• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.707-720
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• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• Journal of the Korean Solar Energy Society
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• v.36 no.3
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Geomechanics and Engineering
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• v.19 no.5
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• pp.463-472
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• 2019

The mode perturbation method (MPM) is suitable and efficient for solving the eigenvalue problem of a nonuniform soil deposit whose property varies with depth. However, results of the MPM do not always converge to the exact solution, when the variation of soil deposit property is discontinuous. This discontinuity is typical because soil is usually made up of sedimentary layers of different geologic materials. Based on the energy integral of the variational principle, a new mode perturbation method, the energy-based mode perturbation method (EMPM), is proposed to address the convergence of the perturbation solution on the natural frequencies and the corresponding mode shapes and is able to find solution whether the soil properties are continuous or not. First, the variational principle is used to transform the variable coefficient differential equation into an equivalent energy integral equation. Then, the natural mode shapes of the uniform shear beam with same height and boundary conditions are used as Ritz function. The EMPM transforms the energy integral equation into a set of nonlinear algebraic equations which significantly simplifies the eigenvalue solution of the soil layer with variable properties. Finally, the accuracy and convergence of this new method are illustrated with two case study examples. Numerical results show that the EMPM is more accurate and convergent than the MPM. As for the mode shapes of the uniform shear beam included in the EMPM, the additional 8 modes of vibration are sufficient in engineering applications.

• Journal of Magnetics
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• v.16 no.3
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• pp.240-245
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• 2011

A new hybrid ON/OFF method is presented for the fast solution of electromagnetic inverse problems in high frequency domains. The proposed method utilizes both topological sensitivity (TS) and material sensitivity (MS) to update material properties in unit design cells. MS provides smooth design space and stable convergence, while TS enables sudden changes of material distribution when MS slows down. This combination of two sensitivities enables a reduction in total computation time. The TS and MS analyses are based on a variational approach and an adjoint variable method (AVM), which permits direct calculation of both sensitivity values from field solutions of the primary and adjoint systems. Investigation of the formulations of TS and MS reveals that they have similar forms, and implementation of the hybrid ON/OFF method that uses both sensitivities can be achieved by one optimization module. The proposed method is applied to dielectric material reconstruction problems, and the results show the feasibility and effectiveness of the method.

• Journal of Environmental Science International
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• v.19 no.8
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• pp.983-999
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• 2010

Wind power energy is one of the favorable and fast growing renewable energies. It is most important for exact analysis of wind to evaluate and forecast the wind power energy. The purpose of this study is to improve the performance of numerical atmospheric model by data assimilation over a complex coastal area. The benefit of the profiler is its high temporal resolution and dense observation data at the lower troposphere. Three wind profiler sites used in this study are inhomogeneously situated near south-western coastal area of Korean Peninsula. The method of the data assimilation for using the profiler to the model simulation is the three-dimensional variational data assimilation (3DVAR). The experiment of two cases, with/without assimilation, were conducted for how to effect on model results with wind profiler data. It was found that the assimilated case shows the more reasonable results than the other case compared with vertical observation and surface Automatic Weather Station(AWS) data. Although the effect of sonde data was better than profiler at a higher altitude, the profiler data improves the model performance at lower atmosphere. Comparison with the results of 4 June and 5 June suggests that the efficiency with hourly assimilated profiler data is strongly influenced by synoptic conditions. The reduction rate of Normalized Mean Error(NME), mean bias normalized by averaged wind speed of observation, on 4 June was 28% which was larger than 13% of 5 June. In order to examine the difference in wind power energy, the wind power density(WPD) was calculated and compared.

• Wind and Structures
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• v.19 no.1
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• pp.35-58
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• 2014

A numerical simultaneous solution involving a linear elastic model was applied to study the fluid-structure interaction (FSI) of membrane structures under wind actions, i.e., formulating the fluid-structure system with a single equation system and solving it simultaneously. The linear elastic model was applied to managing the data transfer at the fluid and structure interface. The monolithic equation of the FSI system was formulated by means of variational forms of equations for the fluid, structure and linear elastic model, and was solved by the Newton-Raphson method. Computation procedures of the proposed simultaneous solution are presented. It was applied to computation of flow around an elastic cylinder and a typical FSI problem to verify the validity and accuracy of the method. Then fluid-structure interaction analyses of a saddle membrane structure under wind actions for three typical cases were performed with the method. Wind pressure, wind-induced responses, displacement power spectra, aerodynamic damping and added mass of the membrane structure were computed and analyzed.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.361-369
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• 2012

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Journal of Korean Society of Transportation
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• v.20 no.1
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• pp.77-90
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• 2002

Network expansion has been an inevitable method for most traffic equilibrium assignments to consider intersection movements such as intersection delays. The drawback of network expansion is that because it dramatically increases network sizes to emulate possible directional movements as corresponding links, not only is complexities for building network amplified, but computational performance is shrunk. This paper Proposes a new variational inequality formulation for a user-optimal traffic equilibrium assignment model to explicitly consider directional delays without building expanded network structures. In the formulation, directional delay functions are directly embedded into the objective function, thus any modification of networks is not required. By applying a vine-based shortest Path algorithm into the diagonalization algorithm to solve the problem, it is additionally demonstrated that various loop-related movements such as U-Turn, P-Turn, etc., which are frequently witnessed near urban intersections, can also be imitated by blocking some turning movements of intersections. The proposed formulation expects to augment computational performance through reduction of network-building complexities.

• Journal of the Korean Magnetics Society
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• v.1 no.2
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• pp.79-84
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• 1991

A variational approach employing localized functional is presented to solve alternating magnetic field problems with open boundary. The functional used in the approach consists of the domain integral of finite element region only and the boundary integral of the interfacial boundary between the finite and infinite element regions. The boundary integral is obtained by transforming the infinite domain integral for the infinite element region into the interfacial boundary integral. The proposed algorithm is then applied to a simple two-dimensional problem where the analytic solutions are available. It is shown that the algorithm makes it possible to yield good agreements between the numerical and analytic solutions. and that it requires less computer storage memory and computation time than the conventional finite element method due to the reduction of the computing region.