Refined Sine Theory Including Transverse Normal Stress in Cylindrical Bending

Abstract

Two new sine models including the transverse normal deformation are presented for the analysis of laminated plates with a cross-ply layout in cylindrical bending. A layer refinement for each component of the displacements is considered. The transverse shear strain is obtained by using a cosine function avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between the layers for the transverse normal and shear stresses, and the boundary conditions on the upper and lower surfaces of the plate. Note that the number of unknowns is independent of the number of layers. The main topics are focused on the evaluation of the transverse normal and shear stresses by the constitutive relation. Mechanical and thermomechanical results within a closed-form solution technique are compared to elasticity reference solutions for thin and very thick plates.