• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.59-68
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• 2022

Prestressed prefabricated hollow core concrete slabs with spans of 5 m and 10 m are commonly used since last century and still in service due to the advantage of construction convenience and durability. However, the end slabs are regularly subjected to cracks at the top and fail with brittleness due to the asymmetric boundary conditions. To better maintain such widely used type of hollow core slabs, the effect of asymmetric constraint in the end slabs are systematically studied through detailed nonlinear finite element analyses and experimental data. Experimental tests of slabs with four prestressed tendons and seven prestressed tendons with different boundary conditions were conducted. Results observe three failure modes of the slabs: the bending failure mode, shear and torsion failure mode, and transverse failure mode. Detailed nonlinear finite element models are developed to well match the failure modes and to reveal potential damage scenarios with asymmetric boundary conditions. Recommendations regarding ultimate capacity of the slabs with asymmetric boundary conditions are made to ensure a safe and rational design of prestressed concrete hollow slabs for short span bridges.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.572-581
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• 2006

This study is to investigate dynamic response of concrete buried pipelines with various end boundary conditions and develop a curve fitted equation to ensure practicality and convenience for the use at the actual field for the test of resistance of earthquake. Dynamic response under the various end boundary conditions is calculated with analysis on values and computing programs. However, such a method of analysis requires skillfulness in using computing programs for dynamic movement of buried pipelines with dynamic analysis formula and has lower efficiency and practicality because, in the nature of analysis program of values, it needs much time to conduct repeated calculations. Therefore, the study is intended to develop a curve fitted equation to ensure more efficient and practical analysis. This paper tests various degrees of equation with non-linear least square method and developments a curve fitted equation based on the transmission speed with the best results. In the use of curve fitted equation, degree of polynomial and determining coefficient are influenced by the speed of transmission.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.159-166
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• 2000

Non-destructive out-hole tests, impact-echo and impact-response are widely applied to evaluate integrity of drilled shafts. In these tests, vibratory motions of drilled shafts are interpreted, which induced by impacts on the shaft head. In applying the tests to evaluating integrity of shaft, it has been attended whether the tests have resolutions enough to distinguish existence of slime at between the shaft end and a bearing soil deposit. To distinguish existence of slime by tests, modes of shaft vibrations need to be reasonably interpreted, which generally vary according to a shaft boundary condition such as, a free-free or a free-fixed condition. The boundary condition of a shaft is, however, found to be significantly affected by stiffness of soil deposits around shaft as well as penetration depths of shaft into a bearing soil deposit. Thus, these effects on the boundary condition of a shaft should be considered reasonably in interpreting test results to decide the existence of slime. To investigate the effects, in this study, vibratory motions of shafts constructed in various soil conditions and end penetration depths are examined analytically. Based on the studies, variations of boundary condition are characterized in terms of soil stiffness contrast between a shaft perimeter and a shaft end, and also the ratio of a penetration depth to a shaft length. The results can be applied to verify the applicability of tests to identify the slime.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.1148-1158
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• 2005

This work reports results of our study on the dynamic responses of the buried pipelines both along the axial and the transverse directions under various boundary end conditions. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends. We have studied the seismic responses of the buried pipelines with the various boundary end conditions both along the axial and the transverse direction. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends for the axial direction, and three more cases including the guided ends, the simply supported ends, and the supported-guided ends for the transverse direction. The buried pipelines are modeled as beams on elastic foundation while the seismic waves as a ground displacement in the form of a sinusoidal wave. The natural frequency and its mode, and the effect of parameters have been interpreted in terms of free vibration. The natural frequency varies most significantly by the soil stiffness and the length of the buried pipelines in the case of free vibration, which increases with increasing soil stiffness and decreases with increasing length of the buried pipeline. Such a behavior appears most prominently along the axial rather than the transverse direction of the buried pipelines. The resulting frequencies and the mode shapes obtained from the free vibration for the various boundary end conditions of the pipelines have been utilized to derive the mathematical formulae for the displacements and the strains along the axial direction, and the displacements and the bending strains along the transverse direction in case of the forced vibration. The negligibly small difference of 6.2% between our result and that of Ogawa et. al. (2001) for the axial strain with a one second period confirms the accuracy of our approach in this study.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.87-94
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• 2000

This paper investigates history and modern developments concerning spatial decay estimates for solutions in a semi-infinite cylinder or strip, in which model equations are defined with appropriate homogeneous lateral boundary conditions and initial conditions but left end boundary data are assumed. Our aim is to show this Saint-Venant type decay rate dependent critically on the Poincare constant resulting from characterizing variational principles.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.328-337
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• 2005

This work reports results of our study on the dynamic responses of the buried pipelines both along the axial and the transverse directions under various boundary end conditions. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends for the axial direction, and three more cases including the guided ends, the simply supported ends, and the supported-guided ends for the transverse direction. In order to investigate the effect of the boundary end conditions for the dynamic responses of the buried pipeline, we have devised a computer program to find the solutions of the formulae on the dynamic responses (displacements, axial strains, and bending strains) under the various boundary end conditions considered in this study. The dynamic behavior of the buried pipelines for the forced vibration is found to exhibit two different forms, a transient response and a steady state response, depending on the time before and after the transfer of a seismic wave on the end of the buried pipeline. The former is identified by a slight change in its behavior before the sinusoidal-shaped seismic wave travels along the whole length of the pipeline whereas the latter by the complete form of a sinusoidal wave when the wave travels throughout the pipeline. The transient response becomes insignificant as the wave speed increases. We have observed a resonance when the mode wavelength matches the wavelength of the seismic wave, where the mode number(k) of resonance for the axial direction is found to be $\overline{\omega}/{\pi}V+1/2$ for the fixed-free ends, $\overline{\omega}/{\pi}V+1$ for the free ends, and $\overline{\omega}/{\pi}V$ for the fixed ends, respectively. By adding 10 more modes to the mode number(k) of resonance, we were able to study all the dynamic responses of the buried pipeline for the axial direction. On the other hand, we have not been able to observe a resonance in the analysis for the transverse direction, because the dynamic responses are found to vanish after the seventh mode. From the results of the dynamic responses at the many points of the pipeline, we have found that the responses appeared to be dependent critically on the boundary end conditions. Such effects are found to be most prominent especially for the maximum values of the displacement and the strain and its position.

• Journal of the Korean Geotechnical Society
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• v.21 no.5
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• pp.33-43
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• 2005

This work reports results of our study on the dynamic responses of the buried pipelines both along the axial and the transverse directions under various boundary end conditions. In order to investigate the effect of the boundary end conditions for the dynamic responses of the buried pipeline, we have devised a computer program to find the solutions of the formulae on the dynamic responses (displacements, axial strains, and bending strains) under the various boundary end conditions considered in this study, The dynamic behavior of the buried pipelines for the forced vibration is found to exhibit two different forms, a transient response and a steady state response, depending on the time before and after the transfer of a seismic wave on the end of the buried pipeline. We have observed a resonance when the mode wavelength matches the wavelength of the seismic wave, where the mode number(k) of resonance f3r the axial direction. On the other hand, we have not been able to observe a resonance in the analysis of the transverse direction, because the dynamic responses are found to vanish after the seventh mode. From the results of the dynamic responses at many points of the pipeline, we have found that the responses appeared to be dependent critically on the boundary end conditions. Such effects are found to be most prominent especially for the maximum values of the displacement, the strain and its position.

• Structural Engineering and Mechanics
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• v.23 no.5
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.