• Geomechanics and Engineering
• /
• 제1권2호
• /
• pp.121-142
• /
• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2005년도 춘계학술대회 논문집
• /
• pp.536-543
• /
• 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
• /
• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
• /
• pp.43-50
• /
• 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.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2005년도 추계학술대회 논문집
• /
• pp.1165-1170
• /
• 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.

• Steel and Composite Structures
• /
• 제9권5호
• /
• pp.473-497
• /
• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

• 한국강구조학회 논문집
• /
• 제20권1호
• /
• pp.81-92
• /
• 2008

일반적인 강구조물의 연결은 강절(rigid) 또는 활절(hinge)로 취급되고 있으나 실제 강구조물은 연결부위에서 부재간의 상대적인회전이 허용됨으로 인해 부분강절(semi-rigid)의 특성을 갖게 된다. 본 연구에서는 부분강절을 회전스프링으로 가정하여 부재 단부에 적용시킨 평면 뼈대구조물의 엄밀한 접선강도행렬을 유도하고 이를 다시 탄성강도행렬과 기하학적 강도행렬로 분리 유도함으로써 부분강절을 갖는 평면 뼈대구조물의 안정성해석을 위한 일반화된 해석방법을 제시하고자 한다. 이를 위하여, 보-기둥부재의 좌굴조건을 만족시키는 처짐함수로부터 안정함수(stability function)를 유도하고, 횡변위(sway)를 고려한 힘-변위관계와 적합조건을 고려하여 정확한 접선강도행렬을 제시하였다. 본 연구의 타당성과 실용성 제고를 위해 두 가지 방법에 의한 수치해석프로그램을 개발하였고 다양한 해석예제를 통해, 타 연구자 해석 결과와 비교하고 부분강절이 구조물의 좌굴강도에 미치는 영향에 대하여 조사한다.

• 한국강구조학회 논문집
• /
• 제14권4호
• /
• pp.509-518
• /
• 2002

비대칭 단면을 갖는 박벽보의 3차원 휨-배틂 좌굴해석 및 정적해석을 위하여, 평형방정식과 힘-변위 관계식을 이용하여 엄밀한 정적요소강성행렬을 수치적으로 산정하는 개선된 기법을 제시한다. 먼저 14개의 변위피라미터를 도입하여 고차의 연립미분방정식을 1차 연립미분방정식으로 변환하고, 복소수 영역에서 선형고유치문제를 해를 구한다. 이 경우 동적강성행렬을 산정하는 경우와는 달리 복수개의 '영'의 고유치가 발생한다. 이에 대응하는 변위피라미터의 다항식을 항등식 조거능로부터 구하고, 이를 고유치와 결합하여 박벽보 요소의 엄밀한 처짐함수를 구한다. 이렇게 구한 엄밀한 처짐함수에 재단력-변위 관계식을 적용하여 세가지 초기단면력 조건에 대응하는 엄밀한 정적요소강성행렬을 산정한다. 본 방법의 타당성을 보이기 위하여 비대칭 박벽보의 좌굴하중과 처짐값을 계산하고 해석해나 ABAQUS 쉘요소를 이용한 해석결과 및 직선보요소를 사용한 유한요소해의 결과와 비교, 검증한다.

• 한국소음진동공학회논문집
• /
• 제12권2호
• /
• pp.161-169
• /
• 2002

Based on the analytic expression for the elasto-dynamic behavior of rotating shaft, the transfer matrix is formulated for the shaft element with uniform cross-section. Timoshenko beam theory is Introduced for modeling the behavior of shaft. Complex variables representing the displacement, slope, moment and shear force are used for deriving the transfer matrix between both ends of the shaft element. Simulation result obtained by applying the transfer matrix to a general rotor model is compared with the reference result and proved to be exact. Natural frequencies and the corresponding modes are analyzed with varying the bearing: stiffness. The generally used bearings are considered for discussions. and the bearing stiffness is shown to affect the vibration characteristics of rotor.

• Steel and Composite Structures
• /
• 제16권6호
• /
• pp.577-593
• /
• 2014

An exact dynamic stiffness method is introduced for investigating the free vibration characteristics of the steel-concrete composite beams consisting of a reinforced concrete slab and a steel beam which are connected by using the stud connectors. The elementary beam theory is used to define the dynamic behaviors of the two beams and the relative transverse deformation of the connectors is included in the formulation. The dynamic stiffness matrix is formulated from the exact analytical solutions of the governing differential equations of the composite beams in undamped free vibration. The application of the derived dynamic stiffness matrix is illustrated to predict the natural frequencies and mode shapes of the steel-concrete composite beams with seven boundary conditions. The present results are compared to the available solutions in the literature whenever possible.

• 한국안전학회지
• /
• 제29권3호
• /
• pp.64-71
• /
• 2014

The generalized tangential stiffness matrix of semi-rigid frame element with shear deformations based on Haringx's shear theory is newly derived and compared with the previous study based on Engesser's shear theory. Also, linearized elastic and geometric stiffness matrices are newly presented from the exact tangential stiffness matrix. In oder to obtain the inelastic system buckling load of shear flexible semi-rigid frame structure, the Ef method by tangential modulus theory is adopted and the FE analysis programs are developed. Finally, the shear and semi-rigid effects of system bucking are investigated by two numerical examples.