Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Eroğlu, Uğurcan; Tüfekçi, Ekrem

doi:10.24107/ijeas.457535

Cited by 3 publications

(5 citation statements)

References 35 publications

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“…If this criterion is met, the trial C t is just a characteristic eigenvalue C i and go to Step (7). (6) If not, increase new trial to C t ¼ C t þ DC and return to Steps (2)- (5). During executions, note the sign of D 1 � D 2 where D 1 is the determinant of previous execution and D 2 is the determinant of present execution.…”

Section: Solution Methods and Validationmentioning

confidence: 99%

“…1,2 In recent years, mega structures such as buildings, bridges, offshore and plant structures have been built, and the static and dynamic problems of columns are still an attractive topic in various engineering fields. [3][4][5] In column analyses, column behaviors are definitively affected by its own weight, which is called heavy column. In particular, since the standing heavy column negatively affects the reduction of the buckling load, this effect should be sufficiently included in the analysis and design of the column.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibration and buckling of heavy column with regular polygon cross-section

Lee

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

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Section: Solution Methods and Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibration and buckling of heavy column with regular polygon cross-section

Lee

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…For tapered beam/column analysis, various taper functions [3,12,13] along the column axis, including linear, parabolic, sinusoidal, and exponential functions, have been considered. The effects of various cross-sectional shapes [14,15], including rectangular, circular, elliptical, and regular polygons, on the optimization of column buckling have been examined.…”

Section: Introductionmentioning

confidence: 99%

Buckling of Tapered Heavy Columns with Constant Volume

Lee

2021

Mathematics

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This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The differential equation governing the buckling shapes of the column is derived based on the equilibrium equations of the buckled column elements. The governing equation is numerically integrated using the direct integration method, and the eigenvalue is obtained using the determinant search method. The accuracy of the method is verified against the existing solutions for particular cases. The effects of side number, taper ratio, self-weight, and end condition on the buckling load and mode shape are investigated. The contribution of self-weight acting alone to the buckling response is also explored. For a given column volume, especially, the buckling length and its stress distribution of the columns with different geometries and end conditions are estimated.

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“…These nonlinearities are also considered for the analytical solutions of composite beams in the literature [41][42][43]. Furthermore, varying cross sections decisively affect the stiffness of the whole beams, and arbitrary cross sections lead to coupling of different vibration and buckling modes (flexural and torsional) [44,45]. For the composite wind turbine blades, the shape of the cross section is complex, and the material properties vary, depending on the position throughout the thickness of the beam and along the axis of the beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study

et al. 2020

Self Cite

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This study focuses on the dynamic modelling and analysis of the wind turbine blades made of multiple layers of fibre reinforced composites and core materials. For this purpose, a novel three-dimensional analytical straight beam model for blades is formulated. This model assumes that the beam is made of functionally graded material (FGM) and has a variable and asymmetrical cross section. In this model, the blades are assumed to be thin, slender and long with a relatively straight axis. They have two main parts, namely the core and the shell. The so-called core consists of a lightweight isotropic foam material, which also adds significant damping to the system. The core material is covered by the shell, which is modelled using homogenous and orthotropic material assumptions as the structure is reinforced with continuous fibres. Therefore, the blades are modelled under a straight beam with varying cross-section assumptions, in which the effective elastic properties are acquired by homogenizing the cross section. The beam formulation for modelling the system is performed both analytically and numerically with the finite element method. The results of both methods are in well agreement. The maximum deviation between the results is found below 4%.

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Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Cited by 3 publications

References 35 publications

Free vibration and buckling of heavy column with regular polygon cross-section

Free vibration and buckling of heavy column with regular polygon cross-section

Buckling of Tapered Heavy Columns with Constant Volume

Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study

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