Dynamic rigid-plastic deformation of arbitrarily shaped plates

A rigid, perfectly-plastic model of solids is applied to study the dynamic behavior of simply supported or clamped, arbitrarily shaped plates on visco-elastic foundation. The role of membrane forces and transverse shear forces in the yield condition and the influence of geometry changes are neglected. The plate is subjected to explosive loads uniformly distributed over the surface. Several mechanisms of dynamic deformation of the plate are considered. For each mechanism, equations of the dynamic behavior are obtained. Operating conditions of these mechanisms are analyzed. Analytical expressions for the limit and high loads and for the maximum final deflections are obtained. Detailed analyses are given for an astroid-shaped plate, for a plate with a contour consisting of two arcs and for a plate with an internal free hole or a rigid insert.