A Unified Shear Deformation Theory for the Bending of Isotropic, Functionally Graded, Laminated and Sandwich Beams and Plates

作者：Sayyad Atteshamuddin S; Ghugal Yuwaraj M

来源：International Journal of Applied Mechanics, 2017, 9(1): 1750007.

DOI：10.1142/S1758825117500077

• Shear deformation
• FG
• laminated
• sandwich
• beams
• plates
• higher order theories

In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy's theory, but trigonometric, hyperbolic and exponential functions are first time used in the present displacement field. The present theory is accounted for an accurate distribution of transverse shear stresses through the thickness of plate, therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived from the principle of virtual work. Navier type closed-form solutions are obtained for simply supported boundary conditions. To verify the global response of the present theory it is applied for the bending of both one-dimensional (beams) and two-dimensional (plates) functionally graded, laminated composite and sandwich structures. The present results are compared with exact elasticity solution and other higher order shear deformation theories to verify the accuracy and efficiency of the present theory.

• 出版日期2017-1