Direct-integration time-history analysis is a nonlinear, dynamic analysis method in which the equilibrium equations of motion are fully integrated as a structure is subjected to dynamic loading. Analysis involves the integration of structural properties and behaviors at a series of time steps which are small relative to loading duration. The equation of motion under evaluation is given as follows:
NOTE: Integration is performed at every time step of the input record, regardless of the output increment.
The Newmark method is unconditionally stable only when 2 β ≥ γ ≥ 1/2, which is why we recommend using β = 1/4. When β = 1/6, which yields the linear acceleration method, formulation is only conditionally stable, and can become unstable when dt/T > 2√ 3/(2π), where dt is the time step and T is the shortest structural period which is excited by loading. The shortest period may be obtained during modal analysis such that time step may be coordinated to ensure convergence.
- Mass and stiffness-proportional damping – Damping of stiff elements with inelastic softening