• 대한토목학회논문집
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• 제3권4호
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• pp.109-122
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• 1983

본(本) 연구(硏究)에서는 전단변형(剪斷變形)(Shear deformation)과 회전관성(回轉慣性)(Rotatory inertia)의 영향(影響)을 고려(考慮)한 4절점(節點) 8자유도(自由度)를 갖는 Timoshenko 보 요소(要素)(TB4)를 3차원(次元) 연속체(連續體)로부터 유도(誘導)하고 있다. TB4보 요소(要素)는 3차(次) 보간함수(補間凾數)(Interpolation function)로 표시(表示)되는 연직(鉛直)처짐(Transverse deflection) W와 평면회전(平面回轉)(Plane rotation) ${\theta}$를 절점(節點)의 자유도(自由度)로 취(取)하고 있다. TB4요소(要素)의 강도(剛度)매트릭스와 질량(質量)매트릭스는 보의 운동방정식(運動方程式)을 Galerkin 가중잔차법(加重殘差法)(Weighted residual method)으로 Discretization하여 3개(個)의 Gauss점(點)을 이용(利用)한 RSI(Reduced shear integration)기법(技法)에 의한 수치적분(數値積分)으로 구해진다. TB4보 요소(要素)의 정확성(正確性)과 수감상태(收歛狀態)를 고찰(考察)하기 위하여 여러 가지 예제(例題)를 해석(解析)한 결과(結果), 보의 L/h 비(比)에 관계없이 보의 정적해석(靜的解析)(Static analysis)이라 자유진동해석(自由振動解析)(Free vibration analysis)에 있어서 TB4보 요소(要素)는 다른 Timoshenko보 요소(要素)들 보다 월등(越等)히 우수(優秀)한 정확도(正確度)와 수감현상(收歛現象)을 보여 주고 있다.

• 대한기계학회논문집
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• 제15권2호
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• pp.478-487
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• 1991

In this study, dynamic stability of discontinuous free Timoshenko beam, barring a concentrated mass, under constant follower force is considered. Governing differential equations are derived based on the extended Hamilton's principle and finite element method is applied for numerical analysis. Conclusions of the study are as follows : (1) Without force direction control, (i) the critical follower force at instability is increased with concentrated mass regardless of discontinuity. (ii) the minimum critical follower force is located in the vicinity of discontinuity position .xi.$_{d}$=0.75. (iii) at mass location .mu. .leq.0.5 the force at instability is decreased as magnitude of concentrated mass is increased but, at .mu. .geq. 0.5 the force is increased as the mass is increased. (2) With force direction control, (i) shear deformation parameter S contributes insignificantly to the force at instability when S>10$^{[-993]}$ (ii) maximum critical follower force can be obtained for the discontinuity location .xi.$_{d}$=0.25. (iii) the critical follower force is increased as magnitude of concentrated mass .alpha. is increased at mass location .mu. .geq.0.4, but is increased, .mu ..leq.0.4.4.

• Structural Engineering and Mechanics
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• 제33권4호
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• pp.447-484
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• 2009

The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thickness-curvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and force-deformation relationships are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers' analytical solutions.

• Structural Engineering and Mechanics
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• 제14권5호
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• pp.575-593
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• 2002

Based on the Mindlin plate theory, a refined discrete 15-DOF triangular laminated composite plate finite element RDTMLC with the re-constitution of the shear strain is proposed. For constituting the element displacement function, the exact displacement function of the Timoshenko's laminated composite beam as the displacement on the element boundary is used to derive the element displacements. The proposed element can be used for the analysis of both moderately thick and thin laminated composite plate, and the convergence for the very thin situation can be ensured theoretically. Numerical examples presented show that the present model indeed possesses the properties of higher accuracy for anisotropic laminated composite plates and is free of locking even for extremely thin laminated plates.

• Structural Engineering and Mechanics
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• 제53권5호
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• pp.981-995
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• 2015

This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Structural Engineering and Mechanics
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• 제34권4호
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• pp.475-490
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• 2010

It is the intention of this study to synthesize the effects of double-edge cracks on the dynamic characteristics of a beam. The stiffness matrix is first determined for a Timoshenko beam containing two same-line edge cracks. The presented model is then developed for elements with two parallel double-sided cracks, considering the interaction between the stress fields of adjacent cracks. Finally, a finite element code is implemented, to examine the influence of depth and location of double cracks, on the natural frequencies of the damaged system.

• Structural Engineering and Mechanics
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• 제34권2호
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• pp.231-245
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• 2010

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.327-334
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• 2001

This paper presents a non-linear analysis procedure for plane frame structures by finite element formulation with assumptions of Timoshenko beam theory. Finite element displacement method based on Lagrangian formulation is used and two-noded and isoparametric line element is adopted to represent finite element model. The layered approach is used for the elasto-plastic analysis of the plane frame structures with rectangular and I cross sections. A load incremental method combined with the tangent stiffness and the initial stiffness methods for each load increment is used for the solution of non-linear equations. Numerical examples are presented to investigate the behavior and the accuracy of the elasto-plastic non-linear application and the results of this study are compared with other solutions using the concept of plastic hinge.

• 한국소음진동공학회논문집
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• 제21권6호
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• pp.580-586
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• 2011

This paper addresses the effect of transverse shear deformation and rotary inertia on the natural frequency of beams under axial loads. It has been reported in the author's paper using a finite element analysis that the Timoshenko effect in a rotating disk deceases and then increases again with increasing rotation speed. To validate the phenomenon, the simply-supported beams under uniform tension are selected in this study since they have exact solutions in vibration problem. The results show that the axial tension in beams would not make the Timoshenko effect decrease monotonically but could make the effect increase again unlike the results reported in the other studies for beams.