Analysis of a curved beam using classical and shear deformable beam theories

Kang, Ki Jun; Han, Ji Won

doi:10.1007/bf02947169

Cited by 8 publications

(3 citation statements)

References 12 publications

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“…The versatility of the DQM to engineering analysis in general and to structural analysis in particular is becoming increasingly evident by the related publications of recent years. Kang and Han [12] applied the method to the analysis of a curved beam using classical and shear deformable beam theories, and Kang [13] studied the vibration analysis of curved beams using DQM, and Kang and Kim [14] studied the in-plane buckling analysis of curved beams using DQM. From a mathematical point of view, the application of the differential quadrature method to a partial differential equation can be expressed as follows:…”

Section: Differential Quadrature Methodsmentioning

confidence: 99%

In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM

Kang¹,

Park²

2013

Journal of the Korea Academia-Industrial cooperation Society

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One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of programming complex algorithms for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. Under in-plane uniform distributed load, the buckling of asymmetric curved beam with varying cross section is analyzed by using differential quadrature method (DQM). Critical load due to diverse cross section variation and opening angle is calculated. Analysis result of DQM is compared with the result of exact analytic solution. As DQM is used with small grid points, exact analysis result is shown. New result according to diverse cross section variation is also suggested.

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Section: Differential Quadrature Methodsmentioning

confidence: 99%

In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM

Kang¹,

Park²

2013

Journal of the Korea Academia-Industrial cooperation Society

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“…Fixed end reactions are the prime requirement for the analysis of the curved beam using matrix methods. The Bernoulli-Euler and Timoshenko theories can be employed for the analysis of the curved beam [1], [2]. The equilibrium equations, compatibility equations and constitutive relationships or energy principles can be used to represent mechanical behavior of the spatial curved beam [3]- [5].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Spatial Curved Bi-Fixed Beam with Varying Curvature and Varying Cross-Sectional Area Using Finite Displacement Transfer Method

2024

IJETER

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This article is focused on determination of fixed-end reactions, displacements, internal forces and internal moments for the spatial curved bi-fixed beam with varying curvature and varying cross-sectional area. The objective is to analyze spatially curved beam without involving analytical differentiation and integration of the governing equations. A finite displacement transfer method to analyze spatially curved beam is used to obtain numerically approximate analysis results and to eliminate analytical differentiation and integration, completely. The results of the analysis procedure are compared with the results of other methods found in the literature. For the specific case of the circular helical beam, the fixed end reactions' values have absolute maximum and minimum percentage differences of 1.23% and 0.06%, respectively. For the specific case of the elliptic-helical beam, the fixed end reactions' values have absolute maximum and minimum percentage differences of 1.13% and 0.0%, respectively. The finite difference method, along with the recursive scheme, gives reasonably accurate results without involving complex calculations

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“…The versatility of the DQM to engineering analysis in general and to structural analysis in particular is becoming increasingly evident by the related publications of recent years. Kang and Han[12] applied the method to the analysis of a curved beam using classical and shear deformable beam theories, and Kang[13] studied the vibration analysis of curved beams using DQM. From a mathematical point of view, the application of the differential quadrature method to a partial differential equation can be expressed as follows:…”

mentioning

confidence: 99%

In-Plane Buckling Analysis of Curved Beams Using DQM

Kang¹,

Kim²

2012

Journal of the Korea Academia-Industrial cooperation Society

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The differential quadrature method (DQM) is applied to computation of the eigenvalues of in-plane buckling of the curved beams. Critical moments and loads are calculated for the beam subjected to equal and opposite bending moments and uniformly distributed radial loads with various end conditions and opening angles. Results are compared with existing exact solutions where available. The DQM gives good accuracy even when only a limited number of grid points is used. More results are given for two sets of boundary conditions not considered by previous investigators for in-plane buckling: clamped-clamped and simply supported-clamped ends. 요 약 곡선보 (curved beam)의 내평면 모멘트 및 등분포하중 하에서 평면내 (in-plane) 좌굴 (buckling)을 미분구적 법(DQM)을 이용하여 해석하였다. 다양한 경계조건 (boundary conditions)과 굽힘각 (opening angles)에 따른 임계모멘 트 및 임계하중을 계산하였다. DQM의 해석결과는 해석적 해답 (exact solution) 결과와 비교하였으며, DQM은 적은 요소 (grid points)를 사용하여 정확한 해석결과를 보여주었다. 두 경계조건(고정-고정, 단순지지-고정)하에서 새 결과를 또한 제시하였다.

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Analysis of a curved beam using classical and shear deformable beam theories

Cited by 8 publications

References 12 publications

In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM

In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM

Analysis of Spatial Curved Bi-Fixed Beam with Varying Curvature and Varying Cross-Sectional Area Using Finite Displacement Transfer Method

In-Plane Buckling Analysis of Curved Beams Using DQM

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