• Computational Structural Engineering
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• v.11 no.4
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• pp.239-251
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• 1998

본 연구에서는 비대칭 박벽단면을 갖는 곡선보의 안정성해석을 수행할 수 있는 이론 및 엄밀해를 제시하기 위하여, 3차원 연속체로부터 유도된 평형방정식으로부터 선형화된 가상일의 원리를 적용하였다. 박벽단면의 구속된 ？(warping)과 곡률효과를 고려하고 유한한 회전각의 2차항을 포함하는 곡선보의 변위장을 도입하여 단면에 대해 적분함으로써 도심축에 대한 박벽 곡선보의 총포텐셜에너지를 유도하였다. 또한, 단순지지되고 일축대칭 단면을 갖는 박벽원형 곡선보의 면내 및 면외좌굴에 대한 엄밀해를 유도하기 위하여, 면내에 대해서는 균일압축을 받는 원형아치의 역대칭 좌굴모드에 대한 좌굴하중을 유도하고 면외좌굴에 대해서는 균일압축 및 순수휨을 받는 아치의 처짐함수를 가정하여 곡선보의 횡좌굴하중에 대한 일반해를 제시하였다.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.509-523
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• 1998

A consistent finite element formulation and analytic solutions are presented for stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential moment is newly derived. Analytic solutions for the out-of-plane buckling of symmetric thin-walled curved beam subjected to pure bending or uniform compression with simply supported boundary conditions are obtained. For finite element analysis, the cubic Hermitian polynomials are utilized as shape functions and $16{\times}16$ stiffness matrix for curved beam elements and $14{\times}14$ stiffness matrix for straight beam elements are evaluated, respectively. In order to illustrate the accuracy of this study, analytical and numerical results for lateral buckling problems of circular arch are presented and compared with available analytical solutions.

• Journal of Korean Society of Steel Construction
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• v.18 no.3
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• pp.349-359
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• 2006

This paper presents a new block stiffness matrix for the analysis an orthogonal Cartesian coordinate system. The displacement fields are defined using the first order shear deformable beam theory. The longitudinal displacement can be expressed as the sum of the projected plane deformation of the cross-section due to Timoshenko's beam theory and axial warping deformation due to modified Vlasov's thin-waled beam theory. The derived element takes into account flexural shear deformation and torsional warping deformation. Three different types of beam elements, namely, the two-noded, three-noded, and four-noded beam elements, are developed. The quadratic and cubic elements are found to be very efficient for the flexural analysis of laminated composite beams. The versatility and accuracy of the new element are demonstrated by comparing the numerical results available in the literature.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.57-68
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• 1998

For free vibration of monosymmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for free vibration behaviors of simply supported thin-walled curved beam element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the FEM using straight beam element.

• Computational Structural Engineering
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• v.11 no.4
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• pp.197-207
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• 1998

전단변형 효과를 무시하는 경우에 비대칭 선형 변단면을 갖는 박벽 공간 보의 안정성 해석을 위한 일반이론을 유도한다. 비대칭 선형 변단면의 임의점을 통과하는 부재축과 단면의 주축의 방향과 무관하고 부재축과 직각을 이루는 두 개의 좌표축을 도입하여 직각좌표계를 정의한다. 정의된 좌표축을 기준으로 유한한 회전각의 2차항을 고려하는 변위장을 도입하여 연속체에 대한 가상일의 원리로부터 탄성변형에너지, 그리고 초기응력에 의한 포텐셜에너지를 유도한다. 이를 이용하여 비대칭 선형 변단면을 갖는 박벽 공간 보의 안정성해석을 위한 평형방정식을 제시한다. 3차 Hermitian 다항식을 변위파라미터의 형상함수로 사용하여 박벽 공간 보의 탄성강도 및 기하강도행렬을 상정할 뿐만 아니라, 단면의 좌표축에 상관없이 임의의 위치에 작용하는 하중에 대한 하중보정강도행렬(load-correction stiffness matrix)을 제시한다. 본 이론 및 방법의 타당성을 검증하기 위하여 수치해석을 수행하고 문헌의 결과 및 쉘요소를 사용한 해석결과와 비교하여 본 이론의 정당성을 입증한다.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.41-49
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• 2002

An efficient algorithm automatically determining cross sectional properties of thin-walled beams is developed using the minimum information about geometry of the cross section. This scheme is applied to automatic calculation of normal and shear stress distribution corresponding to stress resultants as well as sectional constants for complex open and closed thin-walled sections. Numerical examples evaluating section constants and stress distributions is presented and compared with the available reference's results.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.703-713
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• 2001

Derivation procedures of exact dynamic stiffness matrices of thin-walled straight beams subjected to eccentrically axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic 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 displacement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of nonsymmetric thin-walled straight beams are evaluated and compared with analytical solutions or results by thin-walled beam element using the cubic Hermitian polynomials and ABAQU's shell elements in order to demonstrate the validity of this study.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.41-54
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• 1999

For free vibration of non-symmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for in-plane free vibration behaviors of simply supported thin-walled curved beams with monosymmetric cross-sections is newly derived. Also, a finite element formulation using two noded curved beams element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the straight beam element and the ABAQUS's shell element.

• Journal of Korean Society of Steel Construction
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• v.14 no.4
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• pp.509-518
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• 2002

In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.31-40
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• 2002

Free vibration of a thin-walled laminated composite beam is studied. A general analytical model applicable to the dynamic behavior of a thin-walled channel section composite is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes for arbitrary laminate stacking sequence configuration. i.e. unsymmetric as well as symmetric, and various boundary conditions. A displacement-based one-dimensional finite element model is developed to predict natural frequencies and corresponding vibration modes for a thin-walled composite beam. Equations of motion are derived from the Hamilton's principle. Numerical results are obtained for thin-walled composite addressing the effects of fiber angle. modulus ratio. and boundary conditions on the vibration frequencies and mode shapes of the composites.