• Steel and Composite Structures
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• v.9 no.1
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• pp.59-75
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• 2009

In this study, a simple approach for bending analysis of Reissner-Mindlin plates is presented using the four-node quadrilateral domain transformation based on discrete singular convolution. In the proposed approach, irregular physical domain is transformed into a rectangular domain by using the geometric coordinate transformation. The DSC procedures are then applied to discrete the governing equations and boundary conditions. The accuracy of the proposed method is verified by comparison with known solutions obtained by other numerical or analytical methods. Results for Reissner-Mindlin plates show a satisfactory agreement with the analytical and numerical solutions.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1654-1659
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• 2003

This paper introduces a fast Fourier transform (FFT)-based spectral analysis method for the transient responses as well as the steady-state responses of linear discrete systems. The force vibration of a viscously damped three-DOF system is considered as the illustrative numerical example. The proposed spectral analysis method is evaluated by comparing with the exact analytical solutions as well as with the numerical solutions obtained by the Runge-Kutta method.

• International Journal of Highway Engineering
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• v.18 no.3
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• pp.21-32
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• 2016

PURPOSES : In this paper, the analytical solutions suggested to simulate the behavior of rheological fluids were rigorously re-derived and investigated for fixed conditions to evaluate the applicability for the solutions on a mini-cone slump test of cement paste. The selected solutions with proper boundary conditions can be used as reference solutions to evaluate the performance of numerical simulation approaches, such as the discrete element method. METHODS : The slump, height, and spread radius for the given boundary and yield stress conditions that are determined by five different analytical solutions are compared. RESULTS : The analytical solution based on fluid mechanics for pure shear flow shows similar results to that for intermediate flow at low yield stresses. The fluid mechanics-based analytical solution resulted in a very similar trend to the geometry-based analytical solution. However, it showed a higher slump at high yield stress and lower slump at low yield stress ranges than the geometry-based analytical model. The analytical solution based on the mini-cone geometry was not significantly affected by the yield criteria, such as von Mises and Tresca. CONCLUSIONS : Even though differences among the analytical solutions in terms of slump and spread radius existed, the difference can be considered insignificant when the solutions were used as reference to evaluate the appropriateness of numerical approaches, such as the discrete element method.

• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.921-932
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• 2016

This paper presents a theoretical analysis for determining the transverse deflection of simply supported battened beams subjected to a uniformly distributed transverse quasi-static load. The analysis considers not only the shear effect but also the discrete effect of battens on the transverse deflection of the battened beam. The analytical solution is obtained using the principle of minimum potential energy. Numerical validation of the present analytical solution is accomplished using finite element methods. The present analytical solution shows that the shear effect on the transverse deflection of battened beams increases with the cross-section area of the main member but decreases with the cross-section area of the batten. The longer the battened beam is, or the larger the moment of inertia of the main member is, the smaller the shear effect will be.

• Structural Engineering and Mechanics
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• v.29 no.3
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• pp.279-288
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• 2008

In the present study, the discrete singular convolution (DSC) method is developed for buckling analysis of columns and thin plates having different geometries. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The results obtained by DSC method were compared with those obtained by the other numerical and analytical methods.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.369-389
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• 2014

Two-layer coupled or composite beams with discrete shear connectors of finite dimensions are commonly encountered in pre-fabricated construction. This paper presents the development of simplified closed-form solutions for such type of coupled beams for practical applications. A new coupled beam element is proposed to represent the unconnected segments in the beam. General solutions are then developed by an inductive method based on the results from the finite element analysis. A modification is subsequently considered to account for the effect of local deformations. For typical cases where the local deformation is primarily concerned about its distribution over the depth of the coupled beam, empirical modification factors are developed based on parametric calculations using finite element models. The developed analytical method for the coupled beams in question is simple, sufficiently accurate, and suitable for quick calculation in engineering practice.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2004.11a
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• pp.221-231
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• 2004

A kinetic theory analysis is made of low-speed gas flows in a microfluidic system consisted of three microchannels in series. The Boitzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. For the evaluation of the present method results are compared with those from the DSMC method and an analytical solution of the Navier-Stokes equations with slip boundary conditions. Calculations are made for flows at various Knudsen numbers and pressure ratios across the channel. The results compared well with those from the DSMC method. It is shown that the analytical solution of the Navier-Stokes equations with slip boundary conditions which is suited fur fully developed flows can give relatively good results. In predicting the geometrically complex flows up to a Knudsen number of about 0.06. It is also shown that the present method can be used to analyze extremely low-speed flow fields for which the DSMC method is Impractical.

• Architectural research
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• v.14 no.1
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• pp.27-33
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• 2012

This study proposes analytical methods to establish the eigenfunction of continuous system due to substructuring and decoupling of discrete subsystems. The dynamic characteristics of updated continuous system are evaluated by the constraint effect of consistent deformation at the interfaces between two systems. Beginning with the dynamic equation for constrained discrete system, this work estimates the modal eigenmode function for the continuous system due to the addition or deletion of discrete systems. Numerical applications illustrate the validity and applicability of the proposed method.

• Geomechanics and Engineering
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• v.33 no.4
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• pp.353-367
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• 2023

The construction of a protective embankment is a suitable strategy to stop and control high-energy rock blocks' impacts during the rockfall phenomenon. In this paper, based on the discrete element numerical method, by modeling an existing embankment reinforced with geogrid, its stability status under the impact of a rock block with two types of low and high kinetic energy, namely 2402 and 4180 kJ, respectively, has been investigated. The modeling results show that the use of geogrid has caused the displacement in the front and back of the embankment to decrease by more than 30%. In this case, the reinforced embankment has stopped the rock block earlier. The displacements obtained from the DEM modeling are compared with the displacements measured from an actual practical experiment to evaluate the results' validity. Comparison between the results shows that the displacement values are close together, while the maximum percentage error in previous studies by an analytical method and the finite element method was 76.4% and 36.6%, respectively. Therefore, the obtained results indicate the discrete numerical method's high ability compared to other numerical and analytical methods to simulate and design the geogrid-reinforced soil embankment under natural disasters such as rockfall with a minor error.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.09a
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• pp.591-604
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• 2009

This paper presents some important issues in modeling rock behaviour around an underground opening at depth which characterized as stress-induced fractural failure of rock. Unlike other conventional modeling approaches, stress-induced rock failure is highly complex process due to its own heterogeneous and discrete natures. Because of this complexity, many researchers has been struggled to mimic such processes as close as possible to reality with various approaches in both analytical, and numerical approaches for past few decades. Such approaches which are based on continuum mechanics, analytical fracture mechanics, and DEM(Discrete Element Method) were explored in this paper, and fundamental shortcomings for each approaches were illustrated here. In addition, DEM approach using $PFC^{2D}$(Particle Flow Code) was also implemented and illuminated in this paper and discuss the improvement and considerations for the future research.