• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.81-92
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• 2017

Many materials in engineering exhibit different modulus in tension and compression, which are known as bi-modulus materials. Based on the bi-modulus elastic theory, a modified semi-analytical model, by introducing a stress function, is established in this paper to study the mechanical response of a bi-modulus cylinder placed in an axisymmetric temperature field. Meanwhile, a numerical procedure to calculate the temperature stresses in bi-modulus structures is developed. It is proved that the bi-modulus solution can be degenerated to the classical same modulus solution, and is in great accordance with the solutions calculated by the semi-analytical model proposed by Kamiya (1977) and the numerical solutions calculated both by the procedure complied in this paper and by the finite element software ABAQUS, which demonstrates that the semi-analytical model and the numerical procedure are accurate and reliable. The result shows that the modified semi-analytical model simplifies the calculation process and improves the speed of computation. And the numerical procedure simplifies the modeling process and can be extended to study the stress field of bi-modulus structures with complex geometry and boundary conditions. Besides, the necessity to introduce the bi-modulus theory is discussed and some suggestions for the qualitative analysis and the quantitative calculation of such structure are proposed.

• Geomechanics and Engineering
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• v.25 no.4
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• pp.267-273
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• 2021

In this work, we compare the analytical solutions with the numerical solutions for photothermal interactions in semiconductor medium containing cylindrical cavity. This paper is devoted to a study of the photothermal interactions in semiconductor medium in the context of the coupled photo-thermal model. The basic equations are formulated in the domain of Laplace transform and the eigenvalue scheme are used to get the analytical solutions. The numerical solution is obtained by using the implicit finite difference method (IFDM). A comparison between the analytical solution and the numerical solutions are obtained. It is found that the implicit finite difference method (IFDM) is applicable, simple and efficient for such problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1967-1973
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• 1994

The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

• 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.

• Economic and Environmental Geology
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• v.53 no.1
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• pp.11-21
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• 2020

One-dimensional analytical solutions were used for forward and back diffusion of trichloroethylene (TCE) and tetrachloroethylene (PCE) in a single system with high- and low-permeability layers. Concentration profiles in a low-permeability layer, diffusive fluxes at the interface between the high- and low-permeability layers, and contaminant persistence in the high-permeability layer due to back diffusion were simulated with a comparison of semi-infinite and finite analytical solutions. In order to validate the analytical solutions used in this study, the results of one-dimensional analytical solutions developed by Yang et al. (2015) were compared with Nash-Sutcliffe model efficiency coefficient (NSE). When compared with Yang et al. (2015), the analytical solutions used in this study showed good agreements (NSE = 0.99). When compared with semi-infinite analytical solutions, TCE and PCE concentration profiles in the low-permeability layer, the diffusive fluxes, and the contaminant tailings of the high-permeability layer were underestimated. In order to determine the appropriate analytical solutions based on the effective diffusion coefficient, the thickness of the low-permeability layer, and the diffusion time in the TCE and PCE contaminated site, a term of dimensionless diffusion length (Z_d) was used. If the Z_d is less than 0.7, the semi-infinite solutions can be used to simulate accurate concentration profiles in low-permeability layers. If the Z_d is greater than 0.7, the reliability of simulations may be improved by using the finite solutions.

• Journal of the Semiconductor & Display Technology
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• v.20 no.3
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• pp.11-17
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• 2021

I performed a semi-analytical numerical analysis of the effects of core size and electric field intensity on the light emission wavelength of CdSe/ZnS quantum dots (QDs). The analysis used a quantum mechanical approach; I solved the Schrödinger equation describing the electron-hole pairs of QDs. The numerical solutions are described using a basis set composed of the eigenstates of the Schrödinger equation; they are thus equivalent to analytical solutions. This semi-analytical numerical method made it simple and reliable to evaluate the dependency of QD characteristics on the QD core size and electric field intensity. As the QD core diameter changed from 9.9 to 2.5 nm, the light emission wavelength of CdSe core-only QDs varied from 262.9 to 643.8 nm, and that of CdSe/ZnS core/shell QDs from 279.9 to 697.2 nm. On application of an electric field of 8 × 10⁵ V/cm, the emission wavelengths of green-emitting CdSe and CdSe/ZnS QDs increased by 7.7 and 3.8 nm, respectively. This semi-analytical numerical analysis will aid the choice of QD size and material, and promote the development of improved QD light-emitting devices.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.3
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• pp.156-164
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• 1999

Two analytical solutions for wave diffraction by a semi-infinite breakwater, which Penney and Price (1952), and Stoker (1957) presented, are rederived. Since in previous works the derivations were skipped or briefly given, in the paper the derivation is brought into focus. Numerical computations of the solutions are presented and solution behavior of Stoker's method due to a number of terms in the series is analyzed.

• Steel and Composite Structures
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• v.39 no.3
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• pp.291-306
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• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• Steel and Composite Structures
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• v.48 no.6
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• pp.641-648
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• 2023

In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.

• Ocean Systems Engineering
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• v.3 no.1
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• pp.55-70
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• 2013

A composite breakwater with an upper horizontal porous plate and a lower rubble mound is proposed and studied in this work. By means of matched eigenfunction expansions, a semi-analytical solution is developed for analyzing the hydrodynamic performance of the breakwater. The semi-analytical solution is verified by known solutions for special cases and an independently developed multi-domain boundary element method solution. Numerical examples are given to examine the reflection, transmission and energy loss coefficients of the breakwater and the wave force acting on the horizontal porous plate. Some useful results are presented for engineering applications.