fedoo.time.GeneralizedAlpha

class GeneralizedAlpha(alpha_m=0.0, alpha_f=0.0, beta=None, gamma=None)

Generalized-alpha time integrator for second-order evolutions.

The internal force, stiffness, and damping are evaluated at the generalized mid-points t_{n+1-alpha_f} and the inertia at t_{n+1-alpha_m}. The classical endpoint Newmark scheme is the alpha_m = alpha_f = 0 specialization (see fedoo.time.Newmark).

Warning

External loads (Neumann/Dirichlet) are applied by the problem at the step endpoint t_{n+1}, not at t_{n+1-alpha_f}. For alpha_f != 0 combined with time-varying loads this leaves an O(alpha_f*dt) inconsistency in the forced response and degrades the designed spectral damping. With alpha_f = 0 (Newmark) or with loads that are constant over the step the scheme is consistent. Sampling the load factor at the alpha point is a known follow-up.

__init__(alpha_m=0.0, alpha_f=0.0, beta=None, gamma=None)

Methods

GeneralizedAlpha.compile_assembly(assembly)	Compile compatible weakforms in an assembly tree in place.
GeneralizedAlpha.compile_weakform(weakform)	Return a time-integrated version of weakform when applicable.

GeneralizedAlpha.evolution

TimeEvolution category handled by this integrator (set by subclasses).