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**Elastic analysis for rotating functionally graded annular disk with exponentially-varying profile and properties.**
*(English)*
Zbl 1459.74063

Summary: Functionally graded materials have been widely used in engineering and human health applications. The issues about mechanical behavior of functionally graded material have received considerable attention. However, because of the complexity of material property, geometric profile, and mechanical load, there is still lack of proper analytic solutions about deformation and stress in many articles. The principal goal of this research is to study the effect of mechanical load on deformation and stress in rotating thin-walled functionally gradient material annular disk with exponentially-varying profile and properties. The inner and outer surfaces of annular disk are subjected to different pressures simultaneously. For this purpose, the infinitesimal theory of elasticity and axisymmetric plane stress assumptions has been proposed to formulate the governing equation. The governing equation is a generalized confluent hypergeometric differential equation, based on Whittaker’s functions; this is the first time that closed-form solutions of mechanical behaviors are revealed about proposed functionally gradient material model. Besides, another four boundary conditions are also discussed, i.e., the inner and outer surfaces of the annular disk are considered to be the combinations of free and clamped conditions. Numeric examples of two different functionally graded material properties are given to demonstrate displacement and stress solutions. Moreover, uniform disks made of homogeneous material under different boundary conditions are investigated, which are special cases of the proposed rotating functionally gradient material disks. Finally, some conclusions are made at the end of the present paper.

### MSC:

74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |

74K20 | Plates |

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\textit{W.-F. Lin}, Math. Probl. Eng. 2020, Article ID 2165804, 10 p. (2020; Zbl 1459.74063)

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### References:

[1] | Timoshenko, S. P.; Goodier, J. N., Theory of Elasticity (1970), New York, NY, USA: McGraw-Hill, New York, NY, USA · Zbl 0266.73008 |

[2] | Nayak, P.; Saha, K., Elastic limit angular speed of solid and annular disks under thermomechanical loading, International Journal of Engineering, Science and Technology, 8, 2, 30-45 (2016) |

[3] | Yildirim, V., Closed-form formulas for hyperbolically tapered rotating disks made of traditional materials under combined thermal and mechanical loads, International Journal of Engineering and Applied Sciences, 10, 2, 73-92 (2018) |

[4] | Durodola, J. F.; Attia, O., Deformation and stresses in functionally graded rotating disks, Composites Science and Technology, 60, 7, 987-995 (2000) |

[5] | Shi, Z.; Zhang, T.; Xiang, H., Exact solutions of heterogeneous elastic hollow cylinders, CompositeStructures, 79, 1, 140-147 (2007) |

[6] | You, L. H.; Wang, J. X.; Tang, B. P., Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure, Meccanica, 44, 3, 283-292 (2009) · Zbl 1254.74080 |

[7] | Dai, T.; Dai, H.-L., Investigation of mechanical behavior for a rotating FGM circular disk with a variable angular speed, Journal of Mechanical Science and Technology, 29, 9, 3779-3787 (2015) |

[8] | Nejad, M. Z.; Abedi, M.; Lotfian, M.; Ghannad, M., Exact and numerical elastic analysis for the FGM thick-walled cylindrical pressure vessels with exponentially-varying properties, Archives of Metallurgy and Materials, 61 (2016) |

[9] | Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1966), Washington, DC, USA: US Government Printing Office, Washington, DC, USA |

[10] | Gharibi, M.; Zamani Nejad, M.; Hadi, A., Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius, Journal of Computational Applied Mechanics, 48, 1, 89-98 (2017) |

[11] | Sadd, M. H., Theory, Applications, and Numerics (2009), Cambridge, MA, USA: Academic Press, Cambridge, MA, USA |

[12] | Thawait, A. K., Stress analysis of rotating cylindrical pressure vessel of functionally graded material by element based material gradation, Research & Reviews: Journal of Physics, 5, 3, 7-15 (2018) |

[13] | Eraslan, A. N.; Akis, T., On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems, Acta Mechanica, 181, 1-2, 43-63 (2006) · Zbl 1103.74032 |

