Time-history analysis provides for linear or nonlinear evaluation of dynamic structural response under loading which may vary according to the specified time function. Dynamic equilibrium equations, given by K u(t) + C d/dt u(t) + M d2/dt u(t) = r(t), are solved using either modal or direct-integration methods. Initial conditions may be set by continuing the structural state from the end of the previous analysis. Additional notes include:
- Step Size – Direct-integration methods are sensitive to time-step size, which should be decreased until results are not affected.
- HHT Value – A slightly negative Hilber-Hughes-Taylor alpha value is also advised to damp out higher frequency modes, and to encourage convergence of nonlinear direct-integration solutions.
- Nonlinearity – Material and geometric nonlinearity, including P-delta and large-displacement effects, may be simulated during nonlinear direct-integration time-history analysis.
- Multi-support excitation article