Numerical transfer-method with boundary conditions for arbitrary curved beam elements

Gimena, Faustino N.; Gonzaga, Pedro; Gimena, L.

doi:10.1016/j.enganabound.2008.04.004

Cited by 14 publications

(5 citation statements)

References 14 publications

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“…To carry out the structural calculation, the numerical procedure called Finite Transfer Method 28 is used. This procedure solves a system of linear ordinary differential equations with boundary conditions and can address the wide casuistry of the structural problem of the beam 29 – 31 .…”

Section: Analysis Of the Beam By Means Of The Finite Transfer Methods...mentioning

confidence: 99%

Alternative approach to the buckling phenomenon by means of a second order incremental analysis

Gimena,

Goñi,

Gonzaga

et al. 2023

Sci Rep

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This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section.

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Section: Analysis Of the Beam By Means Of The Finite Transfer Methods...mentioning

confidence: 99%

Alternative approach to the buckling phenomenon by means of a second order incremental analysis

Gimena,

Goñi,

Gonzaga

et al. 2023

Sci Rep

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“…Stiffness matrix and equivalent load vector were obtained using transfer matrix. Gimena et al [11] presented first order, second order and forth order Runge-Kutta numerical method for the analysis of arbitrary curved beam. Analysis methods proposed in the literature [7]- [10] needed equations of the tangent, normal, binormal, bending curvature and flexion curvature of the curved beam.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In most of the cases, numerical methods must be employed for the solution of the governing equations of the curved beam [9]- [12]. Researchers use different approaches such as Transfer Matrix Method [9]- [11], [13], [14], Finite Difference Method [15], [16], Finite Element Method [17]- [21] for the analysis of either planer or spatial curved beam to obtain displacements, reactions and internal forces. Finite element method is one of the approximate methods of the analysis.…”

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 field transfer matrix method has also been adopted by many researchers to investigate circular arch problems, such as the work presented by (Fujii and Gong, 1988). Recently, Gimena et al. (2009) introduced a numerical transfer-method based on the method of field transfer matrix, and the solution is attained through utilization of the first-, second-, and the fourth- order Runge–Kutta approximation method (Hoffman, 2001).…”

Section: Circular Beamsmentioning

confidence: 99%

Free in-plane vibration of curved beam structures: A tutorial and the state of the art

Yang

Esmailzadeh

2017

Journal of Vibration and Control

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The study of free in-plane vibration of curved beams, using different beam theories, is more challenging than that of straight beams, since the structural deformations in curved beams depend not only on the rotation and radial displacements, but also on the coupled tangential displacement caused by the curvature of structures. A critical review of the publications on the free in-plane vibration of curved beams to demonstrate the state of the art has been presented. The governing differential equations of motion for the curved beams, based on different hypotheses (including and excluding the axial extensity, rotary inertia and the shear deformation), were discussed and different approaches to solve the developed equations of motion have been identified. Finally, a systematic comparison of the dynamic properties of curved beams evaluated with various forms of curvatures based on different hypotheses were presented.

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Numerical transfer-method with boundary conditions for arbitrary curved beam elements

Cited by 14 publications

References 14 publications

Alternative approach to the buckling phenomenon by means of a second order incremental analysis

Alternative approach to the buckling phenomenon by means of a second order incremental analysis

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

Free in-plane vibration of curved beam structures: A tutorial and the state of the art

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