• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-252
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• 2002

We study the compatibility conditions and the existence of solutions or overdetermined PDE systems that admit complete prolongation. For a complete system of order k there exists a submanifold of the ($\kappa$-1)st jet space of unknown functions that is the largest possible set on which the initial conditions of ($\kappa$-1)st order may take values. There exists a unique solution for any initial condition that belongs to this set if and only if the complete system satisfies the compatibility conditions on the initial data set. We prove by applying the Frobenius theorem to a Pfaffian differential system associated with the complete prolongation.

• Corrosion Science and Technology
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• v.7 no.2
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• pp.112-118
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• 2008

We observed initial rusting process of steel containing Al under wet/dry cyclic condition with NaCl solution film using in situ X-ray diffraction spectroscopy at SPring-8 synchrotron radiation facility. It was found that mass fraction of iron oxides such as ${\alpha}-FeOOH$, ${\beta}-FeOOH$ and ${\gamma}-FeOOH$ varied with Al content. Some kinds of Al oxides were also found at the initial stage of corrosion. Those corrosion products might affect the corrosion process and corrosion rate of the steel.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.167-173
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• 2007

This paper describes a redundancy resolution based method for determining an optimal initial configuration of a humanoid robot for holding an object. There are three important aspects for a humanoid robot to be able to hold an object. Those three aspects are the reachability that guarantees the robot to reach the object, the stability that guarantees the robot to remain stable while moving or holding the object, and the manipulability that makes the robot manipulate the object dexterously. In this paper, a humanoid robot with 20 degrees of freedom is considered. The humanoid robot is kinematically redundant and has infinite number of solutions for the initial configuration problem. The complex three-dimensional redundancy resolution problem is divided into two simple two-dimensional redundancy resolution problems by incorporating the symmetry of the problem, robot's moving capability, and the geometrical characteristics of the given robot. An optimal solution with respect to the reachability, the stability, and the manipulability is obtained by solving these two redundancy resolution problems.

• Geomechanics and Engineering
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• v.16 no.1
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• pp.11-19
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• 2018

Propagation of the generalized Rayleigh waves in an elastic half-space covered by an elastic layer for different initial stress combinations and imperfect contact conditions is investigated. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed, the corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the influence of the initial stress patterns and on the influence of the contact conditions are presented and discussed. The case where the external forces are "follower forces" is considered as well. These investigations provide some theoretical foundations for the study of the near-surface waves propagating in layered mechanical systems and can be successfully used for estimation of the degree of the bonded defects between layers, fault characteristics and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.21-30
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• 2016

In this paper two procedures for determination of the elastic curve of the simply and multiple supported beams are developed. Determination of the elastic curve is complex as it requires to solve a strong nonlinear differential equation with given boundary conditions. For numerical solution the initial guess of the slope at the end of the beam is necessary. Two procedures for obtaining of the initial guess are developed: one, based on transformation of the supported beam into a clamped-free one, and second, on the linearization of the problem. Procedures are applied for calculating of elastic curve of a simply supported beam and a beam with three supports. Obtained results are compared. Advantages and disadvantages of both methods are discussed. It is proved that both suggested procedures give us technically accurate results.

• Membrane and Water Treatment
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• v.11 no.4
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• pp.295-302
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• 2020

In this paper, theoretical approach with applications of the periodic wave solutions in an elastic material is applied by study the effect of initial stress, and rotation, on the radial displacement and the corresponding stresses in non-homogeneous orthotropic material. An Analytical solution for the elastodynamic equation has obtained concerning the component of displacement. The variations of stresses and displacements have shown graphically. Comparisons with previously published results in the absence of initial stress, rotation and non-homogeneity have made. Finally, numerical results have given and illustrated graphically for each case considered.

• Journal of Environmental Science International
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• v.7 no.5
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• pp.697-705
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• 1998

$Pb^{2+}$ removal capacity and initial $Pb^{2+}$ removal rate were compared between non-biomaterials (granular activated carbon, powdered activated carbon, ion exchange resin, zeolite) and biomaterials (activated sludge, Aureobasidium pullulans, Saccharomyces cerevisiae). The $Pb^{2+}$ removal capacity of biomaterials were greater than that of non-biomaterials, generally. The $Pb^{2+}$ removal capacities of non-biomaterials and biomaterials were shown on the order of ion exchange resin ＞ zeolite ＞ granular activated carbon ＞ powdered activated carbon and A. pullulans ＞ S. cerevisiae ＞ activated sludge, respectively. In the initial $Pb^{2+}$ removal rate, the non-biomaterials showed powdered activated carbon ＞ granular activated carbon ＞ zeolite ＞ ion exchange resin and the biomaterials showed A. pullulans ＞ activated sludge ＞ S. cerevisiae. Comparing the $Pb^{2+}$ removal capacity and initial $Pb^{2+}$ removal rate of activated sludge with those of other non-biomaterials and biomaterials, activated sludge may have an availability on the removal of heavy metal ions by the economical and pratical aspects.

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.2
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• pp.11-15
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• 2009

This paper is concerned with the elastic buckling of thin-walled arches that are subjected to uniform bending. Nonlinear strain-displacement relations with the initial curvature are substituted into the second variation of the total potential energy to obtain the energy equation including initial curvature effects. The approximation for initial curvature effects that the bending normal strain distribution is linear across the cross section is applied consistently in the derivation process. The closed form solution is obtained for flexural-torsional buckling of arches under uniform bending and, it is compared with the previous theoretical results.

• Journal of The Korean Astronomical Society
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• v.39 no.4
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• pp.147-150
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• 2006

In this paper, initial value problem for dynamical astronomy will be established using parabolic cylindrical coordinates. Computation algorithm is developed for the initial value problem of gravity perturbed trajectories. Applications of the algorithm for the problem of final state predication are illustrated by numerical examples of seven test orbits of different eccentricities. The numerical results are extremely accurate and efficient in predicating final state for gravity perturbed trajectories which is of extreme importance for scientific researches as well as for military purposes. Moreover, an additional efficiency of the algorithm is that, for each of the test orbits, the step size used for solving the differential equations of motion is larger than 70% of the step size used for obtaining its reference final state solution.

• Transactions of Materials Processing
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• v.3 no.4
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• pp.401-414
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• 1994

Springback for the three point bending is anlayzed and experimented. Neutral axis is assumed to remain at the midthickness for large ratio of radius of curvature to thickness. Pure bending theory is used to be extended to the analysis of the springback for three point bending. The specimen is thought to be divided into numerous small elements. The theory for pure bending is then adopted for analysis of each element to obtain springback in terms of the relationship between initial and final deflections. the boundary conditions between neighborhood elements are the deflection and slope which should be the same. Deflection is calculated by summing up the deflections of each element. Experiments have been performed for different conditions which are punch radius, span length, and initial deflections. Comparisons between the analytical solution and experimental results show the same trends.