fedoo.weakform.SpringEquilibrium

class SpringEquilibrium(K, name='', nlgeom=False, space=None)

Weak formulation of the mechanical equilibrium equation for spring models.

This weak formulation allow to use a simple linear axial spring element with geometrical non linearities (using the updated lagrangian approach).

To ensure numerical stability, a small tangential stiffness is automatically added. This rigidity can be controled by setting the Kt_factor attribute. For instance set Kt_factor=0 to remove any tangential stiffness.

An alternative to the SpringEquilibrium is the InterfaceForce weakform. InterfaceForce weakform allows to use springs with complexe behavior and non axial rigidity, but InterfaceForce is restricted to geometrical linear analyses.

Parameters:

• K (float, numpy array) – Spring axial rigidity If numpy array, len(K) should be the number of elements in the corresponding mesh.

• nlgeom (bool, 'UL', default = False) – if True or ‘UL’, activate the geometrical non linearities

• name (str) – name of the WeakForm

Example

Springs in series submitted to an extension and a 45° rotation.

>>> import fedoo as fd
>>> fd.ModelingSpace("2Dplane")
>>> mesh = fd.mesh.line_mesh(n_nodes=11,x_min=0, x_max=10, ndim=2)
>>> mesh.elm_type = 'spring'
>>> wf = fd.weakform.SpringEquilibrium(1000,nlgeom=False)
>>> assemb = fd.Assembly.create(wf, mesh)
>>> pb = fd.problem.NonLinear(assemb)
>>> pb.bc.add('Dirichlet', [0], 'Disp', 0)
>>> pb.bc.add('Neumann', [10], 'Disp', [5,5])
>>> pb.nlsolve()
>>> res = pb.get_results(assemb, ['Disp', 'Fint'])
>>> res.plot('Fint', show_nodes=True)

__init__(K, name='', nlgeom=False, space=None)

Methods

SpringEquilibrium.get_all()	Return the list of all weak forms.
SpringEquilibrium.get_weak_equation(assembly, pb)
SpringEquilibrium.initialize(assembly, pb)
SpringEquilibrium.nvar(self)	Return the number of variables used in the modeling space associated to the WeakForm.
SpringEquilibrium.reset()
SpringEquilibrium.set_start(assembly, pb)
SpringEquilibrium.sum(wf1, wf2)
SpringEquilibrium.to_start(assembly, pb)
SpringEquilibrium.update(assembly, pb)
SpringEquilibrium.update_2(assembly, pb)

SpringEquilibrium.name	Return the name of the WeakForm.
SpringEquilibrium.space	Return the ModelingSpace associated to the WeakForm if defined.
SpringEquilibrium.nlgeom	Method 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).