• Structural Engineering and Mechanics
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• 제21권1호
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• pp.19-33
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• 2005

An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2005년도 추계학술발표대회 논문집
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• pp.198-201
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• 2005

This study investigates the difference between single-cell and multi-cell cross-sections of thin-walled beams. The variationally and asymptotically consistent theory is used in order to model the two-cell thin- walled beam. The theory is based on an asymptotical analysis of two-dimensional shell energy. In addition, the method allows for the development of closed-form expressions for the displacement, stress field and beam stiffness coefficients. The numerical results show the difference between the cross-sectional stiffness of single-cell and that of multi-cell.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 춘계학술대회 논문집
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• pp.536-543
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• 2005

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly 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, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.345-352
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• 2001

Derivation procedures of exact static element stiffness matrix of shear deformable thin-walled straight beams are rigorously presented for the spatial buckling analysis. An exact static element stiffness matrix is established from governing equations for a uniform 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 dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The buckling loads are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.435-442
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• 2001

Derivation procedures of exact dynamic element stiffness matrix of shear deformable nonsymmetric thin-walled straight beams are rigorously presented for the spatial free vibration analysis. An exact dynamic element stiffness matrix is established from governing equations for a uniform 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 dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The natural frequencies are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.906-915
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• 2004

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly 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, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using clement force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• Structural Engineering and Mechanics
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• 제7권2호
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• pp.181-202
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• 1999

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren't continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

• Steel and Composite Structures
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• 제34권3호
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• pp.361-376
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• 2020

This paper presents a free vibration analysis of shell panels made of functionally graded material (FGM) in the form of the ordinary and sandwich FGM and laminated shells using the isogeometric B3-spline finite strip method (IG-SFSM). B3-spline and Lagrangian interpolation are employed along the longitudinal and transverse directions respectively in this type of finite strip. The introduced finite strip formulation is based on the degenerated shell method, which provides variable thickness, arbitrary geometries, and analysis of thin or thick shells. Validity of the obtained natural frequencies by IG-SFSM is checked by comparison with results extracted from references for similar cases in different examples. These examples incorporate several geometries, materials, boundary conditions, and continuous thickness variation. A comparison of these two kinds of results and their proximity showed that the introduced IG-SFSM is a reliable tool which can be used in analysis of shells with the aforementioned properties.

• Composites Research
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• 제12권5호
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• pp.65-79
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• 1999

본 논문은 단순지지된 복합재료 사각판과 원통쉘이 결합된 구조물의 자유진동해석을 위한 해석적 방법에 대하여 기술하였다. 결합전 단순지시된 사각판과 원통쉘의 응답을 얻기 위하여 고전적 판이론과 Love의 얇은 쉘이론에 기초한 에너지법을 적용하였다. 결합구조물의 해석에는 동적응답법을 적용하였고, 길이방향 판과 쉘의 결합부에서의 동적 주기 하중과 모멘트는 Dirac 델타 함수와 정현 함수를 사용하였을 때 연속조건을 만족함을 보였다. 또한 원통쉘의 기하하적 매개변수인 쉘의 길이 대 반경비와 반경 대 두께비에 따른 진동특성의 변화를 고찰하였고, 복합재료의 섬유 방향각과 직교이방성 매개변수가 결합 원통쉘의 기본 진동수에 미치는 영향에 미치는 영향에 대하여 연구하였다.

• 한국공간구조학회논문집
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• 제8권2호
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• pp.105-113
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• 2008

쉘형 구조물은 외력에 대해 효과적으로 저항할 수 있어, 두께를 얇게하면서 대공간 구조물을 만들 수 있는 장점이 있다. 이러한 장점은 구조형태에 크게 의존한다. 그러므로 많은 설계자들은 최적 형태를 설계에 반영하고자 하지만, 이는 간단치 않다. 지금까지 보다 최적의 형태를 얻기 위한 많은 기법들이 발표되어 왔고, 이들은 각각 장단점을 나타낸다. 본 논문에서는 최적의 곡면을 얻기 위해 기하학적 비선형을 고려한 유한요소법을 이용한 비교적 간단한 방법을 제안한다. 이러한 방법을 이용하여 다양한 쉘형 곡면에 적용하여 최적곡면을 얻고, 이를 비교한다.