• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.81-87
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• 1996

The aerodynamic charateristics of high speed train can be improved by well-designing of its fore-body shape. In this paper, as a way of the design a fore-body shape which has optimal aerodynamic charasteristics, 9 models of fore-body shapes are proposed and the change of aerodynamic charateristics is studied through calculations of flow field around high speed train for each fore-body shape. The flow field around high speed trains are calculated using Thin-Layer Navier-Stokes equation and Chimera grid technique. The application of Chimera grid technique to these flow calculations over high speed train which has ground plane under the train makes grid generation easily. As a computaional algorithm, Pulliam and Chaussee's Diagonal algorithm, the modified form of the Beam and Warming's AF scheme which operates on block-tridiagonal matrices, is selected to reduce computaional time. Introducing hole points flag concept to this Diagonal algorithm. a algorithm for Chimera grid is generated. The variational trends of aerodynamic characteristics are studied from the results of flow calculations around high speed trains for 9 fore-body shapes.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.11a
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• pp.39-44
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• 2005

The effects of aging of PSF/AS4 laminates on fatigue was studied using the new energy release rate analysis. The analysis by the variational mechanics has been useful in providing fracture mechanics interpretation of matrix microcracking in cross-ply laminates. This paper describes the changes of the critical energy release rate (microcracking toughness) according to the aging period under fatigue loading. The master plot by modified Paris-law gives a characterization of a material system's resistance to microcrack formation. PSF $[0/90_{s}]_{s}$ laminates were aged at four different temperature based on the glass transition temperature for 0 to 60 days. At all temperatures, the toughness decreased with aging time. The decrease of the toughness at higher temperature was faster than at lower temperature. To assess the effects of aging on fatigue, the unaged laminates were compared with the laminates which had been aged for 60 days at 170$^{\circ}C$ near 180 $^{\circ}C$ t$_g$. The slope of dD/dN versus ${\Delta}G_m$. of the aged laminates was lower than that of the unaged laminates. There was a significant shift of the aged data to formation of microcracks at the lower values of ${\Delta}G_m$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.2
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• pp.119-126
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• 1984

An analysis is presented for the vibration and stability of Beck's column carring a tip mass at its free and subjected there to a follower compressive force by using variational approach. The influence of transverse shear deformation and rotatory inertial of the mass of the column upon the critical flutter load and frequency is considered, and Timoshenko's shear coefficient K' is calculated by Cowper's formulae. It is, moreover, worth noticing that the influence of inertial moment of tip mass upon the flutter load and frequency is investigated. The centroid of a tip mass is offset from the free end of the beam and located along its extended axis of the two cases, one of which has a tip mass increasing as .xi., the tip mass offset parameter, is augmented, the other has a tip mass constant but the inertial moment is variable according to a magnitude of .eta., the tip mass offset parament. This study reveals that the effects of inertial moment of a tip mass and larger value of P are specially remarkable even a tip mass is a same.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.13 no.1
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• pp.45-51
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• 2014

Generally, marine transmissions contain straight shafts and helical gears, meaning that enginerooms require more space. In order to guarantee a levelengine space for conical involute gears or beveloid gears, both of which are important machine parts, a conical gear was used to replace the traditional cylinder gear. Owing to weak points such as the point contact phenomenon of the teeth, a limitation of the width of each tooth in terms of the addendum, the variational modification coefficient,and the difficulty of processing, research about conical involute gears remains at a standstill. Along with the increasing number of applications of conical involute gears, research on conical gear design technology is necessary. In this paper, in an effort to enhance conical gear design technology, research on the 3D modeling and stress analyses of helical conical involute gears were done.

• Journal of Mechanical Science and Technology
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• v.17 no.2
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• pp.296-309
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• 2003

The periodicity of the physiological flow has been the major interest of analytic research in this field up to now Among the mechanical forces stimulating the biochemical reaction of endothelial cells on the wall, the wall shear stresses show the strongest effect to the biochemical product. The objective of present study is to find the effects of velocity waveform on the wall shear stresses and pressure distribution along the artery and to present some correlation of the velocity waveform with the clinical observations. In order to investigate the complex flow phenomena in the bifurcated tube, constitutive equations, which are suitable to describe the rheological properties of the non-Newtonian fluids, are determined, and pulsatile momemtum equations are solved by the finite volume prediction. The results show that pressure and wall shear stresses are related to the velocity waveform of the physiological flow and the blood viscosity. And the variational tendency of the wall shear stresses along the flow direction is very similar to the applied sinusoidal and physiological velocity waveforms, but the stress values are quite different depending on the local region. Under the sinusoidal velocity waveform, a Newtonian fluid and blood show big differences in velocity. pressure, and wall shear stress as a function of time, but the differences under the physiological velocity waveform are negligibly small.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.3
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• pp.48-54
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• 2000

In this study the characteristics of chip formation of the cold drawn Bi-S free machining steels were assessed. And for comparison those of the cold drawn Pb-S free machining steel the hot rolled low carbon steel which has MnS as free machining inclusions and the conventional steels were also investigated. During chip formation the cold drawn free machining steels show relatively little change in thickness and width of chip compare to those of the conventional carbon steels. And a single parameter which indicates the degree of deformation during chip formation chip cross-section area ratio is introduced. The chip cross-section area ratio is defined as chip cross-section area is divided by undeformed chip cross-section area. The variational patters of the chip cross-section area ratio of the materials cut are similar to those of the shear strain values. The shear stress however seems to be dependent on the carbon content of the materials. The cold drawn Bi-S and Pb-S steels show nearly the same chip forming behaviors and the energy consumed during chip formation is almost same. A low carbon steel without free machining aids shows poor chip breakability due to its high ductility. By introducing a small amount of free machining inclusions such as MnS Bi, Pb or merely increasing carbon content the chip breakability improves significantly.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.375-396
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• 2009

In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.213-234
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• 2010

A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.