• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.29-46
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies of a truncated shallow and deep conical shell with linearly varying thickness along the meridional direction free at its top edge and clamped at its bottom edge. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Strain and kinetic energies of the truncated conical shell with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated. The frequencies from the present 3-D method are compared with those from other 3-D finite element method and 2-D shell theories.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.143-149
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• 2017

In this work, various higher-order shear deformation beam theories for wave propagation in functionally graded beams are developed. The material properties of FG beam are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, the governing equations of the wave propagation in the FG beam are derived by using the Hamilton's principle. The analytic dispersion relations of the FG beam are obtained by solving an eigenvalue problem. The effects of the volume fraction distributions on wave propagation of functionally graded beam are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• Journal of Industrial Technology
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• v.18
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• pp.69-76
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• 1998

이 논문에서는 Dirichlet 경계 조건을 갖는 비선형 빔방정식 $u_{tt}+u_{xxxx}+g(u)=f(x,t)$의 해의 존재에 대한 연구를 하였다. 이 때 $g(u)=bu^+-au^-$으로 나타나고 우변의 외력항이 고유함수 $\{{\phi}_{00},{\phi}_{41}\}$로 확장된 함수로 나타날 때 $c_1{\phi}_{00}+c_2{\phi}_{41}$가 포함될 수 있는 원뿔형 공간을 만들고 사상을 정의하였고 이 사상의 역(逆)사상의 해의 존재여부에 따라서 빔방정식의 존재하는 해의 개수를 찾는데 이용하였다.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.1
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• pp.1-8
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• 1985

The buckling characteristics of cylindrical shells with a circular hole, under axially compressed loads, have been analyzed and the results have been compared with existed experimental results. Deflection function with decay factor is assumed, and stress distribution around a circular hole in tensioned infinite plate is used for formulating buckling energy function. Applying Rayleigh Ritz procedure to this energy function, characteristic equation of eigenvalue problem is determined. Buckling load is defined by the minimum value of eigenvalues calculated according to several decay factors, and as the radius ratios of a circular hole (a/R) and shell thickness ratios (R/t) are varied, the reducing characteristics of buckling load are studied. As a result, buckling loads are reduced by about 50% according to some radius ratios ($a/R{\geq}0.15$) of circular hole and are not nearly affected by shell thickness ratio(R/t).

• Journal of the Earthquake Engineering Society of Korea
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• v.4 no.2
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• pp.47-56
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• 2000

지반-구조물 상호작용 시스템 구조물의 진동제어 시스템 복합재료 구조물과 같은 비비례 감쇠 구조물의 경우 정확한 동적응답을 얻기 위해서는 감쇠행렬을 고려한 고유치 문제를 계산하는 것이 필수적이다 그러나 대부분의 고유치 해법에서는 구하고자 하는 고유치 중 일부를 누락시킬 수 있기 때문에 어떤 고유치 해법이 실제문제에 응용 가능한 방법이 되기 위해서는 누락된 고유치의 존재 여부를 검사하는 기법을 포함하고 있어야만 한다. 비감쇠나 비례감쇠 시스템의 경우에는 널리 알려진 Sturm 수열성질을 이용하여 누락된 고유치를 쉽게 검사할 수 있는 반면에 비비례 감쇠 시스템의 경우에는 널리 알려진 Sturm 수열 성질을 이용하여 누락된 고유치를 쉽게 검사할 수 있는 반면에 비비례 감쇠 시스템의 경우에는 아직까지 검사 기법이 개발되어 있지않다 본 논문에서는 편각의 원리를 이용하여 감쇠행렬을 고려한 고유치 문제의 누락된 고유치의 존재여부를 검사하는 기법을 제안하였다 제안방법의 효용성을 검증하기 위하여 두가지 수치예제를 고려하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.43-50
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• 2002

Main goal of this study is to develop MATLAB programming for exact analysis of distortional deformation of the straight box girder. For this purpose, a theory for distortional deformation theory is firstly summarized and then a BEF (Beam on Elastic Foundation) theory is presented using analogy of the corresponding variables. Finally, the governing equation of the beam-column element on elastic foundation is derived. An element stiffness matrix of the beam element is established via a generalized linear eigenvalue problem. In order to verify the efficiency and accuracy of the element using exact dynamic stiffness matrix, buckling loads for the continuous beam structures with elastic foundation and distortional deformations of box girders are calculated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.171-174
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• 2010

적절한 근사화 과정을 통하여 구축된 축소 시스템은 전체 시스템의 거동을 적은 수의 정보를 통하여 효과적으로 표현할 수 있다. 효과적인 시스템 축소를 위하여 본 연구에서는 주파수 영역 Karhunen-Loeve (Frequency-domain Karhunen-Loeve, FDKL) 기법과 시스템 등가 확장 축소 과정(System equivalent expansion reduction process, SEREP)을 연동한 축소 기법을 제안한다. 적합직교분해(Proper orthogonal decomposition)의 한 방법인 FDKL기법을 통하여 최적모드(Optimal mode)를 구하고 이에 SEREP을 적용하여 자유도 변환 행렬을 구한다. 이때 주자유도 선정은 2단계 축소기법을 적용한다. 최종적으로 제안된 기법은 수치예제를 통하여 검증한다.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.99-111
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• 2004

An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.