• Coupled systems mechanics
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• v.4 no.1
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• pp.1-18
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• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Interaction and multiscale mechanics
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• v.7 no.1
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• International Journal of Internet, Broadcasting and Communication
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• v.11 no.1
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• pp.39-46
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• 2019

This paper proposes an adaptive threshold watershed algorithm, which is the method used for image segmentation and boundary detection, which extends the region on the basis of regional minimum point. First, apply adaptive thresholds to determine regional minimum points. Second, it extends the region by applying adaptive thresholds based on determined regional minimum points. Traditional watershed algorithms create over-segmentation, resulting in the disadvantages of breaking boundaries between regions. These segmentation results mainly from the boundary of the object, creating an inaccurate region. To solve these problems, this paper applies an improved watershed algorithm applied with adaptive threshold in regional minimum point search and region expansion in order to reduce over-segmentation and breaking the boundary of region. This resulted in over-segmentation suppression and the result of having the boundary of precisely divided regions. The experimental results show that the proposed algorithm can apply adaptive thresholds to reduce the number of segmented regions and see that the segmented boundary parts are correct.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• Journal of Biomedical Engineering Research
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• v.30 no.1
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• pp.10-17
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• 2009

Accurate electroencephalography (EEG) forward calculation is of importance for the accurate estimation of neuronal electrical sources. Conventional studies concerning the EEG forward problems have investigated various factors influencing the forward solution accuracy, e.g. tissue conductivity values in head compartments, anisotropic conductivity distribution of a head model, tessellation patterns of boundary element models, the number of elements used for boundary/finite element method (BEM/FEM), and so on. In the present paper, we investigated the influence of modeling errors in the boundary element volume conductor models upon the accuracy of the EEG forward solutions. From our simulation results, we could confirm that accurate construction of boundary element models is one of the key factors in obtaining accurate EEG forward solutions from BEM. Among three boundaries (scalp, outer skull, and inner skull boundary), the solution errors originated from the modeling error in the scalp boundary were most significant. We found that the nonuniform error distribution on the scalp surface is closely related to the electrode configuration and the error distributions on the outer and inner skull boundaries have statistically meaningful similarity to the curvature distributions of the boundary surfaces. Our simulation results also demonstrated that the accumulation of small modeling errors could lead to considerable errors in the EEG source localization. It is expected that our finding can be a useful reference in generating boundary element head models.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.6-6
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• 2003

• Journal of Ocean Engineering and Technology
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• v.32 no.6
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• pp.447-457
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• 2018

In this study, a two-dimensional fully nonlinear transient wave numerical tank was developed using a desingularized indirect boundary integral equation method. The desingularized indirect boundary integral equation method is simpler and faster than the conventional boundary element method because special treatment is not required to compute the boundary integral. Numerical simulations were carried out in the time domain using the fourth order Runge-Kutta method. A mixed Eulerian-Lagrangian approach was adapted to reconstruct the free surface at each time step. A numerical damping zone was used to minimize the reflective wave in the downstream region. The interpolating method of a Gaussian radial basis function-type artificial neural network was used to calculate the gradient of the free surface elevation without element connectivity. The desingularized indirect boundary integral equation using an isolated point source and radial basis function has no need for information about the element connectivity and is a meshless method that is numerically more flexible. In order to validate the accuracy of the numerical wave tank based on the desingularized indirect boundary integral equation method and meshless technique, several numerical simulations were carried out. First, a comparison with numerical results according to the type of desingularized source was carried out and confirmed that continuous line sources can be replaced by simply isolated sources. In addition, a propagation simulation of a $2^{nd}$-order Stokes wave was carried out and compared with an analytical solution. Finally, simulations of propagating waves in shallow water and propagating waves over a submerged bar were also carried and compared with published data.

• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.823-833
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• 2000

In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.