• 대한수학회논문집
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• 제36권3호
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

• 전산구조공학
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• 제6권4호
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• pp.89-98
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• 1993

최근 원자력의 사용이 증가함에 따라 핵폐기물을 효과적으로 처리하는 문제에 관심이 집중되고 있다. 이러한 핵폐기물을 지층내에 저장할 경우 고온의 열에 의해 핵폐기물 구조체에 지대한 영향을 미치므로 지반의 열력학적 거동을 분석할 필요성이 요구된다. 본 연구는 지반내에 처분된 고온의 사용후 핵연료에 의한 열역학적인 응력이 집중되어 비선형 거동이 예상되는 저장구조체 주변에는 비선형 유한요소를 적용하고 선형거동이 예상되는 무한영역에는 선형경계요소를 사용하여, 일반적인 역학적 계와 동일한 방법으로 비선형 유한요소와 경계요소를 조합한 프로그램을 개발하였다. 사용후 핵연료 폐기구조체와 같이 국부적인 비선형거동이 예상되는 구조물에서는 조합방법이 전 영역을 비선형 유한요소로 모형화하여 해석하는 것보다 효율적임을 알 수 있었다. 또한, 지층내 지반에 영향 미치는 주요 지반계수를 변화시킨 경우, 터널경계의 변위에 이러한 계수들이 어떠한 영향을 미치는가를 개발된 방법을 사용하여 검토하였다. 검토결과, 다른 계수들의 변화보다 열팽창계수의 변화가 터널주위의 변위에 상당한 영향을 미침을 알 수 있었다.

• 한국해안해양공학회지
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• 제3권3호
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• pp.176-183
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• 1991

본 연구는 경계요소법을 이용하여 비선형 자유표면파을 해석한 것이며, 가상경계처리는 유체 연속성을 고려하여 mass-flux와 energy-flux를 사용하여 유한진폭파동의 해석수법을 제시했다. 유체의 비선형성 때문에 증분법을 적용했으며 경계요소법에 의해 얻어진 결과는 유한요소법의 결과와 실험치와 비교하여 보았으며 좋은 일치가 얻어 졌다. 따라서, 이 방법은 광범위한 파동문제 해석에 유효하게 이용될 수 있으리라 사료된다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1995년도 봄 학술발표회 논문집
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• pp.28-34
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• 1995

Behavior of underground structural systems is usually complicated because of various unknown parameters. In order to construct those structural systems safely and economically, exact identification of the system parameters and accurate analysis of the system behaviors are essentially required. In this study, a forward analysis program, which is able to eliminate numerical errors due to far field boundary effect, is developed by coupling finite and boundary elements. In this coupled analysis, boundary elements are used in the semi-infinite domain where stress variation is small, and finite elements in the stress concentration region where material nonlinearity should be considered. Then, a back analysis program which can identify the system parameters is developed using the direct method to be combined with the forward analysis program. The elastic modulus and initial stress, which are most important in the description of the behavior of underground structures, are taken as the system parameters. A simple example is examined 0 show that the method can be used effectively.

• Earthquakes and Structures
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• 제12권2호
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• pp.251-262
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• 2017

The present research intends to study the effects of the seismic soil-foundation-structure interaction (SFSI) on the dynamic response of various buildings. Two methods including direct and Cone model were studied through 3D finite element method using ABAQUS software. Cone model as an approximate method to consider the SFSI phenomenon was developed and evaluated for both high and low rise buildings. Effect of soil nonlinearity, foundation rigidity and embedment as well as friction coefficient between soil-foundation interfaces during seismic excitation are investigated. Validity and performance of both approaches are evaluated as reference graphs for Cone model and infinite boundary condition, soil nonlinearity and amplification factor for direct method. A series of calculations by DeepSoil for inverse earthquake record modification was conducted. A comparison of the two methods was carried out by root-mean-square-deviation (RMSD) tool for maximum lateral displacement and story shear forces which verifies that Cone model results have good agreement with direct method. It was concluded that Cone method is a convenient, fast and rather accurate method as an approximate way to count for soil media.

• 한국소음진동공학회논문집
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• 제26권3호
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• pp.281-289
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• 2016

In this paper, a new dynamic model for modal analysis of a rotating cantilever beam with a tip-mass is developed. The nonlinear strain such as von Karman type and the corresponding linearized stress are used to consider the geometric nonlinearity, and Euler-Bernoulli beam theory is applied in the present model. The nonlinear equations of motion and the associated boundary conditions which include the inertia of the tip-mass are derived through Hamilton's principle. In order to investigate modal characteristics of the present model, the linearized equations of motion in the neighborhood of the equilibrium position are obtained by using perturbation technique to the nonlinear equations. Since the effect of the tip-mass is considered to the boundary condition of the flexible beam, weak forms are used to discretize the linearized equations. Compared with equations related to stiffening effect due to centrifugal force of the present and the previous model, the present model predicts the dynamic characteristic more precisely than the another model. As a result, the difference of natural frequencies loci between two models become larger as the rotating speed increases. In addition, we observed that the mode veering phenomenon occurs at the certain rotating speed.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Structural Engineering and Mechanics
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• 제68권2호
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• pp.261-275
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• 2018

A comprehensive study was provided to investigate the buckling behavior of the steel plates with and without through-thickness holes subjected to uniaxial compression using ABAQUS. The method was validated by the results reported in the literature. Using the critical stresses, the buckling coefficients ($K_c$) were calculated. The effects of inclusion of material nonlinearity, plate thickness (t), aspect ratio (AR), and initial imperfection on buckling resistance of the plate was studied. Besides, the effects of having the hole in the plate were also studied. The diameter of the hole was normalized by dividing by plate breadth and was given in the form of ${\alpha}$. Results showed that perforating one hole in the center of a plate increases the plate buckling resistance while the having two holes resulted in a decrease in the plate buckling resistance. The effects of hole eccentricity (Ecc) on the buckling resistance of the plate was studied. The position of the hole center was normalized by half of the plate breadth and length in X- and Y-directions, respectively. In this study, four cases of boundary conditions were considered, and the corresponding buckling behavior were studied combined with plate aspect ratio. It was observed that the boundary condition of the case I resulted in the highest buckling resistance. Finally, a comparison was made between the buckling behavior of the uniaxially and biaxially loaded plate. It was revealed that the buckling resistance of a biaxially loaded plate is lower half than half of that of the uniaxially loaded plate.

• Steel and Composite Structures
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• 제50권2호
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• 대한수학회보
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• 제61권1호
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• pp.161-193
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• 2024

In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term h ∈ L²_b(ℝ; H^-1(ℝ^N)) is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor A, i.e., A is a bounded subset of H²(ℝ^N) × H¹(ℝ^N) × L²_µ(ℝ⁺, H²(ℝ^N)). The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.