## 5 Conclusions  
A few main conclusions can be drawn from the current study. These can be summarized as:  
* Analytical and numerical solutions, using FEA, of the creep problem in rotating thick cylinders made of Al-SiC\({}_{\rm P}\) composite and subjected to internal and external pressures were successfully achieved.
* All results of the stresses, strains, and strain rates distributions obtained are found to be in full agreement with the published data.
* All plotted results of the stresses, strains, and strain rate distributions obtained through the analytical approach were found to be in excellent compliance with those solutions obtained using finite element analysis (FEA).
* FEA Model was verified through a calculated model from exact analytical analysis.
* The radial stresses \(\sigma_{t}\) obtained from analytical and numerical solutions are constant at the inner and outer surfaces, but they are higher at radius \(r\cong(r_{in}+r_{out})/2\) for \(\omega=300,\ \omega=500,\ \text{and}\ \omega=1000\ \text{rad}/\text{sec}\).
* The radial stresses \(\sigma_{t}\) obtained from analytical and numerical solutions, increase gradually with an increase in the rotational velocity \(\omega\).
* The variations of tangential stresses \(\sigma_{t}\) decrease gradually at the outer surface and increase very little at the inner surface with increasing rotational velocity \(\omega\).
* The tangential stresses \(\sigma_{t}\) are also higher at the inner surface than those at the outer surface.
* Tangential stresses attained nearly constant values in the radial direction of the cylinder for \(\omega=300\ \text{rad}/\text{sec}\) and low rotational velocities.
* Variations of Axial stresses \(\sigma_{z}\) have the same behavior as tangential stresses \(\sigma_{t}\).
* All radial strain rate values are higher (in magnitude) at the inner surface and vary with parallel curves in the radial direction of the cylinder.
* All radial strain rates decrease gradually with an increase in the rotational velocity.
* All tangential strain rates and equivalent creep strain rates have the same behavior as radial strain rates.  
Conceptualization, M.H.E.-S.; Methodology, Y.F.; Software, M.H.E.-S.; Validation, Y.F.; Investigation, Y.F.; Resources, M.H.E.-S.; Data curation, M.H.E.-S.; Writing--original draft, M.H.E.-S.; Writing--review & editing, Y.F.; Visualization, M.H.E.-S.; Project administration, Y.F.; Funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript.  
Figure 12: Variation of Equivalent Creep Strain Rate \(\dot{\epsilon}_{e}\) with respect to time at different radii.  
**Funding:** The authors extend their appreciation to the Researchers Supporting Project number (RSPD2023R698), King Saud University, Riyadh, Saudi Arabia, for funding this research work.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The datasets generated during and/or analyzed during the current study are available from the corrsponding author on reasonable request.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
FEA/M Finite Element Analysis/Method  
FGM Functionally Graded Material  
(Si-C) Silicon Carbide  
Al-SiC\({}_{\text{p}}\) Aluminum Silicon Carbide composite  
\(r_{in}\) Inner radius  
\(r_{out}\) Outer radius  
\(p_{in}\) Internal pressure  
\(p_{out}\) External pressure  
\(\rho\) Material density  
\(\omega\) ras/sec Angular/Rotational velocity  
\(\sigma_{r}(r)\) Radial stress  
\(\sigma_{t}(r)\) Tangential stress  
\(\sigma_{z}\) Axial stress  
\(\dot{\varepsilon}_{r}\) Radial strain rate  
\(\dot{\varepsilon}_{t}\) Tangential strain rate  
\(\dot{\varepsilon}_{z}\) Axial strain rate  
\(\sigma_{e}\) effective stress  
\(\dot{\varepsilon}_{t}\) Effective strain rate  
\(B\) and \(n\) Creep materials constants  
\(u\) Radial displacement  
\(C_{1}\) and \(C_{2}\) Boundary constants