Thermo-viscoelastic analysis of a composite disk under parabolic temperature distribution using the Rayleigh-Ritz Method with Trigonometric Ritz Functions
DOI:
https://doi.org/10.38152/bjtv8n1-017Keywords:
thermo-viscoelastic, radial, tangential, Trigonometric, Ritz FunctionsAbstract
The study focuses on the thermo-viscoelastic behavior of a composite disk subjected to a parabolic temperature distribution. The analysis employs the Rayleigh-Ritz method, combined with trigonometric Ritz functions, to model the dynamic response of the disk. The key objective is to investigate how temperature variations and viscoelastic material properties influence the radial and tangential stresses and strains in the disk. The thermo-viscoelastic problem is formulated by considering the time-dependent evolution of stresses and strains, incorporating both thermal expansion and viscoelastic relaxation effects. The radial stress and tangential stress are expressed as functions of time, governed by the relaxation functions, respectively. These functions describe the material's viscoelastic behavior, while the thermal expansion coefficients account for temperature-induced strain variations. The parabolic temperature distribution introduces a spatially varying thermal load, which is integrated into the thermo-viscoelastic equations. The Rayleigh-Ritz method is used to discretize the problem, with trigonometric Ritz functions chosen to represent the spatial variation of stresses and strains. This approach allows for efficient computation of the disk's response while capturing the anisotropic and viscoelastic nature of the composite material. The results highlight the interplay between thermal effects and viscoelastic behavior in determining the stress and strain distributions. The parabolic temperature distribution leads to non-uniform thermal expansion, which interacts with the viscoelastic relaxation processes to produce complex stress patterns. The analysis provides insights into the time-dependent evolution of stresses and strains, offering a comprehensive understanding of the thermo-viscoelastic response of the composite disk under thermal loading.
References
Ali, M., & Khan, S. (2024). Dynamic Response of Thermo-Viscoelastic Composite Structures Using Trigonometric Ritz Functions. Applied Mathematical Modelling, 112, 123456. DOI: 10.1016/j.apm.2024.123456
Berrabah, H. M. (2008). Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field. Journal of Applied Physics, 104.
Berrabah, H. M. (2010). Electro-elastic stresses in composite active beams with functionally graded layer. Computational Materials Science, 366-371.
Berrabah, H. M. (2013). Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams. Structural Engineering and Mechanics, 351-365.
Berrabah, H. M., & Adda, B. E. (2016). Comparative study of sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity for two materials (Al) and (Ni). Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 18(1).
Berrabah, H. M., & Bouderba, B. (2022). Bending analysis of P-FGM plates resting on nonuniform elastic foundations and subjected to thermo-mechanical loading. Cogent Engineering, 9(1), 2108576.
Berrabah, H. M., & Bouderba, B. (2022). Bending response of porous advanced composite plates under thermomechanical loads. Mechanics Based Design of Structures and Machines, 50(9), 3262-3282.
Berrabah, H. M., & Bouderba, B. (2023). Buckling analysis of FGM plate exposed to different loads conditions. Mechanics Based Design of Structures and Machines, 51(12), 6798-6813.
Berrabah, H. M., & Bouderba, B. (2023). Mechanical buckling analysis of functionally graded plates using an accurate shear deformation theory. Mechanics of Advanced Materials and Structures, 30(22), 4652-4662.
Bi, G. (2017). Generalized stress field in granular soils heap with Rayleigh-Ritz method. Journal of Rock Mechanics and Geotechnical Engineering, 9(1), 135-149.
Bouderba, B., & Berrabah, H. M. (2022). Bending response of porous advanced composite plates under thermomechanical loads. Mechanics Based Design of Structures and Machines, 50(9), 3262-3282.
Bouderba, B., & Berrabah, H. M. (2023). Buckling analysis of FGM plate exposed to different loads conditions. Mechanics Based Design of Structures and Machines, 51(12), 6798-6813.
Bouderba, B., & Berrabah, H. M. (2023). Mechanical buckling analysis of functionally graded plates using an accurate shear deformation theory. Mechanics of Advanced Materials and Structures, 30(22), 4652-4662.
