model and Shih's non-linear model are tested for the validation of the prediction accuracy in the 3D separated flow. Comparisons of the mean velocity and turbulence profiles between the numerical predictions and the measurements show good agreement. The Shih's non-linear model is found to predict mean flow and turbulence better than the Standard $k-{\varepsilon}$. Flow patterns have also been examined to explain the difference in the cavity zone between 2D and 3D hills.

• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.1004-1012
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• 2021

High density polyethylene (HDPE) pipe has many advantages over metallic pipe, and has been used in non-safety related application for years in some nuclear power plants (NPPs). Recently, HDPE pipe was introduced into safety related applications. The main difference between safety-related and non-safety-related pipes in NPPs is the design method of extra loadings such as gravity, temperature, and earthquake. In this paper, the mechanical behavior of HDPE pipe under various loads in pipe gallery was studied by finite element analysis (FEA). Stress concentrations were found at the fusion regions on inner surface of mitered elbows of HDPE pipe system. The effects of various factors were analyzed, and the influence of various loads on the damage of HDPE pipe system were evaluated. The results of this paper provide a reference for the design of nuclear safety-related Class 3 HDPE pipe. In addition, as the HDPE pipes analyzed in this paper were suspended in pipe gallery, it can also serve as a supplementary reference for current ASME standard on Class 3 HDPE pipe, which only covers the application for buried pipe application.

• Structural Monitoring and Maintenance
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• v.3 no.4
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• pp.315-333
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• 2016

This study aims to perform damage identification for Da-Sheng-Guan (DSG) high-speed railway truss arch bridge using fuzzy clustering analysis. Firstly, structural health monitoring (SHM) system is established for the DSG Bridge. Long-term field monitoring strain data in 8 different cases caused by high-speed trains are taken as classification reference for other unknown cases. And finite element model (FEM) of DSG Bridge is established to simulate damage cases of the bridge. Then, effectiveness of one fuzzy clustering analysis method named transitive closure method and FEM results are verified using the monitoring strain data. Three standardization methods at the first step of fuzzy clustering transitive closure method are compared: extreme difference method, maximum method and non-standard method. At last, the fuzzy clustering method is taken to identify damage with different degrees and different locations. The results show that: non-standard method is the best for the data with the same dimension at the first step of fuzzy clustering analysis. Clustering result is the best when 8 carriage and 16 carriage train in the same line are in a category. For DSG Bridge, the damage is identified when the strain mode change caused by damage is more significant than it caused by different carriages. The corresponding critical damage degree called damage threshold varies with damage location and reduces with the increase of damage locations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.7
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• pp.849-861
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• 1997

In this study, the effect of hole geometry of the cooling system on the flow and temperature field was numerically calculated. The finite volume method was employed to discretize the governing equation based on the non-orthogonal coordinate with non-staggered variable arrangement. The standard k-.epsilon. turbulence model was used and also the predicted results were compared with the experimental data to validate numerical modeling. The predicted results showed good agreement in all cases. To analyze the effect of the discharge coefficient for slots of different length to width, the inlet chamfering and radiusing holes were considered. The discharge coefficient was increased with increment of the chamfering ratio, radiusing ratio and slot length to width and also the effect of radiusing showed better result than chamfering in all cases. In order to analyze the difference between the predicted results with plenum region and without plenum region, the velocity profiles of jet exit region for a various flow conditions were calculated. The normal velocity components of jet exit showed big difference for the low slot length to width and high blowing rate cases. To analyze the flow phenomena injected from a row of inclined holes in a real turbine blade, three dimensional flow and temperature distribution of the region including plenum, hole and cross stream with flow conditions were numerically calculated. The results have shown three-dimensional flow characteristics, such as the development of counter rotating vortices, jetting effect and low momentum region within the hole in addition to counter rotating vortex structure in the cross stream.

• Geomechanics and Engineering
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• v.38 no.1
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• pp.93-106
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• 2024

The present paper investigates the spatial variability effect of soil property on the three-dimensional probabilistic characteristics of the bearing capacity factor (i.e., mean and coefficient of variation) of a circular footing resting on clayey soil where both mean and standard deviation of undrained shear strength increases with depth, keeping the coefficient of variation constant. The mean trend of undrained shear strength is defined by introducing the dimensionless strength gradient parameter. The finite difference method along with the random field and Monte Carlo simulation technique, is used to execute the numerical analyses. The lognormal distribution is chosen to generate random fields of the undrained shear strength. In the study, the potential failure of the structure is represented through the failure probability. The influences of different vertical scales of fluctuation, dimensionless strength gradient parameters, and coefficient of variation of undrained shear strength on the probabilistic characteristics of the bearing capacity factor and failure probability of the footing, along with the probability and cumulative density functions, are explored in this study. The variations of failure probability for different factors of safety corresponding to different parameters are also illustrated. The results are presented in non-dimensional form as they might be helpful to the practicing engineers dealing with this type of problem.

• Structural Engineering and Mechanics
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• v.58 no.2
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• pp.277-300
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• 2016

Cold-formed steel (CFS) sections are becoming an increasingly popular solution for constructing floors in residential, healthcare and education buildings. Their reduced weight, however, makes them prone to excessive vibrations, increasing the need for accurate prediction of CFS floor modal properties. By combining experimental modal analysis of a full-scale CFS framed building and its floors and their numerical finite element (FE) modelling this paper demonstrates that the existing methods (based on the best engineering judgement) for predicting CFS floor modal properties are unreliable. They can yield over 40% difference between the predicted and measured natural frequencies for important modes of vibration. This is because the methods were adopted from other floor types (e.g., timber or standard steel-concrete composite floors) and do not take into account specific features of CFS floors. Using the adjusted and then updated FE model, featuring semi-rigid connections led to markedly improved results. The first four measured and calculated CFS floor natural frequencies matched exactly and all relevant modal assurance criterion (MAC) values were above 90%. The introduction of flexible supports and more realistic modelling of the floor boundary conditions, as well as non-structural $fa{\c{c}}ade$ walls, proved to be crucial in the development of the new more successful modelling strategy. The process used to develop 10 identified and experimentally verified FE modelling parameters is based on published information and parameter adjustment resulting from FE model updating. This can be utilised for future design of similar lightweight steel floors in prefabricated buildings when checking their vibration serviceability, likely to be their governing design criterion.