Effects of transverse shearing on cylindrical bending, vibration, and buckling of laminated plates

Abstract

The displacements for cylindrical bending and stretching of laminated and thick plates are expressed through-the-thickness by a few algebraic terms and a complete set of trigonometric terms. Only a few terms of this series are needed to get sufficiently accurate results for laminated and thick plates. Equations of equilibrium based on a sufficient number of terms of this series for displacements are determined using variational theorems from three-dimensional elasticity. Several examples are worked out. The displacements and stresses are obtained for simply supported isotropic and layered beams with a rectangular cross section and a sinusoidal lateral load distribution. These results are compared to an exact elasticity solution. Results for several approximations are obtained for a simply supported and a clamped beam with a rectangular cross section loaded at the center and results are compared to experimental results. Results are also obtained for isotropic and layered beams with a rectangular cross section for several approximations for the lowest natural frequency and buckling load.