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)