Thermo-mechanical bending of power and sigmoid FGM sandwich plate using sinusoidal shear deformation theory

Abstract

The present study focuses on the thermo-mechanical bending investigation of functionally graded material (FGM) sandwich plates with temperature-dependent material properties. For engineering applications, FGMs are typically made of metal and ceramic, where metal provides high rigidity and ceramic delivers high thermal resistivity. Material properties of FGM sandwich plate are considered temperature dependent and assumed to be continuously graded in thickness direction. Sigmoid and power law distributions are adopted to obtain the smooth and continuous variation of mechanical and thermal properties of FGM plate. To carry out thermo-mechanical bending, one dimensional heat conduction equation is utilized to obtain temperature variation in thickness direction. Sinusoidal shear deformation theory (SSDT) is a type of non-polynomial shear deformation theory which accounts for sinusoidal distribution of transverse shear stress and satisfies the traction free boundary condition. The governing equations for thermo-mechanical bending analysis for FGM sandwich plates are derived using Hamilton’s variational principle following SSDT and Navier’s solution. Closed form solutions are obtained to predict centre deflection, and normal and shear stresses of simply supported FGM sandwich plates. The effect of temperature-dependent material properties, power and sigmoid law, gradation index, temperature difference, side to thickness ratio, and aspect ratio over central deflection, normal stress, and shear stress are carried out and analysed. It may be concluded from the analysis that temperature-dependent material properties and gradation index for power and sigmoid law considerably influence the central deflection, normal stress, and shear stress. A good agreement amongst the obtained and available results of existing shear deformation theory is found to validate the accuracy of the SSDT.