• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.326-329
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• 2005

In the development of sheet-handling .machinery, it is important to predict the static and dynamic behavior of the sheets with a high degree of reliability because the sheets are fed and stacked at suck a high speed flexible media behaves geometric nonlinearity of large displacement and small strain. In this paper, static analysis of flexible media are performed by FEM considering geometric nonlinearity. Linear stiffness matrix and geometric nonlinear stiffness matrix based m the updated Lagrangian approach are derived using $C^1$ beam element and numerical simulations are performed by Updated Newton-Raphson(UNR) method.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.41-47
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• 2008

The nonlinear structural analyses of high-aspect-ratio structures were performed. For the high-aspect-ratio structures, it is important to understand geometric nonlinearity due to large deflections. To consider geometric nonlinearity, finite element analyses based on the large deflection beam theory were introduced. Comparing experimental data and the present nonlinear analysis results, the current results were proved to be very accurate for the static and dynamic behaviors for both isotropic and anisotropic beams.

• 한국강구조학회 논문집
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• 제11권4호통권41호
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• pp.417-424
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• 1999

본 논문에서는 3차원 강뼈대구조물의 비선형 해석 기법을 개발하였다. 본 해석은 재료적 비선형과 기하학적 비선형을 고려하였다. 재료적 비선형으로 휨에 의한 점진적인 소성화를 고려하였다. 기하학적 비선형으로 $P-{\delta}$와 $P-{\Delta}$ 효과를 고려하였다. 절점에서의 재료적 비선형성은 여러개의 화이버로 구성되어 있는 P-M 힌지 개념을 사용함으로써 고려하였다. 기하학적 비선형성은 안정함수 (Stability function)를 사용하여 고려하였다. 단 전단과 비틀림에 의해 발생하는 비선형형은 고려하지 않았다. 수치해석법으로는 수정변위증가법을 사용하였다. 본 연구에서 제안된 해석방법으로 예측된 하중-변위가 다른 해석기법의 결과들과 잘 일치하였다.

• 대한기계학회논문집
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• 제17권12호
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• pp.2915-2925
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• 1993

A finite element program using degenerated shell element was developed to solve the geometric, material and combined nonlinear behaviors of composite laminated plates. The total Lagrangian method was implemented for geometric nonlinear analysis. The material nonlinear behavior was analyzed by considering the matrix degradation due to the progressive failure in the matrix and matrix-fiber interface after initial failure. The results of the geometric nonlinear analyses showed good agreements with the other exact and numerical solutions. The results of the combined nonlinear analyses considered both geometric and material nonlinear behaviors were compared to the experiments in which a concentrated force was applied to the center of the square laminated plate with clamped four edges.

• 대한기계학회논문집A
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• 제28권12호
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.793-798
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• 2004

The vibration of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the extended Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the vibration characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. From these results, we should consider the geometric nonlinearity to analyze the dynamics of a curved pipe conveying fluid more precisely.

• Steel and Composite Structures
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• 제20권2호
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• pp.379-397
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• 2016

Due to creep and shrinkage of the concrete core, concrete-filled steel tubular (CFST) arches continue to deform in the long-term under sustained loads. This paper presents analytical investigations of the effects of geometric nonlinearity on the long-term in-plane structural performance and stability of three-pinned CFST circular arches under a sustained uniform radial load. Non-linear long-term analysis is conducted and compared with its linear counterpart. It is found that the linear analysis predicts long-term increases of deformations of the CFST arches, but does not predict any long-term changes of the internal actions. However, non-linear analysis predicts not only more significant long-term increases of deformations, but also significant long-term increases of internal actions under the same sustained load. As a result, a three-pinned CFST arch satisfying the serviceability limit state predicted by the linear analysis may violate the serviceability requirement when its geometric nonlinearity is considered. It is also shown that the geometric nonlinearity greatly reduces the long-term in-plane stability of three-pinned CFST arches under the sustained load. A three-pinned CFST arch satisfying the stability limit state predicted by linear analysis in the long-term may lose its stability because of its geometric nonlinearity. Hence, non-linear analysis is needed for correctly predicting the long-term structural behaviour and stability of three-pinned CFST arches under the sustained load. The non-linear long-term behaviour and stability of three-pinned CFST arches are compared with those of two-pinned counterparts. The linear and non-linear analyses for the long-term behaviour and stability are validated by the finite element method.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the 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 axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.809-827
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• 2015

In this paper, seismic energy response of inelastic steel structures under earthquake excitations is investigated. For this purpose, a numerical procedure based on nonlinear dynamic analysis is developed by considering material, geometric and connection nonlinearities. Material nonlinearity is modeled by the inversion of Ramberg-Osgood equation. Nonlinearity caused by the interaction between the axial force and bending moment is also defined considering stability functions, while the geometric nonlinearity caused by axial forces is described using geometric stiffness matrix. Cyclic behaviour of steel connections is taken into account by employing independent hardening model. Dynamic equation of motion is solved by Newmark's constant acceleration method in the time history domain. Energy response analysis of space frames is performed by using this proposed numerical method. Finally, for the first time, the distribution of the different energy types versus time at the duration of the earthquake ground motion is obtained where in addition error analysis for the numerical solutions is carried out and plotted depending on the relative error calculated as a function of energy balance versus time.