Accuracy of bounds of plastic deformation for dynamically loaded plates and shells

Abstract

Both upper and lower bounds on final displacements of dynamically loaded, rigid-plastic structures can be easily calculated. These bounds are obtained from an assumed, statically admissible stress field and a kinematically admissible velocity field, respectively. The range between these bounds is a function of the difference between stresses in these assumed fields and the actual stress distribution in the structure. This paper identifies the manner in which structural characteristics and the load distribution influence accuracy of the bounds. Generally, the range between the bounds is small for one-dimensional deformations in response to uniformly distributed loads and larger for two-dimensional deformations and more concentrated loads.