fedoo.weakform.BeamEquilibrium

class BeamEquilibrium(material, A=None, Jx=None, Iyy=None, Izz=None, k=0, name='', nlgeom=None, space=None, *, consistent_tangent=False)

Weak formulation of the mechanical equilibrium equation for beam models.

Geometrical are implemented with the updated lagrangian approach.

Parameters:

• material (ConstitutiveLaw name (str) or ConstitutiveLaw object) – material can be either a Beam constitutive laws or a material constitutive law with attributes E and G for elastic and shear modulus (for instance fedoo.constitutivelaw.ElasticIsotrop). If material is a beam constitutive law, the following parameters A, Jx, Iyy, Izz and k are ignored.

• A (scalar or arrays of gauss point values, optional) – Beam section area.

• Jx (scalar or arrays of gauss point values, optional) – Torsion constant.

• Iyy (scalar or arrays of gauss point values, optional) – Second moment of area with respect to y (beam local coordinate system).

• Izz (scalar or arrays of gauss point values, optional) – Second moment of area with respect to z (beam local coordinate system).

• k (scalar or arrays of gauss point values, optional) – Shear coefficient. If k=0 (default) the beam use the bernoulli hypothesis.

• consistent_tangent (bool, default=False) – For standard two-node beam elements with nlgeom=True or 'UL', differentiate the complete existing internal-force residual. Includes the changing length, frame and local finite rotations. The resulting tangent may be nonsymmetric. Set False for the historical material plus axial-force geometric tangent. Alternative beam interpolations retain that historical tangent. This option is read-only after construction. Create a new weak form to select a different tangent, including when sharing forms across assemblies.

• name (str) – name of the WeakForm.

Notes

The current beam formulation supports isotropic linear elastic materials only. Material orientations are ignored; the beam cross-section orientation is defined by the assembly element frame.

__init__(material, A=None, Jx=None, Iyy=None, Izz=None, k=0, name='', nlgeom=None, space=None, *, consistent_tangent=False)

Methods

BeamEquilibrium.copy()	Return a shallow copy sharing the weak form's model objects.
BeamEquilibrium.get_all()	Return the list of all weak forms.
BeamEquilibrium.get_dissipation()	Return the optional dissipative provider for a time integrator.
BeamEquilibrium.get_storage()	Return the optional storage weakform for a time integrator.
BeamEquilibrium.get_weak_equation(assembly, pb)
BeamEquilibrium.initialize(assembly, pb)
BeamEquilibrium.iter_leaf()	Iterate over the leaf weakforms contained in this object.
BeamEquilibrium.reset()
BeamEquilibrium.set_damping([damping])	Mechanical alias for set_dissipation.
BeamEquilibrium.set_dissipation([...])	Attach a dissipative contribution.
BeamEquilibrium.set_inertia(density_or_storage)	Mechanical alias for set_storage.
BeamEquilibrium.set_start(assembly, pb)
BeamEquilibrium.set_storage(storage[, evolution])	Attach a time-storage weakform to this static weakform.
BeamEquilibrium.sum(wf1, wf2)
BeamEquilibrium.to_start(assembly, pb)
BeamEquilibrium.update(assembly, pb)
BeamEquilibrium.update_2(assembly, pb)

BeamEquilibrium.consistent_tangent	Read-only tangent selection, set through the constructor.
BeamEquilibrium.name	Return the name of the WeakForm.
BeamEquilibrium.nvar	Number of variables in the modeling space associated to the WeakForm.
BeamEquilibrium.space	Return the ModelingSpace associated to the WeakForm if defined.
BeamEquilibrium.nlgeom	Property used to treat the geometric non linearities. * Set to False if geometric non linarities are ignored (default). * Set to True or 'UL' to use the updated lagrangian method (update the mesh) * Set to 'TL' to use the total lagrangian method (base on the initial mesh with initial displacement effet).
BeamEquilibrium.geometric_stiffness	Whether to include initial-stress stiffness.