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

Shrikant Gunjal, S. A. Bhalchandra


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.


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

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