Dynamic Stability Analysis by Matrix Function

Abstract

The matrix function method is applied to the dynamic stability problems of initially imperfected columns and plates under time‐dependent axial compression in elastic and elastic‐plastic regions. Matrix functions are derived from the solution of ordinary differential equation systems in a manner similar to that for scalar equations. The rigid body spring mode (RBSM) is adopted for presenting the spatial properties of the structural members. In this model, each element consists of rigid bodies with a rotational spring, which allows the restoring forces to be taken into consideration. In the numerical examples in the elastic and elastic‐plastic regions, the propoosed method, based on the reanalysis technique, is compared with other methods based on the incremental procedure. It is concluded that the proposed method is numerically efficient, general, and practical for the dynamic stability analysis of structural systems.