Bending analysis of FGM plates using sinusoidal shear and normal deformation theory

Abstract

This paper presents the bending analysis of functionally graded material (FGM) plates using sinusoidal shear and normal deformation theory. The in-plane displacements include sinusoidal functions in the thickness coordinate to consider the effect of transverse shear deformation, and transverse displacement includes the effect of transverse normal strain using the cosine function in thickness coordinate. The displacement field of the theory enforces to satisfy shear stress-free boundary conditions on the top and bottom surfaces of the plate with realistic variations across the thickness. Plate material properties vary across thickness directions according to a power law. The boundary value problem of the theory is derived using the principle of virtual work. Simply supported plate bending problems are solved using the Navier solution technique. Response of the plate is obtained with respect to the type of load, type of plate, aspect ratio, and power law index. The results of present theory are compared with those of quasi-3D discrete layer theory and semi-analytical solutions based on the theory of elasticity to ensure the accuracy of theory. The current theory showed excellent agreement with more exact theories in bending response.

Keywords

• Sinusoidal shear deformation theory
• Power law
• FGM
• Thick plate
• Displacements
• Stresses