• Structural Engineering and Mechanics
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• v.10 no.1
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• pp.67-79
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• 2000

Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.2
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• pp.184-192
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• 1998

This paper deals with an extended analytical solution for the mixture solidification problem, in which temperature is inherently coupled with the solute transport due to the presence of volume contraction induced flow. A new exact solution to the energy equation accounting for the convection effect in the melt is successfully derived, which allows the present analysis to cover a high initial superheating. Difference in properties between the solid and liquid phases is rigorously incorporated into the model equations in the solid fraction weighted form. Taking advantage of linearized correction factors, a systematic and easy-to-implement algorithm for determining the solidus and liquidus positions is introduced, which proves not only to converge stably but also to be very efficient. For a specific case, the present results show excellent agreements with the existing solution. The effect of convection in the melt becomes appreciable with increasing the initial superheating. It is revealed that variable properties in the mushy region significantly affect the solidification behaviors. The present study is also capable of resolving the interaction between microsegregation and macrosegregation.

• Proceedings of the KIEE Conference
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• 2005.07b
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• pp.1035-1037
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• 2005

The analysis of magnetic fields(2-D) induced by line currents, such as Overhead Trolley Lines or Transmission Lines, is not so easy by using the standard Finite Element Method(FEM). Mesh generation is one of the most important processes in the standard FEM. Because, the current region is relatively small compared with whole region, and actually is a line without thickness, the mesh refinement around the source lines yields many demerits. A way of supplement such a defect, we proposed the coupling scheme of analytical solution and FEM. In this study, the analytical solution is adopted around the region of line currents and FE solution is a lied to the rest of source region. And the two types of solution are coupled at the artificial boundary. To verify the usefulness of proposed algorithm, simplified model with magnetic material in FE region is chosen and analyzed. The results are compared with those of standard FEM. And the errors between them can be reduced by increasing harmonic orders.

• Journal of the Korea Society for Simulation
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• v.10 no.3
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• pp.83-94
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• 2001

In this paper, the consumable spare parts requirement determination problem of newly procured equipment systems is considered. The problem is formulated as the cost minimization problem with operational availability constraint. Assuming part failure rate is constant during operational period, an analytical method is developed to obtain spare part requirements. Since this solution tends to overestimate the requirements, a fast search simulation procedure is introduced to adjust it to the realistic solution. The analytical solution procedure and the simulation procedure are performed recursively until a near optimal solution is achieved. The experimental results show that the near optimal solution is approached in a fairly short amount of time.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.6
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• pp.1001-1008
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• 2017

This study was to evaluate the stream depletion rate from groundwater pumping with varying stream-well distance, aquifer transmissivity, storage coefficient, leakage coefficient, streambed hydraulic conductance using the Zlotnik and Tartakovsky analytical solution which considers a two-layer leaky aquifer-stream-well system. For the hydraulic conditions applied in this study, the streambed hydraulic conductance and the aquitard leakage coefficient were assessed to have a dominant influence on the stream depletion rate. In order to evaluate the applicability of Zlotnik and Tartakovsky analytical solution ignoring the change in the drawdown in the lower aquifer and applying the fixed head boundary condition, the solution was compared with Hunt analytical solution derived from the more practical conditions simultaneously taking into account the drawdown changes in the upper and lower aquifers. As a result, the Zlotnik and Tartakovsky analytical solution is suitable for predicting short-term effects of less than one year in the pumping period, and when the stream depletion factor (SDF) is greater than 2,500 days, or when the product of the leakage coefficient and the stream-well distance is less than 10 cm/s.

• Geomechanics and Engineering
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• v.20 no.4
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• pp.275-285
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• 2020

Excavation usually induces considerable ground settlement in soft ground, which may result in damage of adjacent buildings. Generally, the settlement is predicted through elastic-plastic finite element method and empirical method with defects. In this paper, an analytical solution for predicting ground settlement induced by excavation is developed based on the definition of three basic modes of wall displacement: T mode, R mode and P model. A separation variable method is employed to solve the problem based on elastic theory. The solution is validated by comparing the results from the analytical method with the results from finite element method(FEM) and existing measured data. Good agreement is obtained. The results show that T mode and R mode will result in a downward-sloping ground settlement profile. The P mode will result in a concave-type ground settlement profile.

• Structural Engineering and Mechanics
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• v.59 no.4
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• pp.671-682
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• 2016

In this paper, a new analytical approach has been presented for solving nonlinear conservative oscillators. Variational approach leads us to high accurate solution with only one iteration. Two different high nonlinear examples are also presented to show the application and accuracy of the presented approach. The results are compared with numerical solution using runge-kutta algorithm in different figures and tables. It has been shown that the variatioanl approach doesn't need any small perturbation and is accurate for nonlinear conservative equations.

• Journal of Industrial Technology
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• v.19
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• pp.391-402
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• 1999

The numerical model predicting the behaviours of submerged mound constructed by dredged material is developed in this paper. The model is based on the Bailard's sediment transport formula, Stokes' second-order wave theory and the sediment balance equation. Nonlinear partial differential equation which is the same form as convection-dispersion equation which represents change of bed section can be obtained by substituting sediment transport equation for equation of sediment conservation. By this process, the analytical solution by which the characteristic of the behaviours of submerged mound can be estimated is derived by probably combining the convention coefficient and the dispersion coefficient governing the behaviours of submerged mound and the probability density function representing the wave characteristics. The validity of the analytical solution is verified by comparing the analytical solution which is assumed to estimate the movement rate submerged mound by bed-load with the field data of the past and its characteristic is analyzed quantitatively by obtaining the mean of the dispersion coefficient representing the extent of the decrease rate of the submerged mound height.

• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.645-658
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• 2010

In this study, the Differential Transform Method (DTM) is employed in order to solve the governing differential equation of a moving Bernoulli-Euler beam with axial force effect and investigate its free flexural vibration characteristics. The free vibration analysis of a moving Bernoulli-Euler beam using DTM has not been investigated by any of the studies in open literature so far. At first, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Bernoulli-Euler beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equation of the motion. The calculated natural frequencies of the moving beams with various combinations of boundary conditions using DTM are tabulated in several tables and are compared with the results of the analytical solution where a very good agreement is observed.