• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.1089-1094
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• 2004

Numerical methods to estimate behaviors of jointed rock mass can be roughly divided into two method : discontinuous model and continuum model. Generally, distinct element method (DEM) is applied in discontinuous model, and finite element method (FEM) or finite difference method (FDM) is utilized in continuum model. To predict a behavior of discontinuous model by DEM, it is essential to understand characteristics of joints developed in rock mass through field tests. However, results of field tests can not provide full information about rock mass because field tests is conducted in limited area. In this paper, discontinuous analysis by UDEC and continuous analysis by FLAC is utilized to estimate a behavior of a tunnel in jointed rock mass. For including discontinuous analysis in continuous analysis, joints in rock mass is considered by reducing rock mass properties obtained by RMR and decreasing shear strength of rock mass. By comparing and revising two analysis results, analysis results similar with practical behavior of a tunnel can be induced and appropriate support system is decided.

• 로봇학회논문지
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• 제15권4호
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• pp.301-308
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• 2020

In this paper, we deal with the static modeling of a continuum robot that can perform surgical interventions. The proposed continuum robot is made of stainless steel wires and a multi lumen flexible tube using a thermoplastic elastomer. This continuum robot could be most severely deformed in physical contact with narrow external environments, when a lateral external force acts at the distal tip of the continuum robot. In order to predict the shape and displacement under the lateral external force loading, the forward kinematics, the statics modeling, the force-moment equilibrium equation, and the virtual work-energy method of the continuum robot are described. The deflection displacements were calculated using the virtual work-energy method, and the results were compared with the displacement obtained by the conventional cantilever beam theories. In conclusion, the proposed static modeling and the virtual work-energy method can be used in arrhythmia procedure simulations.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제54권6호
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• pp.287-293
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• 2005

Equations have been derived for computing electromagnetic forces by using the Continuum Design Sensitivity Analysis based on the Continuum Mechanics and the Virtual Work Principle. The resultant expressions have similar terms relating to the Korteweg-Holmholz force density, Maxwell Stress Tensor and Magnetic Charge Method but numerical implementation of the proposed scheme leads to efficient calculation and improved accuracy. In addition, the method can be easily applied to computing the magnetic force distribution as well as the global force. Results show the aforementioned advantages in comparison with the conventional methods.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.527-531
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• 2007

The classical continuum theory-based thin film model is independent of their size and the surface effect can be ignored. But the surface to bulk ratio becomes very large in nano-size structures such as nano film, nano wire and nano beam. In this case, surface effect plays an important role and its contribution of the surface effect must be considered. Molecular dynamics simulation has been a conventional way to analyze these ultra-thin structures but structures in the range between submicro and micro are difficult to analyze by classical molecular dynamics due to the restriction of computing resources and time. Therefore, in present study, the continuum-based method is considered to predict the overall physical and mechanical properties of the structures in nano-scale, especially, for the thin-film. The proposed continuum based-thin plate finite element is efficient and reliable for the prediction of nano-scale film behavior.

• 한국수학사학회지
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• 제33권6호
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• pp.327-343
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• 2020

This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

• Structural Engineering and Mechanics
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• 제30권4호
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• pp.467-480
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• 2008

An aggregation multigrid method (AMM) is a leading iterative solver in solid mechanics. Recently, AMM is applied for solving Schur Complement system in the FE analysis of shell structures. In this work, an extended application of AMM for solving Schur Complement system in the FE analysis of continuum elements is presented. Further, the performance of the proposed AMM in multiple load cases, which is a challenging problem for an iterative solver, is studied. The proposed method is developed by combining the substructuring and the multigrid methods. The substructuring method avoids factorizing the full-size matrix of an original system and the multigrid method gives near-optimal convergence. This method is demonstrated for the FE analysis of several elastostatic problems. The numerical results show better performance by the proposed method as compared to the preconditioned conjugate gradient method. The smaller computational cost for the iterative procedure of the proposed method gives a good alternative to a direct solver in large systems with multiple load cases.

• Structural Engineering and Mechanics
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• 제44권4호
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.621-629
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• 2018

By employing the nonlocal continuum field theory of Eringen and Von Karman nonlinear strains, this paper presents an analytical model for linear and nonlinear dynamics analysis of single-walled carbon nanotubes (SWNTs) conveying fluid with different boundary conditions. In the linear analysis the natural frequencies and critical flow velocities of SWNTs are computed. However, in the nonlinear analysis the effect of nonlocal parameter on nonlinear dynamics of cantilevered SWNTs conveying fluid is investigated by using bifurcation diagram, phase plane and Poincare map. Numerical results confirm existence of chaos as well as a period-doubling transition to chaos.

• 한국농공학회논문집
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• 제51권3호
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• pp.45-52
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• 2009

Generally, structures are analyzed as continuum. However, sometimes it is more efficient to analyze structure as a discrete model rather than as a continuum model in case of the structure has complex shape or loading condition. This study, therefore, suggests an improved analysis discrete model, named Equivalent Truss Model (further as "ETM"), which can obtain similar results with analyzing continuums analysis. ETM adopts a lattice truss to compose the members of the model, and analyses the structures. As a consequence, the ETM produced the identical outcome with the continuums analysis in section force of different structures and loading conditions. Similar results have been shown in internal stress analysis as well. Make use of that ETM is discrete, fractural path of beam was analyzed by ETM and the result was reasonable.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 가을 학술발표회 논문집
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• pp.270-278
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• 1997

The purpose of this paper is to evaluate the effectiveness of eigen modes by modal analysis and the application of approximate eigen modes for continuum. This study proposes the appropriate selection technique of eigen modes by modal analysis and the method for the reasonable survey of post-buckling path. And the buckling characteristics of a latticed dome is studied by the application of these approximate eigen modes which have sufficient accuracy and praticallity for response analysis in symmetric and anti-symmetric state of continuous shell. To prove the effectiveness of eigen modes and application of approximate eigen modes for continuum, these results are compared with those of direct method.