Open Access Open Access  Restricted Access Subscription or Fee Access

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

Shrikant Gunjal, S. A. Bhalchandra

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.

Full Text:

PDF

References


Rameshchandra P. Shimpi, “Refined plate theory and its variants,” AIAA Journal, vol. no. 40, issue

no. 1, pp. 137 – 146, (2002).

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).

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).

Metin Aydogdu, “A new shear deformation theory for laminated composite plates,” Composite

Structures, vol. no. 89, pp. 94-101, (2009).

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).

J. N. Reddy, “A simple higher-order theory for laminated composite plates,” Journal of Applied

Mechanics, vol. no. 51, pp. 745-752, (1984).

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).

K P Soldatos, “On certain refined theories for plate bending,” ASME Journal of Applied Mechanics,

vol. no. 55, pp. 994-995, (1988).

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.

, pp. 1907-1919, (2007).

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).

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).

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.

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-

, (1999).

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).

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).

Reddy J. N., Mechanics of laminated composite plates: theory and analysis, CRC Press, Inc, New

York.




DOI: https://doi.org/10.37591/joeam.v12i3.6189

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Journal of Experimental & Applied Mechanics