• Geomechanics and Engineering
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• v.6 no.1
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• pp.65-77
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• 2014

Geosynthetic tubes inflated with water, clay slurry or sand have been widely used for large dike construction in land reclamation projects. In this paper, analytical solutions for geosynthetic tube resting on rigid foundation is presented by adopting an approach similar to that presented by Leshchinsky et al. (1996). The proposed method allows a quick preliminary design to be made for using a closed-form solution. To simplify the analysis, relationships between geometrical parameters and pumping pressure are established using numerical method. The analytical solutions were compared with several existing solutions and good agreements were achieved.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.491-502
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• 2019

This paper explores the analytical buckling solution of rectangular thin plates by the finite integral transform method. Although several analytical and numerical developments have been made, a benchmark analytical solution is still very few due to the mathematical complexity of solving high order partial differential equations. In solution procedure, the governing high order partial differential equation with specified boundary conditions is converted into a system of linear algebraic equations and the analytical solution is obtained classically. The primary advantage of the present method is its simplicity and generality and does not need to pre-determine the deflection function which makes the solving procedure much reasonable. Another advantage of the method is that the analytical solutions obtained converge rapidly due to utilization of the sum functions. The application of the method is extensive and can also handle moderately thick and thick elastic plates as well as bending and vibration problems. The present results are validated by extensive numerical comparison with the FEA using (ABAQUS) software and the existing analytical solutions which show satisfactory agreement.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.583-612
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• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.

• Journal of the Optical Society of Korea
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• v.18 no.4
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• pp.365-369
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• 2014

We present accurate analytical solutions of the lineshapes of birefringence (rotation) and dichroism (absorption) spectroscopy for a circular anisotropic medium composed of atoms of the transition $J_g=0{\rightarrow}J_e=1$. The susceptibility of a weak probe beam was analytically calculated and was averaged over a Maxwell-Boltzmann velocity distribution. The lineshapes of the two spectroscopies were then presented in analytical forms at arbitrary values of the linewidths of the inhomogeneous (Doppler) broadening and the homogeneous (natural) broadening of the atoms.

• Smart Structures and Systems
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• v.3 no.2
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• pp.173-188
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• 2007

The general solution for two-dimensional magneto-electro-elastic media in terms of four harmonic displacement functions is proposed analytically. The expressions of specific solutions of magneto-electro-elastic plane problems with specific body forces are derived. Finally, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally gradient media, two kinds of beam problems with body forces depending only on the z or x coordinate are solved by the trial-and-error method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.6
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• pp.1773-1783
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• 1996

Finite element method(FEM) is one of the most popularly used method analyzing the dynamic behaviors of structures. But unless number of finite elements is large enough, the results from FEM some what different from exact analytical solutions, especially at high frequency range. On the other hand, as the spectral analysis method(SAM) deals directly with the governing equations of a structure, the results from this melthod cannot but be exact regardless of any frequency range. However, the SAM can be applied only to the case where a structure is subjected to the concentrated loads, despite a structure could be unddergone distributed loads more generally. In this paper, therefore, new spectral analysis algorithm is introduced through the spectral element method(SEM), so that it can be applied to anlystructures whether they are subjected to the concentrated loads or to the distributed loads. The results from this new SEM are compared with both the results from FEM and the exact analytical solutions. As expected, the results from new SEM algorithm are found to be almost identical to the exact analytical solutions while those from FEM are not agreed well with the exact analytical solutions as the mode number increases.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.208-215
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• 2003

Convective-diffusion equations appear in various disciplines such as hydrology, chemical engineering and oceanography dealing with the transport problem of scalar quantities. Since it is nonlinear, numerical methods are generally used to obtain its solution. Very limited number of analytical solutions are available usually in cases when the convective velocity is constant or has a simple functional form (for some collection of the solutions, see Noye, 1987). There is however a continuing need to develop analytical solutions because of its practical importance. Analytical solutions of the convection-diffusion equation are valuable not only for the better understanding on the transport process but the verification of numerical schemes. (omitted)

• Geomechanics and Engineering
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• v.18 no.3
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• pp.299-313
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• 2019

This research investigated the nonlinear compressibility, permeability, the yielding due to structural degradation and their effects on consolidation behavior of structured soft soils. Based on oedometer and hydraulic conductivity test results of natural and reconstituted soft clays, linear log (1+e) ~ $log\;{\sigma}^{\prime}$ and log (1+e) ~ $log\;k_v$ relationships were developed to capture the variations in compressibility and permeability, and the yield stress ratio (YSR) was introduced to characterize the soil structure of natural soft clay. Semi-analytical solutions for one-dimensional consolidation of soft clay under time-dependent loading incorporating the effects of soil nonlinearity and soil structure were proposed. The semi-analytical solutions were verified against field measurements of a well-documented test embankment and they can give better accuracy in prediction of excess pore pressure compared to the predictions using the existing analytical solutions. Additionally, parametric studies were conducted to analyze the effects of YSR, compression index (${\lambda}_r$ and ${\lambda}_c$), and permeability index (${\eta}_k$) on the consolidation behavior of structured soft clays. The magnitude of the difference between degree of consolidation based on excess pore pressure ($U_p$) and that based on strain ($U_s$) depends on YSR. The parameter ${\lambda}_c/{\eta}_k$ plays a significant role in predicting consolidation behavior.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.34 no.3
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• pp.58-71
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• 2022

Analytical solutions for two-dimensional velocities of regular waves generated by bottom wave makers in a flume were derived in this study. Triangular and rectangular bottom wave makers were adopted. The velocity potential was derived based on the linear wave theory with the bottom moving boundary condition, kinematic and dynamic free surface boundary conditions. Then, analytical solutions of two-dimensional particle velocities were derived from the velocity potential. The velocity potential and two-dimensional particle velocities which were derived as complex integral equations were numerically calculated. The solutions showed physically valid results as velocities of regular waves generated by bottom wave makers in a flume.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.