• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.127-136
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• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• Computers and Concrete
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• v.27 no.3
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• pp.199-210
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• 2021

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.823-835
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• 2019

A solution for Nevanlinna-Pick interpolation problem with low complexity is constructed via non-recursive method. More precisely, a stable rational function satifying the given interpolation data in the complex right half plane is found by solving a homogeneous interpolation problem related to a minial interpolation problem for the given data in the right half plane together with its mirror-image data.

• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.473-479
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• 2021

The propagation of plane waves in a linear, homogeneous and isotropic nonlocal generalized thermoelastic solid medium is considered in the framework of Lord and Shulman generalization. The governing field equations are formulated and specialized in a plane. Plane wave solutions of governing equations show that there exists three plane waves, namely, P, thermal and SV waves which propagate with distinct speeds. Reflection of P and SV waves from thermally insulated or isothermal boundary of a half-space is considered. The relevant boundary conditions are applied at stress free boundary and a non-homogeneous system of three equations in reflection coefficients is obtained. For incidence of both P and SV waves, the expressions for energy ratios of reflected P, thermal and SV waves are also obtained. The speeds and energy ratios of reflected waves are computed for relevant physical constants of a thermoelastic material. The speeds of plane waves are plotted against nonlocal parameter and frequency. The energy ratios of reflected waves are also plotted against the angle of incidence of P wave at a thermally insulated stress-free surface. The effect of nonlocal parameter is shown graphically on the speeds and energy ratios of reflected waves.

• Earthquakes and Structures
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• v.5 no.2
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• pp.161-205
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• 2013

We study seismically induced, anti-plane strain wave motion in a non-homogeneous geological region containing tunnels. Two different scenarios are considered: (a) The first models two tunnels in a finite geological region embedded within a laterally inhomogeneous, layered geological profile containing a seismic source. For this case, labelled as the first boundary-value problem (BVP 1), an efficient hybrid technique comprising the finite difference method (FDM) and the boundary element method (BEM) is developed and applied. Since the later method is based on the frequency-dependent fundamental solution of elastodynamics, the hybrid technique is defined in the frequency domain. Then, an inverse fast Fourier transformation (FFT) is used to recover time histories; (b) The second models a finite region with two tunnels, is embedded in a homogeneous half-plane, and is subjected to incident, time-harmonic SH-waves. This case, labelled as the second boundary-value problem (BVP 2), considers complex soil properties such as anisotropy, continuous inhomogeneity and poroelasticity. The computational approach is now the BEM alone, since solution of the surrounding half plane by the FDM is unnecessary. In sum, the hybrid FDM-BEM technique is able to quantify dependence of the signals that develop at the free surface to the following key parameters: seismic source properties and heterogeneous structure of the wave path (the FDM component) and near-surface geological deposits containing discontinuities in the form of tunnels (the BEM component). Finally, the hybrid technique is used for evaluating the seismic wave field that develops within a key geological cross-section of the Metro construction project in Thessaloniki, Greece, which includes the important Roman-era historical monument of Rotunda dating from the 3rd century A.D.

• Structural Engineering and Mechanics
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• v.82 no.3
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• pp.401-416
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• 2022

The aim of this study is to examine the frictionless double receding contact problem for two functionally graded (FG) layers pressed with a uniformly distributed load and resting on a homogeneous half plane (HP) using analytical and numerical methods. The FG layers are made of a non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layers and FG layer-HP interface is frictionless. The body force of the FG layers and homogeneous HP are ignored in the study. Firstly, an analytical solution for the contact problem has been realized using the theory of elasticity and the Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using the ANSYS package program based on FEM. Numerical results for contact lengths and contact pressures between FG layers and FG layer-HP were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio, and the heights of the FG layers for both methods. The results obtained using FEM were compared with the results found using the analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.