• 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)].

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.13-22
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• 2019

This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

• 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.

• Journal of Industrial Technology
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• v.31 no.A
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• pp.21-25
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• 2011

A comparison of temperature distributions along the fin length coordinate between two different fin tip boundary conditions for a circular pin fin is made by using the one-dimensional analytic method. One tip boundary condition is the actual fin tip boundary condition and fin tip temperature is arbitrarily given for another fin tip boundary condition. The value of the fin base temperature is depend on the fin base thickness and fin radius. One of the results shows that the temperature distribution along the fin length coordinate for the actual fin tip boundary condition and that for the arbitrarily given fin tip temperature are the same if the arbitrarily given fin tip temperature and the fin tip temperature for the actual fin tip boundary condition are the same.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.713-722
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• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• The Journal of Engineering Geology
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• v.32 no.4
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• pp.535-545
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• 2022

Improving the stability of the ground in seismic design requires an understanding of the dynamic behavior of the ground under seismic loads. The shaking table test is an important methodology to provide this understanding. This study aimed to assess the influence on boundary conditions, as they are among the most important factors affecting the test. This was achieved by testing the influence of boundary conditions on the seismic responses of model slopes at different locations in the testing apparatus. A model slope was fabricated at different locations in a laminar shear box, and the influence of the boundary conditions was then measured. Each model slope was created at 100, 50, and 25 cm from the soil wall, and sine wave seismic loads of the same size were inputted. The results confirmed that the acceleration was amplified by the influence of the boundary in the case of the slope being located 25 cm from the boundary, whereas the influence of the boundary conditions decreased when the slope was located at 50~100 cm.

• Journal of Power Electronics
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• v.13 no.2
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• pp.232-242
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• 2013

To obtain phase currents information in AC drives, shunt sensing technology is known to show great performance in cost-effectiveness and therefore it is widely used in low cost applications. However, shunt sensing methods are unable to acquire phase currents in certain operation conditions. This paper deals with the derivation of the boundary conditions for phase current reconstruction in three-shunt sensing inverters and proposes a voltage injection method to expand the measurable areas. As the boundary conditions are deeply dependent on the switching patterns, they are typically analyzed on the voltage vector plane for space vector pulse width modulation (SVPWM) and discontinuous pulse width modulation (DPWM). In the proposed method, the voltage injection and its compensation are conducted within one sampling period. This guarantees fast current reconstruction and the injected voltage is decided so as to minimize the current ripple. In addition to the voltage injection method, a sampling point shifting method is also introduced to improve the boundary conditions. Simulation and experimental results are presented to verify the boundary condition derivation and the effectiveness of the proposed voltage injection method.

• Smart Structures and Systems
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• v.6 no.8
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• pp.905-920
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• 2010

Changes in temperature, loads and boundary conditions may have effects on the dynamic properties of large civil structures. Taking the Run Yang Suspension Bridge as an example, modal properties obtained from ambient vibration tests and from the structural health monitoring system of the bridge are used to identify and evaluate the modal parameter variability. Comparisons of these modal parameters reveal that several low-order modes experience a significant change in frequency from the completion of the bridge to its operation. However, the correlation analysis between measured modal parameters and the temperature shows that temperature has a slight influence on the low-order modal frequencies. Therefore, this paper focuses on the effects of the boundary conditions on the dynamic behaviors of the suspension bridge. An analytical model is proposed to perform a sensitivity analysis on modal parameters of the bridge concerning the stiffness of expansion joints located at two ends of bridge girders. It is concluded that the boundary conditions have a significant influence on the low-order modal parameters of the suspension bridge. In addition, the influence of vehicle load on modal parameters is also investigated based on the proposed model.