• Interaction and multiscale mechanics
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• v.6 no.4
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• pp.395-409
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• 2013

Molecular dynamics (MD) systems are highly nonlinear and nonlocal, and the conventional model order reduction methods are ineffective for MD systems. The RBF-POD method (Lee and Chen, 2013) employed a radial basis function (RBF) approximated potential energies and inter-atomic forces of MD systems under the framework of the proper orthogonal decomposition (POD) method for the reduced-order modeling of MD systems. In this work, we focus on the numerical procedures of the RBF-POD method and demonstrate how to apply this approach to the modeling of ds-DNA molecules under stretching and bending conditions.

• Interaction and multiscale mechanics
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• v.5 no.4
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• pp.385-397
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• 2012

In this paper the dynamic stiffness matrix method was used for the free vibration analysis of axially moving micro beam with constant velocity. The extended Hamilton's principle was employed to derive the governing differential equation of the problem using the modified couple stress theory. The dynamic stiffness matrix of the moving micro beam was evaluated using appropriate expressions of the shear force and bending moment according to the Euler-Bernoulli beam theory. The effects of the beam size and axial velocity on the dynamic characteristic of the moving beam were investigated. The natural frequencies and critical velocity of the axially moving micro beam were also computed for two different end conditions.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.299-308
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• 2010

The indirect approach for measuring the bridge frequencies from the dynamic responses of a passing vehicle is a highly potential method. In this study, the effect of road surface roughness on such an approach is studied through finite element simulations. A two-dimensional mathematical model with the vehicle simulated as a moving sprung mass and the bridge as a simply-supported beam is adopted. The dynamic responses of the passing vehicle are solved by the finite element method along with the Newmark ${\beta}$ method. Through the numerical examples studied, it is shown that the presence of surface roughness may have negative consequence on the extraction of bridge frequencies from the test vehicle. However, such a shortcoming can be overcome either by introducing multiple moving vehicles on the bridge, besides the test vehicle, or by raising the moving speed of the accompanying vehicles.

• Journal of computational fluids engineering
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• v.2 no.1
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• pp.21-28
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• 1997

This paper presents a two-dimensional horizontal implicit model to general circulation in estuaries and coastal seas. The model is developed in non-orthogonal curvilinear coordinates system, using the Interpolating Matrix Method (IMM), in combination with a technique of multi-domain. In the propose model, the Saint-Venant equations are solved by a splitting-up technique, in the successive steps; convection, diffusion and wave propagation. The ability of the proposed model to deal with full scale nature is illustrated by the interpretation of a dye-tracing experiment in the Gironde estuary.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.353-374
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• 2009

A new seamless multiscale simulation was developed for coupling the continuum model with its molecular dynamics. Kriging-based Finite Element Method (K-FEM) is employed to model the continuum base of the entire domain, while the molecular dynamics (MD) is confined in a localized domain of interest. In the coupling zone, where the MD domain overlaps the continuum model, the overall Hamiltonian is postulated by contributions from the continuum and the molecular overlays, based on a quartic spline scaling parameter. The displacement compatibility in this coupling zone is then enforced by the Lagrange multiplier technique. A multiple-time-step velocity Verlet algorithm is adopted for its time integration. The validation of the present method is reported through numerical tests of one dimensional atomic lattice. The results reveal that at the continuum/MD interface, the commonly reported spurious waves in the literature are effectively eliminated in this study. In addition, the smoothness of the transition from MD to the continuum can be significantly improved by either increasing the size of the coupling zone or expanding the nodal domain of influence associated with K-FEM.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.333-352
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• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.107-125
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• 2013

A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

• Interaction and multiscale mechanics
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• v.4 no.1
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• pp.1-16
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• 2011

The inverse problem about the theoretical analysis of a drill string bending in a channel of an inclined bore-hole with localized geometrical imperfections is studied. The system of ordinary differential equations is first derived based on the theory of curvilinear flexible elastic rods. One can then use these equations to investigate the quasi-static effects of the drill string bending that may occur in the process of raising, lowering and rotation of the string inside the bore-hole. The method for numerical solution of the constructed equations is described. With the proposed method, the phenomenon of the drill column movement, its contact interaction with the bore-hole surface, and the frictional seizure can be simulated for different combinations of velocities, directions of rotation and axial motion of the string. Geometrical imperfections in the shape of localized smoothed breaks of the bore-hole axis line are considered. Some numerical examples are presented to illustrate the applicability of the method proposed.

• Korean Journal of Materials Research
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• v.27 no.11
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• pp.624-630
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• 2017

In this study, we investigated the overpotential of precipitation related to the catalytic activity of electrodes on the initial process of electrodeposition of Co and Co-Ni alloys on polycrystalline Cu substrates. In the case of Co electrodeposition, the surface morphology and the magnetic property change depending on the film thickness, and the relationship with the electrode potential fluctuation was shown. Initially, the deposition potential(-170 mV) of the Cu electrode as a substrate was shown, the electrode potential($E_{dep}$) at the $T_{on}$ of electrodeposition and the deposition potential(-600 mV) of the surface of the electrodeposited Co film after $T_{off}$ and when the pulse current was completed were shown. No significant change in the electrode potential value was observed when the pulse current was energized. However, in a range of number of pulses up to 5, there was a small fluctuation in the values of $E_{dep}$ and $E_{imm}$. In addition, in the Co-Ni alloy electrodeposition, the deposition potential(-280 mV) of the Cu electrode as the substrate exhibited the deposition potential(-615 mV) of the electrodeposited Co-Ni alloy after pulsed current application, the $E_{dep}$ of electrodeposition at the $T_{on}$ of each pulse and the $E_{imm}$ at the $T_{off}$ varied greatly each time the pulse current was applied. From 20 % to less than 90 % of the Co content of the thin film was continuously changed, and the value was constant at a pulse number of 100 or more. In any case, it was found that the shape of the substrate had a great influence.

• Interaction and multiscale mechanics
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• v.4 no.4
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• pp.321-336
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• 2011

This paper presents the results of static vertical load tests carried out on a model building frame supported by pile groups embedded in cohesionless soil (sand). The effect of soil interaction on displacements and rotation at the column base and also the shears and bending moments in the columns of the building frame were investigated. The experimental results have been compared with those obtained from the finite element analysis and conventional method of analysis. Soil nonlinearity in the lateral direction is characterized by the p-y curves and in the axial direction by nonlinear vertical springs along the length of the piles (${\tau}-z$ curves) at their tips (Q-z curves). The results reveal that the conventional method gives the shear force in the column by about 40-60%, the bending moment at the column top about 20-30% and at the column base about 75-100% more than those from the experimental results. The response of the frame from the experimental results is in good agreement with that obtained by the nonlinear finite element analysis.