Lower bounds to large displacements of impulsively loaded plastically orthotropic structures

Abstract

Impulsively loaded plastic structures deform beyond the limits of applicability of the geometrically linear theory. It was experimentally observed that due to the membrane action actual permanent displacements are smaller than those predicted by the infinitesimal theory. Exact solutions for deformed shapes in the geometrically nonlinear range are not known for anisotropic structures.The note advances a technique allowing to bound from below the permanent, moderately large deflection at a chosen point of a rigid-plastic, dynamically loaded structure. The method originally developed for isotropic solids and introducing an auxiliary kinematically admissible velocity field allowing to estimate the dissipation due to the nonlinear terms in the strain rates is extended to orthotropic plates and shells.Lower bounds are obtained to maximum deflections of circular orthotropic plates obeying a piece-wise linear yield criterion when accounting for moderately large displacements. The influence of orthotropy on the permanent deflections is discussed and the results are compared to those of the linear theory. Meaningful differences are noticed, particularly for more intense impulses. Results for a cylindrical shell are also presented.