Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks

Hassani, Ali; Hojjati, Mehdi; Farrahi, G.H.; Alashti, R. Akbari

doi:10.1016/j.compstruct.2011.06.001

Cited by 34 publications

(32 citation statements)

References 30 publications

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“…In 2011, Hasan Callioglu et al [5] analyzed the state of the stresses on the rotating annular disc made of Functionally Graded Materials (FGM). Similary in 2011, Hassani et al [6] obtained distributions of stress and strain components of rotating hyperbolic disks with nonuniform material properties subjected to a power form thermoelastic loading under different boundary conditions by semiexact methods of Liao's homotopy analysis method. In 2012, Roberta Sburlati [7] obtained analytical solutions for thick wall cylinders subjected to internal and external pressure, where the entire wall was made of FGM.…”

Section: Introductionmentioning

confidence: 94%

“…Optimizing the design of such a cylinder requires an understanding of the elastoplastic behavior of the material [4]. Many numerical and analytical works have been done on this subject, especially on uniform rotating discs, to predict the stress field, deformations, and rupture, to avoid the risk of damage when the device is subjected to different loading conditions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In 2005, Ahmet N. Eraslan et al [4] obtained in the context of the small deformation theory analytical solutions on flat deformations in elastic tubes operably under pressure grades.…”

Section: Introductionmentioning

confidence: 99%

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Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials

Leroy

Ndop

Nkene

et al. 2018

Journal of Engineering

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Drilling tools or drilling pipes, such as drill bit and mill drill, are often subjected to various forces, including essentially tangential forces, centered on their axis of rotation. The main objective of this work is to find analytical and numerical solutions of the distribution of stress field, deformation, and displacement, when such tools are subjected to such forces. It will be assumed that the instrument in the chosen model in this work is a rotating hollow cylinder constructed from a Functional Graded Material (FGM). Because of the graduation of the FGM, the mechanical and elastic properties such as Young’s modulus, density, and Poisson’s ratio vary in the radial direction according to a power law function. By choosing that the inhomogeneity parameter is between -0.5 and 0.5, we have established the differential equation which describes the equilibrium of the hollow cylinder in rotation under an axial load. The calculations performed have allowed finding an analytical solution which was compared with numerical solutions obtained by using the shooting method and the fourth-order Runge-Kutta algorithm. These analytical and numerical results have shown that the values of tangential stresses are greater than the radial stresses. The radial stresses and tangential and vertical stresses progressively increase with the axial force Fz. The force Fz affects more tangential stresses that the radial stresses. The tangential stress, tangential deformations, and displacements are higher on the inner walls of the cylinder than on the exterior surfaces. The results obtained are very important and can be applied in the modeling and designing wicks and drilling strawberries in order to reduce their rapid wear and damage.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials

Leroy

Ndop

Nkene

et al. 2018

Journal of Engineering

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“…Lettingẍ = 0, the nonlinear restoring force of the discontinuous system (8) can be written as Fig. 6a.…”

Section: The Analytical Expressions For the Heteroclinic-like Orbitsmentioning

confidence: 99%

“…The earliest applications such as water wheels [5] and grinding wheels [6] can be dated back to the times of Archimedes and Aristotle. In modern times, rotating disk has been widely studied in various fields such as mechanics [7], material science [8], thermodynamics [9], chemistry [10] and so on. In this paper, nonlinear dynamics techniques are used to investigate a novel rotating disk model with irrational nonlinearities whose dynamic behaviors is similar to the conventional pendulum coupled with SD oscillator [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A rotating disk linked by a pair of springs

2014

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In this paper, we propose a novel model which consists of a rotating disk linked by a pair of springs exhibiting both smooth and discontinuous dynamics. This model provides a cylindrical dynamical system with irrational restoring force due to the geometry configuration. The dynamic behaviors of the unperturbed system are similar to the conventional pendulum coupled with SD oscillator of the homoclinic orbits of the first and second type. A new-type heteroclinic orbit connecting a standard saddle equilibrium and a nonstandard saddle-like equilibrium is presented and investigated analytically in the discontinuous case. Furthermore, the conventional and the extended Melnikov methods are employed to detect the chaotic thresholds for the homoclinic orbits of the first and second type and the heteroclinic-like orbits under the perturbation of both viscous damping and external harmonic forcing for both smooth and discontinuous cases, respectively. The results presented herein this paper demonstrate the predicated periodic solutions and the chaotic attractors of SD type and pendulum type.

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“…Çallıoğlu et al (2011) performed an exact stress analysis of annular rotating discs made of functionally graded materials by assuming that both elasticity modulus and material density vary radially as a function of a simple power rule with the same inhomogeneity parameter. Hassani et al (2011) obtained distributions of stress and strain components of rotating hyperbolic disks with non-uniform material properties subjected to a power form thermo-elastic loading under different boundary conditions by semi-exact methods of Liao's homotopy analysis method. Argeso (2012) presented analytical solutions for two different annular rotating disk problems for the elastic stress state: The first problem involves an exponentially variable profile rotating disk made of an isotropic and homogeneous material, the second is a uniform disc made of exponentially functionally graded materials.…”

Section: Introductionmentioning

confidence: 99%

A Parametric Study on the Centrifugal Force-Induced Stress and Displacements in Power-Law Graded Hyperbolic Discs

Yıldırım

2018

Lat. Am. j. solids struct.

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An extensive parametric study on the variation of the centrifugal-force-induced stress and displacements with the inhomogeneity indexes, profile parameters and boundary conditions is conducted based on the author's recently published analytical formulas for radially functionally power-law graded rotating hyperbolic discs under axisymmetric conditions. The radial variation of the thickness of the disc is chosen to obey a hyperbolic function defined either convergent or divergent. In the present work, contrary to the published one, it is assumed that both Young's modulus and density radially vary with the same inhomogeneity index to enable to conduct a parametric study. Under this additional assumption, for the values of the chosen powerlaw indexes 5, 0, 5    for the material grading rule, and the chosen profile parameters 1, 0.75, 0.5, 0.25, 0, 0.25, 0.5, 0.75, 1 m      for a hyperbolic disc; the variations of the radial stress, the hoop stress and the radial displacement are all illustrated graphically for a rotating disc whose both surfaces are stress-free, for a rotating disc mounted a rigid shaft at its center and its outer surface is stress-free, and finally for a rotating disc attached a rigid shaft at its center and guided at its outer surface (a rigid casing exists at the outer surface).

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Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks

Cited by 34 publications

References 30 publications

Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials

Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials

A rotating disk linked by a pair of springs

A Parametric Study on the Centrifugal Force-Induced Stress and Displacements in Power-Law Graded Hyperbolic Discs

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