An optimal family of controllable numerically dissipative time integration algorithms for structural dynamics

Based on the generalized single-step representations within the scope of the classical linear multi-step (LMS) algorithms, an optimal family of controllable numerically dissipative time integration algorithms are developed which are fundamentally useful for structural dynamics computations. The optimality of the algorithms are in the sense of achieving optimal algorithmic properties in all aspects within the limit of the Dahlquist theorem which pertains to only a special class referred to as the so-called linear multi-step (LMS) methods with attention to: unconditionally stable, second-order accurate, zero-order displacement and velocity overshoot, minimal dissipation and dispersion with respect to the selected magnitude of the principal roots in the high-frequency limit. The comparisons of the optimal family of algorithms with the currently available controllable numerically dissipative algorithms are shown which demonstrate the superiority of most of the algorithmic properties. An illustrative elasto-plastic large deformation structural dynamic problem is also presented from an application viewpoint.