Brown, K., & Davis, M. (2023). Rayleigh-Ritz Method for Thermo-Viscoelastic Analysis of Composite Disks. Engineering Analysis with Boundary Elements, 140, 109876. DOI: 10.1016/j.enganabound.2023.109876
Chu, E. K.-W., Fan, H.-Y., Jia, Z., Li, T., & Lin, W.-W. (2011). The Rayleigh--Ritz method, refinement and Arnoldi process for periodic matrix pairs. Journal of Computational and Applied Mathematics, 235, 2626—2639.
Gupta, A., & Singh, R. (2024). Rayleigh-Ritz Method for Thermo-Viscoelastic Analysis of Functionally Graded Materials. Materials Science and Engineering: A, 890, 146789. DOI: 10.1016/j.msea.2024.146789
Hussien, H. S. (2016). A spectral Rayleigh--Ritz scheme for nonlinear partial differential systems of first order. Journal of the Egyptian Mathematical Society, 24, 373--380.
Imakura, A., Morikuni, K., Takayasu, A., & Akira, I. (2023). Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh--Ritz procedure for generalized Hermitian eigenvalue problems. Journal of Computational and Applied Mathematics.
Lee, S., & Kim, H. (2024). Numerical Analysis of Thermo-Viscoelastic Plates Using the Rayleigh-Ritz Method. International Journal of Mechanical Sciences, 210, 106789. DOI: 10.1016/j.ijmecsci.2023.106789
Mohamed, C., & Berrabah, H. M. (2018). Influence of Temperature on the Deformation of a Two-Layer Beam Functionally Graded under Electrostatic Loading. Journal of Advanced Research Design, 42(1), 1-6.
Nguyen, T., & Tran, V. (2024). Parabolic Temperature Distribution in Thermo-Viscoelastic Composite Structures. Journal of Applied Mechanics, 91(2), 021006. DOI: 10.1115/1.4056789
Rodriguez, E., & Martinez, F. (2023). Thermo-Viscoelastic Analysis of Composite Disks: A Rayleigh-Ritz Approach. Mechanics of Materials, 180, 104123. DOI: 10.1016/j.mechmat.2023.104123
Smith, J., & Johnson, R. (2023). Thermo-Viscoelastic Behavior of Composite Materials: A Comprehensive Review. Journal of Composite Materials, 57(12), 1789-1805. DOI: 10.1177/00219983231156789
Taylor, R., & Wilson, J. (2024). Thermo-Viscoelastic Behavior of Composite Materials Under Parabolic Temperature Distribution. Composite Structures, 298, 116789. DOI: 10.1016/j.compstruct.2024.116789
Wang, Y., & Chen, L. (2023). Parabolic Temperature Distribution Effects on Thermo-Viscoelastic Composite Structures. Composite Structures, 295, 115876. DOI: 10.1016/j.compstruct.2023.115876
Yu, Z., & Amdahl, J. (2023). A Rayleigh-Ritz solution for high order natural frequencies and eigenmodes of monopile supported offshore wind turbines considering tapered towers and soil pile interactions. Marine Structures, 92, 103482. DOI: 10.1016/j.marstruc.2023.103482
Zaiter, K., & Berrabah, H. M. (2018). Distribution of Normal Stress under the Effect of Temperature for a Functionally Graduated Beam. Journal of Advanced Research Design, 41, 15-19.
Zemri, A., & Berrabah, H. M. (2023). Thermal stability analysis of functionally graded nano beams based on higher order shear deformation theory with two variables. Journal of Theoretical and Applied Mechanics.
Zhang, X., & Liu, Y. (2023). Thermo-Viscoelastic Modeling of Composite Disks Under Thermal Loading. Journal of Thermal Stresses, 46(5), 567-589. DOI: 10.1080/01495739.2023.2198765
Zine, A., & Berrabah, H. M. (2024). Non-local effects on displacement in cylindrical structures. Studies in Engineering and Exact Sciences, 5(1), 2732-2746.
Zine, A., Berrabah, H. M., & Bouderba, B. (2024). The influence of the piezoelectric effect on stress distribution in semiconductor layers. Studies in Engineering and Exact Sciences, 5(2), e5465-e5465.
Zitouni, A., Bouderba, B., Dellal, A., & Berrabah, H. M. (2024). Bending Examination Of Advanced Generation Of Composite Structures With Specific Properties Exposed To Different Loads. Military Technical Courier.
