Noniterative Integration Algorithms with Controllable Numerical Dissipations for Structural Dynamics

Abstract

A new family of noniterative algorithms with controllable numerical dissipations for structural dynamics is studied. Particularly, this paper provides nine members of the proposed algorithms and two existing methods are included as two special cases. The proposed algorithms achieve unconditional stability and are second-order accurate for linear elastic systems. The explicit expressions of stability conditions for nonlinear stiffness systems are completely presented, which shows that new algorithms possess unconditional and conditional stability for stiffness softening and hardening systems, respectively. A comprehensive stability and accuracy analysis, including numerical energy dissipations and dispersions, are studied in order to gain insight into spectral properties of new algorithms. Due to the existence of the nonzero spurious root, this paper also pays attention to the influence of the spurious root, which shows that the spurious root does not influence numerical accuracy at low-frequency domains. Although the proposed algorithms exhibit the unusual overshoot behaviors in either displacement or velocity, numerical damping ratios in new algorithms can significantly eliminate this overshoot at a few steps. The new dissipative algorithms are appropriate to solve numerical transient responses of the structure. Numerical examples are also presented to demonstrate the analytical results.