An Unconditionally Stable Explicit Algorithm for Nonlinear Structural Dynamics

Abstract

An unconditionally stable explicit algorithm with second-order accuracy is proposed in state space. Stability, relative period error, and amplitude decay of the proposed algorithm are studied. It is shown that the proposed algorithm is unconditionally stable for linear systems and nonlinear systems whether the stiffness of the structure is the softening or hardening type. This stability property is appealing because currently, explicit algorithms cannot be unconditionally stable when the stiffness is the hardening type. In addition, the stability and accuracy of the proposed algorithm are demonstrated by several nonlinear numerical examples.