# Thermo-mechanical Analysis of Orthotropic plate under Sinusoidally Distributed Thermal load by using Trigonometric shear Deformation Theory (TSDT)

Year : 2022 | Volume : | Issue : 3 | Page : 10-33
By

1. ### S.A. Bhalchandra

1. Post Graduate Student, Department of Applied Mechanics, Government College of Engineering, Aurangabad, Maharashtra, India
2. Professor, Department of Applied Mechanics, Government College of Engineering, Aurangabad, Maharashtra, India

#### Abstract

For the thermal analysis of simply supported square and rectangular plates applied to sinusoidal distributed linear thermal load throughout the plate thickness and in combination with sinusoidal distributed transverse mechanical loading, a trigonometric shear deformation theory is proposed. In this work, a sinusoidal function in terms of thickness coordinates is being used in the displacement field in conjunction with the transverse shear deformation effect. The normal and shear stress can be determined by using the strain-displacement equation of elasticity. The transverse shear stress can be calculated simply by applying constitutive relations to the top and bottom of the plate which fulfill the shear stress-free boundary conditions, also termed as traction-free boundary conditions. As a result, the shear correction factor is not required by the theory. The virtual work principle is used to derive the governing equation and boundary conditions of the plate theory. The responses like thermal stresses and displacements for orthotopic plates subjected to linear sinusoidal distributed thermal load in combination with transverse mechanical load are obtained. The result is obtained in form of normalized stresses and displacement by using normalized formed given in the literature. By comparing the results to classical plate theory, first-order order shear deformation theory, and higher-order order shear deformation theory, the proposed theory is validated.

## Keywords: Trigonometric shear deformation theory, Isotropic, orthotropic, bending, sinusoidal distributed thermal load.

How to cite this article: Shrikant Gunjal, S.A. Bhalchandra Thermo-mechanical Analysis of Orthotropic plate under Sinusoidally Distributed Thermal load by using Trigonometric shear Deformation Theory (TSDT) joeam 2022; 12:10-33
How to cite this URL: Shrikant Gunjal, S.A. Bhalchandra Thermo-mechanical Analysis of Orthotropic plate under Sinusoidally Distributed Thermal load by using Trigonometric shear Deformation Theory (TSDT) joeam 2022 {cited 2022 Feb 09};12:10-33. Available from: https://journals.stmjournals.com/joeam/article=2022/view=91940/

#### References

1. Rameshchandra P. Shimpi, “Refined plate theory and its variants,” AIAA Journal, vol. no. 40, issue no. 1, pp. 137 – 146, (2002).
2. J. L. Mantari, A. S. Oktem, C. Guedes Soares, “A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates,” International Journal of Solids and Structures, vol. no. 49, pp. 43-53, (2012).
3. Eshwar G. Pawar, Sauvik Banerjee, Yogesh M. Desai, “Stress analysis of laminated composite and sandwich beam using novel shear and normal deformation theory,” Latin American Journal of Solids and Structures, vol. no. 12, pp. 1340-1361, (2015).
4. Metin Aydogdu, “A new shear deformation theory for laminated composite plates,” Composite Structures, vol. no. 89, pp. 94-101, (2009).
5. Chorng- Fuh Liu, Chih-Hsing Huang, “Free vibration of composite laminated plates subjected to temperature changes,” Computers and Structures, vol. no. 60, issue no. 1, pp. 95-101, (1996).
6. J. N. Reddy, “A simple higher-order theory for laminated composite plates,” Journal of Applied Mechanics, vol. no. 51, pp. 745-752, (1984).
7. A S Sayyad, B M Shinde, Y M Ghugal, “Thermoelastic bending analysis of laminated composite plates according to various shear deformation theories,” Open Engineering, vol. no. 5, pp. 18-30, (2015).
8. K P Soldatos, “On certain refined theories for plate bending,” ASME Journal of Applied Mechanics, vol. no. 55, pp. 994-995, (1988).
9. S S Akavci, “Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation,” Journal of Reinforced Plastics and Composites, vol. no. 26, pp. 1907-1919, (2007).
10. M Karama, K S Afaq, S Mistou, “A new theory for laminated composite plates,” Proc. IMechE Part L: Journal of Materials: Design and Applications, vol. no. 223, pp. 53-62, (2009).
11. S. Sayyad, Y. M. Ghugal, B. M. Shinde, “Thermal stress analysis of laminated composite plate using exponential shear deformation theory,” International Journal of Automotive Composites, vol. no. 2, issue no. 1, pp. 23 – 40, (2016).
12. S. Sayyad, B. M. Shinde, Y. M. Ghugal, “Thermoelastic bending analysis of orthotropic plates using hyperbolic shear deformation theory,” Composite: Mechanics., Computations and Applied, An Int. Journal, 2013, 4(3), 257–278.
13. J. S. M. Ali, K. Bhaskar, T. K. Varadan, “A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates,” Composites Structures, vol. no. 45, issue no. 3, pp. 227-232, (1999).
14. T. Kant, S. M. Shiyekar, “An assessment of a higher-order theory for composite laminates subjected to thermal gradient,” Composites Structures, vol. no. 96, pp. 698-707, (2013).
15. X. Zhao, Y. Y. Lee, K. M. Liew, “Mechanical and thermal buckling analysis of functionally graded plates,” Composites Structures, vol. no. 90, pp. 161-171, (2009).
16. Reddy J. N., Mechanics of laminated composite plates: theory and analysis, CRC Press, Inc, New York.

Regular Issue Open Access Article

## Journal of Experimental & Applied Mechanics

ISSN: 2230-9845
 Volume 12 Issue 3 Received December 24, 2021 Accepted February 2, 2022 Published February 9, 2022