Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters

Essa, Saad; Argeso, Hakan

doi:10.1007/s00707-017-1896-2

Cited by 16 publications

(18 citation statements)

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“…In the case of circular discs and cylinders, a common type of anisotropy is polar orthotropy. In particular, the effect of plastic anisotropy on stress and strain fields in rotating discs has been studied in [34][35][36][37][38][39], using different material models and boundary conditions. Various boundary value problems for orthotropic cylinders have been solved in [40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

2019

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Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke’s law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials.

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Section: Introductionmentioning

confidence: 99%

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

2019

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“…Using anisotropic/orthotropic materials to form FG new kind nonhomogeneous materials is also one of the new trends in engineering design. There are, therefore, a limited number of works on FG disks composed of anisotropic materials in the open literature [1][2][3][4][5][6][7][8]. From those, Durodola and Attia [1] considered FG orthotropic materials to study deformation and stresses in rotating hollow uniform disks.…”

Section: Introductionmentioning

confidence: 99%

“…Kacar and Yıldırım [6] offered analytical formulas for the displacement and stress determination in polar orthotropic functionally power-law graded polar orthotropic rotating uniform disks under three boundary conditions. Essa and Argeso [7] developed analytical solutions for the analysis of elastic polar orthotropic FG annular free-free and fixed-free disks rotating with constant angular velocity. The elasticity moduli and thickness were assumed to be varied radially by a nonlinear function controlled by three parameters, while the radial variation of density may be defined by any form of continuous function.…”

Section: Introductionmentioning

confidence: 99%

The Complementary Functions Method Solution to the Functionally Graded Polar Orthotropic Rotating Hyperbolic Disks with Both Radially and Circumferentially Aligned Fibers

Yıldırım

2019

International Journal of Engineering and Applied Sciences

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In the present study, efforts have been made to numerically evaluate elastic displacements and stresses in a convergent or divergent hyperbolic disk subjected to a centrifugal force of constant circular velocity. The disk material is assumed to be continuously radially functionally graded (FG) with two orthotropic materials based on the simplest Voigt rule with a power of volume fraction of two constituents. The fibers are assumed to be aligned along either radial (RR) or circumferential (CR) directions. Having been a second order differential equation with variable coefficients, the governing equation so-called Navier equation is first derived and then put in the form of two differential equations of first order. These two ordinary differential equation set is originally solved based on the initial value problem (IVP) by employing the Complementary Functions Method (CFM). The numerical results are verified with the corresponding benchmark results for uniform thickness FG polar orthotropic disks. The radial variation of the elastic fields in a hyperbolic disk is investigated for several boundary conditions, disk profile parameters, and the gradient parameter for both the radially and circumferentially aligned fibers. Some numerical results are also presented. Under the case that is considered in this study, it is revealed that the CR disk offers much higher elastic fields than RR disk under all boundary conditions. For a composite rotating disk rotating at a constant speed, it will be better to align fibers along the radial directions, to use convergent disk profiles, and to locate the material having higher radial stiffness at the outer surface. It is also disclosed that the location of the maximum Von-Mises equivalent stress in fixed-free disks varies regarding the fiber orientation.

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“…In quest of searching more advanced materials, scholars have begun to apply anisotropic materials as functionally graded material constituents to form both anisotropic and inhomogeneous structures. For annular structures made of functionally graded anisotropic and inhomogeneous materials, there may be provided relatively a few studies on the stress and displacement analyses in the available literature (Gurushankar 1975, Mian and Spencer 1998, Durodola and Attia 2000, Chen et al 2007, Wang and Sudak 2008, Zenkour 2009, Lubarda 2012, Peng and Li 2012, Boga 2016, Kacar and Yıldırım 2017, Zeng et al 2017Essa and Argeso 2017). Gurushankar (1975) obtained closed form solution for the elastic fields in a rotationally symmetric, nonhomogeneous, polar orthotropic, annular disk of varying thickness and density, subjected to thermal loading.…”

Section: Introductionmentioning

confidence: 99%

“…Zeng et al (2017) considered variable thickness rotating discs made of a functionally graded fiber-reinforced material. Recently Essa and Argeso (2017) developed analytical solutions for the analysis of elastic polar orthotropic functionally graded annular disks rotating with constant angular velocity. Traction-free inner and outer surfaces, and annular disks mounted on a circular rigid shaft having traction-free outer surface were studied separately by Essa and Argeso (2017).…”

Section: Introductionmentioning

confidence: 99%

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2019

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Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters

Cited by 16 publications

References 40 publications

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

The Complementary Functions Method Solution to the Functionally Graded Polar Orthotropic Rotating Hyperbolic Disks with Both Radially and Circumferentially Aligned Fibers

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