Elastic/plastic buckling of thick plates

This paper is concerned with the elastic/plastic buckling of thick plates o f rectangular and circular shapes. For thick plates, the significant effect of transverse shear deformation on the critical buckling load may be accou nted for by adopting the Mindlin plate theory. To capture the elastic/plast ic 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 d erived for (a) uniaxially and equibiaxially loaded rectangular plates with two opposite edges simply supported while the other two edges may take on a ny combination of free, simply supported or clamped boundary condition and (b) uniformly inplane loaded circular plates with either simply supported e dge or clamped edge. Extensive buckling stress factors are tabulated for th ese 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 str ess factor but the divergence of the results from the two theories increase s with increasing plate thicknesses, E/sigma (0) values and e values of the Ramberg-Osgood relation. The buckling results from the two theories and th eir 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. (C) 2001 E lsevier Science Ltd. All rights reserved.