Elastk‐plastic dynamic analysis of structures using known elastic solutions

Abstract

AbstractA numerical method is shown to analyse the dynamic elastic‐plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained.This method is applied to simply supported beams with bilinear stress‐strain relations with different strain‐hardening rates and to a simply supported elastic‐ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.