GeneralizedAlpha Integrator

The GeneralizedAlpha integrator is an advanced implicit time integration method for dynamic analysis with controllable numerical damping across frequency ranges.

Description

This integrator is particularly suitable for:

  • Structural dynamics problems requiring targeted numerical damping

  • Cases where specific frequency content should be preserved

  • Problems with high-frequency noise

  • Nonlinear dynamic analysis

  • Multi-physics simulations with different time scales

The GeneralizedAlpha method provides second-order accuracy and unconditional stability while allowing for controlled high-frequency damping.

Parameters

The GeneralizedAlpha integrator requires the following parameters:

Parameter

Description

Default

Notes

alpha_m

Alpha_m factor

None

Required

alpha_f

Alpha_f factor

None

Required

gamma

Gamma factor

0.5 + alpha_m - alpha_f

Optional

beta

Beta factor

(1 + alpha_m - alpha_f)^2/4

Optional

Usage Example

# Create a GeneralizedAlpha integrator with basic parameters (gamma and beta calculated automatically)
integrator = fm.analysis.integrators.create_integrator("generalizedalpha",
                                                alpha_m=0.2,
                                                alpha_f=0.4)

# Create a GeneralizedAlpha integrator with all parameters explicitly defined
integrator = fm.analysis.integrators.create_integrator("generalizedalpha",
                                                alpha_m=0.2,
                                                alpha_f=0.4,
                                                gamma=0.3,
                                                beta=0.25)