• Geomechanics and Engineering
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• v.11 no.4
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• pp.587-605
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• 2016

This study aimed to develop upper and lower bounds to predict the tunnel support pressure under the pile tip during the circular tunnel excavation. Most previous studies on the upper and lower bound methods were carried out for the single ground structures, e.g., retaining wall, foundation, ground anchor and tunnel, in the homogeneous ground conditions, since the pile-soil-tunnel interaction problem is very complicated and sophisticated to solve using those bound methods. Therefore, in the lower bound approach two appropriate stress fields were proposed for single pile and tunnel respectively, and then they were superimposed. In addition, based on the superimposition several failure mechanisms were proposed for the upper bound solution. Finally, these upper bound mechanisms were examined by shear strain data from the laboratory model test and numerical analysis using finite element method.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1549-1559
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• 2008

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.399-407
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• 2006

In this paper, we consider the problem of achieving a prescribed scalar curvature on warped product manifolds according to fiber manifolds with zero scalar curvature.

• Journal of the Society of Naval Architects of Korea
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• v.56 no.5
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• pp.418-426
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• 2019

To derive a simplified analytic solution which can be utilized as a fundamental solution for the wave maker design, a segment of the wave board has been idealized as a submerged line segment in a two dimensional domain of a wave flume. The lower end of the line segment could be located at arbitrary depth of the wave flume and the upper end of the board could be also submerged to any depth from the free surface. The freely oscillating motion of the wave board is assumed to be defined by determining the condition of horizontal oscillation on both ends differently. The submerged wave board oscillating in horizontal direction could be specified by selecting the amplitude, frequency and the phase lag differently on lower and upper ends of the board. The simplified two dimensional wave generated by the wave board segment has been obtained by the first order perturbation method. It is found that the general solution of the freely oscillating wave board in two dimensional domain could be decomposed into the solution of flap motion with lower end hinge and swing motion with upper end hinge. The case study of the analytic solutions has been carried out to evaluate the effect on the wave height due to the difference of oscillation frequency, phase difference and variation of stroke between for the motion of both ends. It is found that the solution of the freely oscillating wave board could be utilized for the development of high performance wavemaker especially for irregular waves.

• Journal of the Korean Operations Research and Management Science Society
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• v.41 no.4
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• pp.113-128
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• 2016

This paper proposes a Bi-level Genetic Algorithm for the Fixed Charge Transportation Problem with Non-linear Unit Cost. The problem has the property of mixed integer program with non-linear objective function and linear constraints. The bi-level procedure consists of the upper-GA and the lower-GA. While the upper-GA optimize the connectivity between each supply and demand pair, the lower-GA optimize the amount of transportation between the pairs set to be connected by the upper-GA. In the upper-GA, the feasibility of the connectivity are verified, and if a connectivity is not feasible, it is modified so as to be feasible. In the lower-GA, a simple method is used to obtain a pivot feasible solution under the restriction of the connectivity determined by the upper-GA. The obtained pivot feasible solution is utilized to generate the initial generation of chromosomes. The computational experiment is performed on the selected problems with several non-linear objective functions. The performance of the proposed procedure is analyzed with the result of experiment.

• 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.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.221-228
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• 2013

The method of upper and lower solutions and the generalized quasilinearization technique is developed for the existence and approximation of solutions to boundary value problems for higher order fractional differential equations of the type $^c\mathcal{D}^qu(t)+f(t,u(t))=0$, $t{\in}(0,1),q{\in}(n-1,n],n{\geq}2$ $u^{\prime}(0)=0,u^{\prime\prime}(0)=0,{\ldots},u^{n-1}(0)=0,u(1)={\xi}u({\eta})$, where ${\xi},{\eta}{\in}(0,1)$, the nonlinear function f is assumed to be continuous and $^c\mathcal{D}^q$ is the fractional derivative in the sense of Caputo. Existence of solution is established via the upper and lower solutions method and approximation of solutions uses the generalized quasilinearization technique.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.625-637
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• 2010

In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions, we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1361-1370
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• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.