• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.301-308
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• 1998

This paper deals with the influence of elastic foundations on natural frequencies of curved beams. Taking into account the effects of rotatoy inertia and shear deformation, the differential equations governing free, out-of-plane vibrations of circular curved beams resting on Winkler-type foundations are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The lowest three natural frequencies are claculated over a range of non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation. The effects of rotatory inertia and shear deformation are also analyzed.

• Journal of the Korean Society of Safety
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• v.14 no.1
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• pp.199-207
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• 1999

The differential quadrature method (DQM) is applied to computation of eigenvalues of the equations of motion governing the free in-plane and out-of-plane vibrations for circular curved beams. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with existing exact solutions and numerical solutions by other methods (Rayleigh-Ritz, Galerkin or FEM) for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.17-38
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• 2018

In this paper, we compare and assess the performance of the standard 3- and 6-node MITC shell elements (Lee and Bathe 2004) with the recently developed MITC triangular elements (Lee et al. 2014, Jeon et al. 2014, Jun et al. 2018) which were based on the partitions of unity approximation, bubble node, or both. The convergence behavior of the shell elements are measured in well-known benchmark tests; four plane stress tests (mesh distortion test, cantilever beam, Cook's skew beam, and MacNeal beam), two plate tests (Morley's skew plate and circular plate), and six shell tests (curved beam, twisted beam, pinched cylinder, hemispherical shells with or without hole, and Scordelis-Lo roof). To precisely compare and evaluate the solution accuracy of the shell elements, different triangular mesh patterns and distorted element mesh are adopted in the benchmark problems. All shell finite elements considered pass the basic tests; namely, the isotropy, the patch, and the zero energy mode tests.

• Journal of Korean Society of Steel Construction
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• v.18 no.2
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• pp.123-135
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• 2006

This paper investigates the design equations and the strength behavior of the diaphragm for steel box beams and circular-column connections. The strength of the connection is decided by the strength of the diaphragm and the strength of the beam and the column, because the connection diaphragm supports the concentration forces from the box beam's lower flange. In previous researches, however, the calculation procedure of the diaphragm stress from the indeterminate curved-beam model is to complicated to apply in process of the equation. Moreover, no reasonable design has yet ben made because the diaphragm's effect on the strength of the connection has not ben considered. Therefore, through nonlinear FEM analysis of the connection diaphragm, this study examines the strength behavior of a connection with diaphragm details. In addition, a great difference is confirmed between the theoretical and analytic behaviors. Fi naly, considering the strength of the connection and the rigidity capacity of the diaphragm, the diaphragm design method is proposed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.4
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• pp.661-669
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• 1999

이 논문은 탄성지반위에 놓인 원호형 곡선보의 자유진동에 관한 연구이다. 회전관성 및 전단변형을 고려하여 두 개의 매개변수로 표현되는 탄성지반위에 놓인 원호형 곡선보의 자유진동을 지배하는 미분방정식을 유도하고, 이를 수치적분기법과 시행착오적 행렬값탐사법이 결합된 수치해석기법으로 해석하였다. 회전-회전, 회전-고정 및 고정-고정의 단부조건을 갖는 곡선보의 최저차모드 3개의 고유진동수를 산출하였다. 곡선보의 수평높이 지간길이비, Winkler 지반계수, 전단지반계수에 따른 고유진동수 변화를 분석하였으며, 회전관성 및 전단변형의 영향을 고찰하였다.

• Plant Journal
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• v.17 no.3
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• pp.42-46
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• 2021

The equation of motion of the drill string along the excavation trajectory was analyzed using the Lagrangian approach together with the finite element method (FEM). A drill string of circular cross section is constructed by combining a plurality of circular axes each having 12 degrees of freedom (DOF). FEM analysis can observe the vibration and dynamic changes of the entire drill string, and it is easy to apply comprehensive boundary conditions to reproduce the simulation of a realistic drill string. In this study, the constructed FEM motel was simulated. In order to apply the FEM program to the actual drill trajectory, the dynamic analysis of the curved beam was verified by comparison with the actual values. The dynamic change over time was observed.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.131-152
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• 2012

In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant cross-sections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.503-526
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• 2016

In-plane and out-of-plane free vibration analysis of Timoshenko curved beams is addressed based on the isogeometric method, and an effective scheme to avoid numerical locking in both of the two patterns is proposed in this paper. The isogeometric computational model takes into account the effects of shear deformation, rotary inertia and axis extensibility of curved beams, and is applicable for uniform circular beams, and more complicated variable curvature and cross-section beams as illustrated by numerical examples. Meanwhile, it is shown that, the $C^{p-1}$-continuous NURBS elements remarkably have higher accuracy than the finite elements with the same number of degrees of freedom. Nevertheless, for in-plane or out-of-plane vibration analysis of Timoshenko curved beams, the NURBS-based isogeometric method also exhibits locking effect to some extent. To eliminate numerical locking, the selective reduced one-point integration and $\bar{B}$ projection element based on stiffness ratio is devised to achieve locking free analysis for in-plane and out-of-plane models, respectively. The suggested integral schemes for moderately slender models obtain accurate results in both dominated and non-dominated regions of locking effect. Moreover, this strategy is effective for beam structures with different slenderness. Finally, the influence factors of structural parameters of curved beams on their natural frequency are scrutinized.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.111-130
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• 2016

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

• 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.