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A successive approximation method for thermo-elasto-plastic analysis of a reinforced functionally graded rotating disc

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Abstract

Thermo-elasto-plastic analysis of a rotating disc made of Functionally Graded Materials (FGMs) is studied in this paper using Successive Approximation Method (SAM). The plane stress condition is assumed for formulation of the problem. After computation of effective material properties based on modified mixture rule, the governing equations are derived analytically and then is solved using the Differential Quadratic Method (DQM). After obtaining the displacements and stresses, the yield conditions are calculated by von-Mises failure criteria. The rotating disc is made of an Aluminum–Silicon Carbide functionally graded material. The plastic behavior of Aluminum is considered as strain hardening one. The effects of angular speed, percentage of ceramic particles, particle reinforcement power, and boundary conditions such as temperature gradient on the radial and tangential thermo-elasto-plastic strains, stresses, and equivalent stresses is investigated. The results show that the radial stresses through the disc are significantly less than tangential stresses, therefor the tangential stresses has a significant effect on the equivalent stress and yield conditions.

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Abbreviations

\({C}_{ij}\) :

Weighting coefficient of n − th order derivative of an arbitrary function

\(E\) :

Young's Modulus

\(f\) :

Fraction of a material's phase

\(H\) :

Plastic modulus

\(k\) :

Thermal conductivity coefficient

\(n\) :

Power of ceramic particles distribution

\(p\) :

Applied load

\(q\) :

Stress to strain transfer ratio

\(T\) :

Temperature

\(u\) :

Displacement

\(r\) :

Radius

\(\alpha\) :

Thermal expansion coefficient

\(\varepsilon\) :

Strain

\(\theta\) :

Arbitrary angle

\(\nu\) :

Poisson's ratio

\(\rho\) :

Density

\(\sigma\) :

Stress

\(\omega\) :

Rotational velocity

\(1\) :

First phase

\(2\) :

Second phase

\(c\) :

Ceramic phase

\(co\) :

Ceramic phase at outer side

\(cr\) :

Critical

\(e\) :

Equal

\(i\) :

Inner side

\(m\) :

Metal phase

\(o\) :

Outer side

\(r\) :

Radial direction

\(von\) :

Von misses

\(y\) :

Yield

\(z\) :

Axial direction

\(\theta\) :

Tangential direction

\(i\) :

Number of step

\(m\) :

Metal phase

\(p\) :

Plastic regime

SAM:

Successive approximation method

FGM:

Functionally graded material

DQM:

Differential quadratic method

VMP:

Variable material property

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This study was funded by X (4005278/024).

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Authors and Affiliations

  1. Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan, 87317-51167, Kashan, Iran

    Mohsen Kholdi, Soheil Saeedi, Seyed Ali Zargar Moradi, Abbas Loghman & Mohammad Arefi

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  1. Mohsen Kholdi
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  2. Soheil Saeedi
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Correspondence to Mohammad Arefi.

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Kholdi, M., Saeedi, S., Zargar Moradi, S.A. et al. A successive approximation method for thermo-elasto-plastic analysis of a reinforced functionally graded rotating disc. Archiv.Civ.Mech.Eng 22, 2 (2022). https://doi.org/10.1007/s43452-021-00321-4

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