• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.788-791
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• 2005

Nodal displacements are referred to the Initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian formulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid fer structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One closed loop structure undergoing large deformations is analyzed to demonstrate the efficiency and validity of the proposed method.

• Structural Engineering and Mechanics
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• v.50 no.4
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.6
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• pp.555-560
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• 2014

This paper presents a microparticle separator using a spiral microchannel. A particle separator based on the dean vortex was designed, fabricated, and characterized. Two different spiral microchannels were fabricated. Width and initial radius of rotation in the spiral microchannel were fixed to $300{\mu}m$ and 1.75 mm, respectively. Two different depths of the microchannels were designed at $50{\mu}m$ and $80{\mu}m$. In this experimental study, the equilibrium position of microparticles was monitored by using fluorescent microbeads. In the case of a low dean number (<1.0), lift force and dean drag force were similar, indicating that microbeads were distributed to almost all areas across microchannels. However, in the case of a high dean number (>1.0), dean drag force rather than lift force was dominant, indicating that microbeads moved toward the inner wall of the spiral microchannel.

• Journal of the Korean Society of Propulsion Engineers
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• v.25 no.3
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• pp.1-13
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• 2021

Effects of the nozzle wall angles on the supersonic flow field in a thrust optimized nozzle were numerically investigated. The combustor and operating condition of 30-tonf rocket engine was selected to study the optimum nozzle shape. The nozzle flow of combustion products was realized by the shifting equilibrium calculation for the propellant of kerosene-LOx. The change of nozzle wall angles induced different developing patterns of the internal and secondary shock wave. The optimum nozzle was obtained when the internal shock was in a specific position at the nozzle outlet. The nozzle wall angles of the optimum nozzle were very similar to those of the optimum nozzle which does not consider the shock wave.

• Journal of Korean Society of Steel Construction
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• v.24 no.3
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• pp.337-348
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• 2012

This study investigated the characteristics of bifurcation and the instability due to the initial imperfection of the space truss, which is sensitive to the initial conditions, and the calculated buckling load by the analysis of Eigen-values and the determinant of tangential stiffness. A two-free nodes model, a star dome, and a three-ring dome model were selected as case studies in order to examine the unstable phenomenon due to the sensitivity to Eigen mode, and the influence of the rise-span ratio and the load parameter on the buckling load were analyzed. The sensitivity to the imperfection of the two-free nodes model changed the critical path after reaching the limit point through the bifurcation mode, and the buckling load level was reduced by the increase in the amount of imperfection. The two sensitive buckling patterns for the model can be explained by investigating the displaced position of the free node, and the asymmetric Eigen mode was a major influence on the unstable behavior due to the initial imperfection. The sensitive mode was similar to the in-extensional mechanism basis of the simplified model. Since the rise-span ratio was higher, the effect of local buckling is more prominent than the global buckling in the star dome, and bifurcation on the equilibrium path occurring as the value of the load parameter was higher. Additionally, the buckling load levels of the star dome and the three-ring model were about 50-70% and 80-90% of the limit point, respectively.

• Journal of Korean Ophthalmic Optics Society
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• v.7 no.2
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• pp.1-11
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• 2002

A mathematical model is proposed to analyze the force; acting on the hard contact lens fitted on the cornea. The model incorporates the nonlinear equations and their numerical solution program, based on the formulations of surface tension force arising from the capillary action in the tear-film layer between the lens and cornea. The model simulates how the adhesion between lens and cornea varies according to the base curves and diameters of the lenses. When the spherical lens is fitted on the spherical cornea it is to rotate downward due to the weight of lens itself until it reaches an equilibrium position along the cornea where the counter(upward) moment caused by net force between the upper and lower portion of the periphery of lens. It is found that both the adhesion and displacement of lens along the cornea, where the gravity of lens balances the capillary-induced upward force, increases rapidly as the base curve of lens increases, i.e., as the lens gets flatter, while the increase in the diameter of lenses has resulted in the less increase in the rotation and adhesion. With the base curve and diameters of lenses being remained constant the increase in surface tension of tear film yields the increase in the adhesion between the cornea and lens while the initial rotation of lens is inversely proportional to the surface tension of the tear film.

• Journal of the Korea institute for structural maintenance and inspection
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• v.16 no.5
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• pp.112-120
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• 2012

A numerical model considering the internal vaporization and the creep effect, in the form of a analytical program, for tracing the behavior of high strength concrete(HSC) members exposed to fire is presented. The two stages, i.e., spalling procedure and fire resistance time, associated with the thermal, moisture flow, creep and structural analysis, for the prediction of fire resistance behavior are explained. The use of the analytical program for tracing the response of HSC member from the initial pre-loading stage to collapse, due to fire, is demonstrated. Moisture evaporates, when concrete is exposed to fire, not only at concrete surface but also at inside the concrete to adjust the equilibrium and transfer properties of moisture. Finite element method is employed to facilitate the moisture diffusion analysis for any position of member, so that the prediction method of the moisture distribution inside the concrete members at fire is developed. The validity of the numerical model used in this program is established by comparing the predictions from this program with results from others fire resistance tests. The analytical program can be used to predict the fire resistance of HSC members for any value of the significant parameters, such as load, sectional dimensions, member length, and concrete strength.