Mode‐Superposition Methods for Elastoplastic Systems

Abstract

In the framework of modal analysis the dynamic correction method is applied to evaluate the response of elastic perfectly plastic systems having numerous degrees of freedom. According to this method, the nodal structural response is evaluated as the sum of a pseudo‐static response, which is the particular solution of the differential equations of motion in nodal coordinates, and a dynamic response evaluated using a reduced number of natural modes. Once the modal analysis is applied, the elastoplastic response is evaluated by using a stepwise approach in modal space and by solving at each step a linear complementarity problem or equivalent quadratic programming problems. In a numerical example it is shown that by using the dynamic correction method greater accuracy, especially for elastoplastic systems, is obtained with respect to the traditional mode‐displacement methods, without considerable increase in the computational effort.