Buckling for an elastoplastic plate with an incremental constitutive relation (Q1116810)

The authors study in a precise mathematical formulation and careful analysis the buckling problem of a plate loaded by a planar thrust which is time dependent. A quasistatic model of an elastoplastic material with memory is used which is much more general than those used for the von Kármán and Hencky models. The mathematical formulation leads to the solution of nonlinear integro-differential equations. Precise results on necessary and sufficient conditions for bifurcation are given. The interesting result is found that the whole loading history is of importance. Furthermore, it is shown that buckling might occur even when the loading is decreasing.