Buckling of Long Orthotropic Plates Including Higher-Order Transverse Shear

Abstract

The problem of buckling of long orthotropic plates under combined in-plane loading is considered. An approximate analytical solution is presented. The concept of a mixed Rayleigh-Ritz method is used considering higher-order shear deformations. The achieved load function of the half-buckling wavelength and the inclination of the nodal lines are minimized via a simplex search method. For low transverse shear stiffnesses the model predicts buckling coefficients under in-plane shear load that are of the same order of magnitude as those resulting from a uniaxial compressive load. For a thin plate, the critical shear load is larger by 42% compared to the uniaxial case. The model also suggests that for highly anisotropic materials, such as paper, the critical load solution is still influenced by the shear deformation effect at width-to-thickness ratios above 100.