Elastic/plastic buckling of thick plates

This paper is concerned with the elastic/plastic buckling of thick plates of rectangular and circular shapes. For thick plates, the significant effect of transverse shear deformation on the critical buckling load may be accounted for by adopting the Mindlin plate theory. To capture the elastic/plastic behaviour, two competing theories of plasticity are considered; viz. the incremental theory (IT) of plasticity (with the Prandtl–Reuss constitutive relations) and the deformation theory (DT) of plasticity (with the Hencky constitutive relation). Analytical elastic/plastic stability criteria are derived for (a) uniaxially and equibiaxially loaded rectangular plates with two opposite edges simply supported while the other two edges may take on any combination of free, simply supported or clamped boundary condition and (b) uniformly inplane loaded circular plates with either simply supported edge or clamped edge. Extensive buckling stress factors are tabulated for these plates with material properties defined by the Ramberg–Osgood relation. Comparing the results obtained from the DT and the IT, it can be seen that not only the DT in general gives consistently lower values of buckling stress factor but the divergence of the results from the two theories increases with increasing plate thicknesses, E/σ0 values and c values of the Ramberg–Osgood relation. The buckling results from the two theories and their marked difference from each other for thick plates may be exploited in the design of experimental tests to ascertain which one of the two theories provides good estimates of the buckling loads for thick plates