• Steel and Composite Structures
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• v.19 no.3
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• pp.635-659
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• 2015

In this study, natural frequency analysis of a large deflected cantilever laminated composite beam fixed at both ends, which forms the case of a pre-stressed curved beam, is investigated. The laminated beam is considered to have symmetric and asymmetric lay-ups and the effective flexural modulus of the beam is used in the analysis. In order to obtain the pre-stressed composite curved beam case, an external vertical concentrated load is applied at the free end of a cantilever laminated composite beam and then the loading point of the deflected beam is fixed. The non-linear deflection curve of the flexible beam undergoing large deflection is obtained by the Reversion Method. The curved laminated composite beam is modeled by using the Finite Element Method with a straight-beam element approach. The effects of orientation angle and vertical load on the natural frequency parameter for the first four modes are examined and the results obtained are given in graphics. It has been found that the effect of the load parameter, which forms the curved laminated beam, on the natural frequency parameter, almost disappears after a certain value of the load parameter. This certain value differs for each laminated curved beam and each vibration mode.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.8
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• pp.2734-2740
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• 2010

The free in-plane vibration of asymmetric circular curved beams with varying cross-section is analyzed by the differential quadrature method (DQM) neglecting transverse shearing deformation. Natural frequencies are calculated for the beams with various opening angles and boundary conditions. Results obtained by the DQM are compared with available results by other methods in the literature. It is found that the DQM gives the good accuracy even with a small number of grid points.

• Steel and Composite Structures
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• v.39 no.1
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• pp.1-20
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• 2021

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1 + z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1 + z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.10
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• pp.4706-4712
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• 2013

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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.594-600
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• 2021

Curved beam structures are generally used as components in structures such as railroad bridges and vehicles. The stability analysis of curved beams has been studied by a large number of researchers. Due to the complexities of structural components, it is difficult to obtain an analytical solution for any boundary conditions. In order to overcome these difficulties, the differential quadrature method (DQM) has been applied for a large number of cases. In this study, DQM was used to solve the complicated partial differential equations for buckling analysis of curved beams. The governing differential equation was deduced and solved for beams subjected to uniformly distributed radial loads. Critical loads were calculated with various opening angles, boundary conditions, and parameters. The results of the DQM were compared with exact solutions for available cases, and the DQM gave outstanding accuracy even when only a small number of grid points was used. Critical loads were also calculated for the in-plane inextensional buckling of the asymmetric curved beams, and two theories were compared. The study of a beam with extensibility of the arch axis shows that the effects on the critical loads are significant.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.193-201
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• 1992

A new equivalent curved beam theory is developed for the analysis of the corner part of ship structures, in which effects of distributed loads and asymmetricity with two or three connected parts are considered. Equivalent loads are obtained from equilibrium conditions between the distributed loads and the member forces and moments at the ends of curved beam. And an equivalent curved beam for the asymmetric structure is obtained by superposing the equivalent symmetric parts which have equivalent stiffness. From the sample calculation, it is found that the results of the new equivalent curved beam theory are well agreed with those of finite element method using membrane elements with little computing time and sufficient accuracy.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.5
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• pp.612-620
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• 2019

The increasing use of curved beams in buildings, vehicles, ships, and aircraft has results in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of a large number of investigations. Solutions of the relevant differential equations have traditionally been obtained by the standard finite difference. These techniques require a great deal of computer time as the number of discrete nodes becomes relatively large under conditions of complex geometry and loading. One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method(DQM) has been applied to a large number of cases to overcome the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In this study, the in-plane extensional vibration for asymmetric curved beams with linearly varying cross-section is analyzed using the DQM. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results are compared with the result by other methods for cases in which they are available. According to the analysis of the solutions, the DQM, used only a limited number of grid points, gives results which agree very well with the exact ones.