Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian's decomposition methods. Part I: Elastic solution

Hojjati, Mehdi; Jafari, Sanaz

doi:10.1016/j.ijpvp.2008.06.001

Cited by 37 publications

(28 citation statements)

References 27 publications

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“…You et al [11] assumed that Young's modulus, thermal expansion coefficient, and mass density are all varying in the radial direction of the disk according to power-law functions of r. They considered the disk is to be subjected to a uniform temperature change to derive the closed-form solutions of such rotating FG disks. Hojjati and Jafari [12] assumed that the rotating annular elastic disks may be of uniform or variable thicknesses and mass densities. They used both the homotopy perturbation and Adomian's decomposition analytical methods to find stresses and displacements in such disks.…”

Section: Introductionmentioning

confidence: 99%

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Allam

Tantawy

Yousof

et al. 2017

Archive of Mechanical Engineering

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Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young's moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

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Section: Introductionmentioning

confidence: 99%

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Allam

Tantawy

Yousof

et al. 2017

Archive of Mechanical Engineering

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“…Therefore, the usage of the homotopy theory has been effective in deriving the approximate solutions of different types of problems, including nonlinear second order differential equations [7,8] or nonlinear fractional equations [9] that model the behavior of physical and engineering systems. Hojjati and Jafari compared the HPM and the ADM to obtain the distributions of stresses and displacements in a rotating annular elastic disk [10]. They have concluded that, although the numerical results are almost the same, the HPM is much easier, more convenient and efficient than the ADM and the VIM.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

Olvera

Elı́as-Zúñiga

2014

Abstract and Applied Analysis

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We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM) that is based on the homotopy perturbation method (HPM) and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM). At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

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“…Some additional numerical methods are used in the literature. In [15], the rotating annular disks with uniform and variable thicknesses and densities are solved using homotopy perturbation method and Adomian's decomposition method. This work is a predictive assessment of the stresses in and deformation of a rotating annular disk with variable thickness variation.…”

Section: Introductionmentioning

confidence: 99%

Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical Methods

Zenkour¹,

Mashat²

2011

ENG

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In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is available for the first disk while the exact analytical solution is not available for the second annular disk. Both exact and numerical results for stress function, stresses, strains and radial displacement will be investigated for the first annular disk of variable thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second rotating variable-thickness annular disk is investigated. Finally, the distributions of stress function, displacement, strains, and stresses will be presented. The appropriate comparisons and discussions are made at the same angular velocity.

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Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian's decomposition methods. Part I: Elastic solution

Cited by 37 publications

References 27 publications

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical Methods

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