Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finite element method

Ahmed, Saad; Bensaid, Ismail; Fellah, Ahmed

doi:10.1007/s00419-023-02429-w

Cited by 9 publications

(2 citation statements)

References 57 publications

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“…In order to formulate the real life problems, 3D-FEM is well suited numerical scheme for the solutions of the problems that don't have the analytical result. Therefore addition to 2-D case, we will pay attention to 3-D FEM applications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein).…”

Section: Introductionmentioning

confidence: 99%

3D Stabilized FEM Solution of the MHD Equations in an External Medium and Around a Solid

AYDIN,

ERDOĞAN

2023

Cumhuriyet Science Journal

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In this study, we consider 3-D MagnetoHydroDynamic (MHD) flow problems with different configurations which are mathematically expressed by system of coupled partial differential equation with coupled boundary conditions. These equations are solved numerically using one of the most popular schemes named as the finite element method (FEM) with SUPG type stabilized version in order to obtain accurate and stable solutions especially for the high values of the problem parameters. Obtained numerical solutions are visualized in terms of figures by taking the 2-D slices of the 3-D data in order to emphasize the accuracy of the proposed formulation.

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Section: Introductionmentioning

confidence: 99%

3D Stabilized FEM Solution of the MHD Equations in an External Medium and Around a Solid

AYDIN,

ERDOĞAN

2023

Cumhuriyet Science Journal

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“…Using this methodology (as well as other equivalent alternatives that consider flexural stiffness singularities using the Dirac delta function), the problem of buckling in cracked beams has been studied in other works [12][13][14][15][16]. Recently, this methodology has also been applied to the analysis of buckling instabilities in FG beams [17] and in nanocantilevers [18].…”

Section: Introductionmentioning

confidence: 99%

Buckling of Cracked Euler–Bernoulli Columns Embedded in a Winkler Elastic Medium

Loya

Santiuste

Aranda-Ruiz

et al. 2023

MCA

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This work analyses the buckling behaviour of cracked Euler–Bernoulli columns immersed in a Winkler elastic medium, obtaining their buckling loads. For this purpose, the beam is modelled as two segments connected in the cracked section by a mass-less rotational spring. Its rotation is proportional to the bending moment transmitted through the cracked section, considering the discontinuity of the rotation due to bending. The differential equations for the buckling behaviour are solved by applying the corresponding boundary conditions, as well as the compatibility and jump conditions of the cracked section. The proposed methodology allows calculating the buckling load as a function of the type of support, the parameter defining the elastic soil, the crack position and the initial length of the crack. The results obtained are compared with those published by other authors in works that deal with the problem in a partial way, showing the interaction and importance of the parameters considered in the buckling loads of the system.

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Elastic medium and torsional spring effects on the nonlocal dynamic of functionally graded porous nanotubes

Uzun,

Yaylı,

Civalek

2024

Arch Appl Mech

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In this study, Eringen’s nonlocal elasticity theory that applies the small size effects in functionally graded porous nanotubes embedded in an elastic matrix is discussed. The material properties of functionally graded porous nanotubes are taken into account to vary over the radius direction with a rule of mixture. The free torsional vibration relation according to nonlocal elasticity theory, via Hamilton’s principle, is obtained and an eigenvalue solution is constructed for the free torsional vibration response of the presented work. The presented analytical model is validated by comparing the calculated mathematical results for homogeneous nanotubes with rigid and non-rigid boundary conditions. Special attention is given to deformable boundary conditions, porosity coefficient, material grading coefficient and also to the influence of elastic medium on the free torsional vibration frequencies. In this paper, it has been proven that the influence of length, elastic medium, elastic torsional spring rigidities, material grading and porosity coefficients on the vary in the torsional vibration frequency of the functionally graded nanotube is not small.

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Effect of crack presence on the dynamic and buckling responses of bidirectional functionally graded beams based on quasi-3D beam model and differential quadrature finite element method

Cited by 9 publications

References 57 publications

3D Stabilized FEM Solution of the MHD Equations in an External Medium and Around a Solid

3D Stabilized FEM Solution of the MHD Equations in an External Medium and Around a Solid

Buckling of Cracked Euler–Bernoulli Columns Embedded in a Winkler Elastic Medium

Elastic medium and torsional spring effects on the nonlocal dynamic of functionally graded porous nanotubes

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