An efficient finite element formulation for bending, free vibration and stability analysis of Timoshenko beams

Karkon, Mohammad

doi:10.1007/s40430-018-1413-0

Cited by 10 publications

(5 citation statements)

References 31 publications

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“…In order to obtain the shape functions of the element, indirect method is used. In this strategy, the element's field functions u, w and , and nodal displacement vector {D} are expressed by the following equations [39]…”

Section: Fig 1 Three-node Proposed Beam Elementmentioning

confidence: 99%

“…It should be mentioned, the proposed element free of shear locking. Because for thin beams, parameters and will be very small ( ≈ 0, ≈ 0) and the presented shape functions and stiffness matrix approach to the shape functions and stiffness matrix of three-node Euler-Bernoulli element [39]. Also, the nodal force vector of the element can be obtained from below equation: where q, m distributed load and moment on the element, respectively.…”

Section: Fig 1 Three-node Proposed Beam Elementmentioning

confidence: 99%

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A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

Karkon

2020

J Braz. Soc. Mech. Sci. Eng.

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In this paper, a new three-node element with three degrees of freedom per node is proposed for bending, free vibration and buckling analysis of laminated beams. The element's formulation is based on the first-order shear deformation theory (FSDT). For this aim, transverse displacement and rotation field of the element are selected from fifth and fourth order, respectively. Moreover, the shear strain is varied as quadratic function throughout the element. It is worth noting that the quadratic function can be used for axial displacement field. By employing equilibrium equation, curvature and shear strain relations of laminated beam with FSDT theory, the exact and explicit shape functions of the displacement fields are obtained. By utilizing the obtained shape functions, the explicit form of the stiffness matrix is calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. It should be mentioned, the proposed element is free of shear locking. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, bending, free vibration and buckling analysis of laminated beams with different boundary conditions and aspect ratios are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.

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Section: Fig 1 Three-node Proposed Beam Elementmentioning

confidence: 99%

Section: Fig 1 Three-node Proposed Beam Elementmentioning

confidence: 99%

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

Karkon

2020

J Braz. Soc. Mech. Sci. Eng.

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“…Besides the above studies, there are some remarkable papers related to static and dynamic analyses of nano/microbeam models in the open literature. 27–42…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of short-fiber reinforced composite nanobeams based on nonlocal strain gradient theory

Gul

2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study deals with the dynamic behavior of short-fiber reinforced composite nanobeams. It is assumed that short-fibers are aligned or randomly distributed in the composite nanobeams. Nonlocal strain gradient theory is applied to composite nanobeam mechanics including Euler–Bernoulli and Timoshenko beam models. The transverse vibration of these composite nanobeams is investigated for various boundary conditions. Approximate Ritz method is used for obtaining the natural frequencies of short-fiber reinforced composite nanobeams. In addition to vibration analysis, wave propagation in short-fiber reinforced composite nanobeams is investigated and wave dispersion relations are analytically obtained for both Euler-Bernoulli and Timoshenko beam models. The vibration and wave dispersion results of short-fiber reinforced composite nanobeams are obtained for aligned and randomly distributed cases. The results obtained from this paper showed that there is no significant difference between the aligned and randomly oriented short-fiber composite nanobeams. This provides great convenience to designers where it is not possible to orient the reinforcement material in composites. The present study may be useful for the mechanical analysis and design of micro/nano-electromechanical systems (MEMS/NEMS), nanoprobes, nanosensors, nanoactuators, and atomic force microscopes.

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“…Ragesh et al (2016) conducted a free vibration analysis of a four-noded Kirchoff rectangular element with three DOFs per node resting on a Winkler model elastic foundation with varied boundary conditions for different thicknesses and foundation properties. Karkon and Karkon (2016) performed the free vibration analysis of the Timoshenko beam on a two-parameter elastic foundation using the FEM. The two-nodded element was used for modeling with two DOFs.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis of rigid pavement resting on two-parameter soil foundation model using finite element framework

Wani,

Nallasivam K.

2023

WJE

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Purpose The purpose of this study is to numerically model the rigid pavement resting on two-parameter soil and to examine its modal parameters. Design/methodology/approach This study is carried out using a one-dimensional beam element with three rotational and three translational degrees of freedom based on the finite element method. MATLAB programming is used to perform the free vibration analysis of the rigid pavement. Findings Cyclic frequency and their corresponding mode shapes were determined. It has been investigated how cyclic frequency changes as a result of variations in the thickness, span length of pavement, shear modulus, modulus of subgrade, different boundary conditions and element discretization. Thickness of the pavement and span length has greater effect on the cyclic frequency. Maximum increase of 29.7% is found on increasing the thickness, whereas the cyclic frequency decreases by 63.49% on increasing span length of pavement. Research limitations/implications The pavement's free vibration is the sole subject of the current investigation. This study limits for the preliminary design phase of rigid pavements, where a complete three-dimensional finite element analysis is unnecessary. The current approach can be extended to future research using a different method, such as finite element grilling technique, mesh-free technique on reinforced concrete pavements or jointed concrete pavements. Originality/value The finite element approach adopted in this paper involves six degrees of freedom for each node. Furthermore, to the best of the authors’ knowledge, no prior study has done seven separate parametric investigations on the modal analysis of rigid pavement resting on two-parameter soil.

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An efficient finite element formulation for bending, free vibration and stability analysis of Timoshenko beams

Cited by 10 publications

References 31 publications

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

Dynamic analysis of short-fiber reinforced composite nanobeams based on nonlocal strain gradient theory

Modal analysis of rigid pavement resting on two-parameter soil foundation model using finite element framework

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