[14] | Zenkour, A. M., On the magneto-thermo-elastic responses of FG annular sandwich disks, International Journal of Engineering Science, 75, 54-66 (2014) · Zbl 1423.74254 |

[15] | Akbari, M. R.; Ghanbari, J., Analytical exact solution for functionally graded rotating disks under non-symmetric thermal and mechanical loads, Materials Research Express, 6, 5 (2019) |

[16] | Strashnov, S.; Alexandrov, S.; Lang, L., Description of residual stress and strain fields in FGM hollow disc subject to external pressure, Materials, 12, 3, 440 (2019) |

[17] | Salehi Kolahi, M. R.; Karamooz, M.; Rahmani, H., Elastic analysis of shrink-fitted thick FGM cylinders based on linear plane elasticity theory, Mechanics of Advanced Composite Structures, 7, 1, 121-127 (2020) |

[18] | Yildirim, A.; YarimpabuĂ§, D.; Celebi, K., Transient thermal stress analysis of functionally graded annular fin with free base, Journal of Thermal Stresses, 43, 9, 1138-1149 (2020) |

[19] | You, L. H.; Tang, Y. Y.; Zhang, J. J.; Zheng, C. Y., Numerical analysis of elastic-plastic rotating disks with arbitrary variable thickness and density, International Journal of Solids and Structures, 37, 52, 7809-7820 (2000) · Zbl 1001.74050 |

[20] | Bayat, M.; Sahari, B. B.; Hamouda, A. M. S.; Saleem, M.; Mahdi, E., On the stress analysis of functionally graded gear wheels with variable thickness, International Journal for Computational Methods in Engineering Science and Mechanics, 9, 2, 121-137 (2008) · Zbl 1372.74005 |

[21] | Jalali, M. H.; Shahriari, B., Elastic stress analysis of rotating functionally graded annular disk of variable thickness using finite difference method, Mathematical Problems in Engineering, 2018 (2018) · Zbl 1426.74200 |

[22] | Yildirim, S.; Tutuncu, N., On the inertio-elastic instability of variable-thickness functionally-graded disks, Mechanics Research Communications, 91, 1-6 (2018) |

[23] | Thawait, A. K.; Sondhi, L.; Sanyal, S.; Bhowmick, S., Stress and deformation analysis of clamped functionally graded rotating disks with variable thickness, Mechanics and Mechanical Engineering, 23, 1, 202-211 (2019) |

[24] | Bayat, M.; Sahari, B.; Saleem, M.; Dezvareh, E.; Mohazzab, A., Analysis of functionally graded rotating disks with parabolic concave thickness applying an exponential function and the Mori-Tanaka scheme, IOP Conference Series: Materials Science and Engineering, 17, 1 (2011) |

[25] | Leu, S.-Y.; Chien, L.-C., Thermoelastic analysis of functionally graded rotating disks with variable thickness involving non-uniform heat source, Journal of Thermal Stresses, 38, 4, 415-426 (2015) |

[26] | Zheng, Y.; Bahaloo, H.; Mousanezhad, D.; Mahdi, E.; Vaziri, A.; Nayeb-Hashemi, H., Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity, International Journal of Mechanical Sciences, 119, 283-293 (2016) |

[27] | Yildirim, V., Thermomechanical characteristics of a functionally graded mounted uniform disc with/without rigid casing, Journal of Aerospace Technology and Management, 11 (2019) |

[28] | Shahriari, B.; Safari, M., Stress analysis of FGM rotating disk subjected to mechanical and thermal loads in aircraft gas turbine engine, Mechanics of Advanced Composite Structures, 7, 1, 1-13 (2020) |

[29] | Gao, Y.; Xiao, W.-S.; Zhu, H., Nonlinear vibration of functionally graded nanotubes using nonlocal strain gradient theory and a two-steps perturbation method, Structural Engineering and Mechanics, 69, 2, 205-219 (2019) |

[30] | Yu, T.; Zhang, J.; Hu, H.; Bui, T. Q., A novel size-dependent quasi-3D isogeometric beam model for two-directional FG microbeams analysis, Composite Structures, 211, 76-88 (2019) |

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