• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.15-30
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• 2009

The theoretical framework of the interaction fields for multiple scales based on field theory is applied to one-dimensional problem mimicking dislocation substructure sensitive intra-granular inhomogeneity evolution under fatigue of Cu-added steels. Three distinct scale levels corresponding respectively to the orders of (A)dislocation substructures, (B)grain size and (C)grain aggregates are set-up based on FE-RKPM (reproducing kernel particle method) based interpolated strain distribution to obtain the incompatibility term in the interaction field. Comparisons between analytical conditions with and without the interaction, and that among different cell size in the scale A are simulated. The effect of interaction field on the B-scale field evolution is extensively examined. Finer and larger fluctuation is demonstrated to be obtained by taking account of the field interactions. Finer cell size exhibits larger field fluctuation whereas the coarse cell size yields negligible interaction effects.

• Steel and Composite Structures
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• v.35 no.1
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• pp.43-59
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• 2020

In this study, free vibration analysis of laminated composite parabolic thick plate frames by using finite element method is introduced. Governing equations of an eigenvalue problem are obtained from First Order Shear Deformation Theory (FSDT). Finite element method is employed to obtain natural frequency values from the governing differential equations. The frames consist of two flat square plates and one singly curved plate. Parameters like radii of curvature, aspect ratio, ply orientation and boundary conditions are investigated to understand their effect on dynamic behavior of such a structure. In addition, multi-bay structures of such geometry with different stacking order are also taken into account. The composite frame structures are also modeled and simulated via ANSYS to verify the accuracy of the present study.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1669-1673
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• 2008

In this study, we simulated the atrial arrhythmia numerically. By using electro-physiological model of atrial cell from Nygren et al. and applying reaction-diffusion partial differential equation, we simulated electrical conduction in atrium. A 3-D mesh system representing the human atrium was reconstructed from the surface geometry of atrium. We used a stimulus in the form of an archetype around pulmonary vessels in the left atrium to cause the atrial arrhythmia. The septal atrial tarchycardia was developed after the stimulus.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.11a
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• pp.283-288
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• 1999

The sealing performance of an elastomeric O-ring seat with a temperature gradient has been analyzed for the contact stress behaviors that develop between the O-ring seal and the surfaces with which it comes into contact. The leakage of an O-ring seal will occur when the pressure differential across the seal just exceeds the initial (or static) peak contact stress. The contact stress behaviors that develop in compressed O-rings, in common case of restrained geometry (grooved), are investigated using the finite element method. The analysis includes material hyperelasticity and axisymmetry. The computed FEM results show that the contact stress behaviors are related to a compression rate and a temperature gradient between the vacuum chamber with a groove and the contacting plate with a cooling jacket.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.31-46
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• 2010

Theory of minimal surfaces has always been in the center of differential geometry. The most difficult part in minimal surfaces is how to find meaningful examples. In this paper we survey the history of search for minimal surfaces. We also introduce examples of recently emerging maximal surfaces in the Lorentz-Minkowski space and compare the processes in the search for the minimal and the maximal surfaces.

• Journal of electromagnetic engineering and science
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• v.7 no.2
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• pp.59-63
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• 2007

This paper suggests a novel method to efficiently calculate the spatial-domain Green's functions of 2D electromagnetic problems Briefly speaking, this method combines spectral and spatial domain calculation schemes and prevents the Green's functions from poor convergence due to the singularities that complicate the process of the Method of Moment(MoM) applications For the validation of this proposed method, fields will be evaluated along the spatial distance including zero distance for 2D free-space and periodic homogeneous geometry The numerical results show the validity of the prosed method and correspondng physics.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1618-1621
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• 2002

In this paper, the constructive modeling procedure of nonholonomic mobile robot system is carried out with the help of controllability Lie algebra used in differential geometry field, and their geometrical properties are also analyzed. And, a new trajectory controller is suggested to guarantee its convergence to reference trajectory. Design procedure of the suggested trajectory controller is back-stepping scheme which was introduced recently in nonlinear control theory. The performance of the proposed trajectory controller is verified via computer simulation. In the simulation the trajectory controller is applied to differentially driven mobile robot system on the assumption that the trajectory planner be given.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2787-2789
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• 2000

In this paper. the constructive modeling procedure of nonholonomic mobile robot system is carried out with the help of controllability Lie algebra used in differential geometry field. and their geometrical properties are also analyzed. And, a new trajectory controller is suggested to guarantee its convergence to reference trajectory. Design procedure of the suggested trajectory controller is back-stepping scheme which was introduced recently in nonlinear control theory. The performance of the proposed trajectory controller is verified via computer simulation. In the simulation the trajectory controller is applied to differentially driven robot system on the assumption that the trajectory planner be given.

• International Journal of Naval Architecture and Ocean Engineering
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• v.1 no.2
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• pp.89-94
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• 2009

The current focus of development in industrial Computational Fluid Dynamics (CFD) is integration of CFD into Computer-Aided product development, geometrical optimisation, robust design and similar. On the other hand, in CFD research aims to extend the boundaries of practical engineering use in "non-traditional" areas. Requirements of computational flexibility and code integration are contradictory: a change of coding paradigm, with object orientation, library components, equation mimicking is proposed as a way forward. This paper describes OpenFOAM, a C++ object oriented library for Computational Continuum Mechanics (CCM) developed by the author. Efficient and flexible implementation of complex physical models is achieved by mimicking the form of partial differential equation in software, with code functionality provided in library form. Open Source deployment and development model allows the user to achieve desired versatility in physical modeling without the sacrifice of complex geometry support and execution efficiency.