Concise formula for the critical buckling stresses of an elastic plate under biaxial compression and shear

This study aims to develop a concise formula for the critical buckling stresses of a simply supported plate under biaxial compression and shear. The critical stresses are obtained for different aspect ratios using classical plate theory and the Ritz method. The four-dimensional critical stress formula, which is expressed in terms of the three in-plane stresses and the aspect ratio, is developed empirically according to the two-dimensional relationships between the in-plane stresses. The findings that are of interest are: (1) the critical stress relationship is linear for the aspect ratios within the range 1 to 2 and nonlinear for the aspect ratios within the range 2 to 5; and (2) as shear stress approaches its critical value, the critical stress relationship becomes increasingly linear and less dependent on aspect ratio.