Ultimate carrying capacity of elastic-plastic plates on Pasternak foundation.

In the present work, the problem of an infinite elastic-perfectly plastic plate under axisymmetrical loading conditions resting on a Pasternak elastic foundation is considered. The plate is assumed thin, thus making possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen’s yield criterion with associative flow rule. An uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elastic-plastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, under the collapse load the inner elastic-plastic region can be separated into two or three different regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows to estimate the elastic-plastic behavior of the plate up to the onset of collapse, thus providing the collapse load of the plate, the corresponding plastic mechanism and the size of the elastic-plastic regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.