Influence of Thickness Variation on Elastic Critical Buckling of Compressed Thin Plate

In the plane-stress problem of the classical plate theory, the constant thickness assumption is conventionally used as one of the assumptions in the Kirchhoff-Love hypothesis, which almost becomes a fixed concept for such thin-plate models. However, for some situations of uniformly stretched mid-surface (variable plate thickness), such as the elastic buckling of an in-plane uniformly compressed thin plate, this assumption is a deformation constraint on the plate free surface, thereby increasing the unnecessary anti-deformation stiffness. Herein, by introducing the mean stress and strain into Hooke’s law of a three-dimensional infinitesimal element, transforming the corresponding stress–strain relations, shrinking (dimension-reducing) them, and copying them onto the mid-surface of the plane-stress plate, the corresponding two-dimensional stress–strain relations can be obtained, which include a variable thickness strain. Furthermore, by combining with the corresponding stretching-type geometric relations at the mid-surface, the resultant stretching force on the transverse cross-section can be determined. Simultaneously, the Kirchhoff-Love hypothesis (bending geometric relations) can still be considered applicable to such an already uniformly stretched mid-surface, thereby the cross-section resultant moment relations throughout the thickness can also be determined. Finally, a modified approach is proposed to evaluate the influence of thickness variation on the elastic critical buckling of uniformly compressed thin plates by replacing the flexural stiffness value, which is believed to have a better prediction accuracy.