Elastoplastic Analysis Method for Dynamic Agencies

Abstract

A method for the analysis of discrete elastoplastic structural systems with proportional damping and subjected to dynamic loads is presented. Firstly, it is shown that, using the mode superposition method, the actual node displacements and generalized stresses can be given suitable integral representations in terms of the known load history and of the unknown plastic strain history; secondly, considering the evolution of the system in a small time step and imposing the relevant laws of (holonomic) plasticity theory at the step extreme times only, it is shown that the step plastic strain increments can be obtained by solving algebraic problems shaped either in the form of a linear complementarity problem, or in the forms of two alternative quadratic programming problems. The formats of these problems are recursive and thus sequentially applicable, such as to cover the entire loading process, in much the same way quasistatic elastoplastic problems can be solved. The resulting numerical procedure turns out to be unconditionally stable, while the only error sources are due to the modeling of the unknown plastic strain history. Imposed strain‐like loads (e.g., thermal shocks) can be considered. A simple numerical example is also presented and a preliminary comparison of the proposed method with other known methods is discussed.