Rigid tie constraint

Example of a 2D rigid tie. The bottom face of a square is clamped. A rigid body rotation is imposed on the top face.

Iter 1 - Time: 0.20000 - dt 0.20000 - NR iter: 3 - Err: 0.00208
Iter 2 - Time: 0.40000 - dt 0.20000 - NR iter: 3 - Err: 0.00382
Iter 3 - Time: 0.60000 - dt 0.20000 - NR iter: 3 - Err: 0.00522
Iter 4 - Time: 0.80000 - dt 0.20000 - NR iter: 3 - Err: 0.00634
Iter 5 - Time: 1.00000 - dt 0.20000 - NR iter: 3 - Err: 0.00838

import fedoo as fd
import numpy as np

fd.ModelingSpace("2D")  # plane strain assumption

NLGEOM = True
E = 200e3
nu = 0.3

mesh = fd.mesh.rectangle_mesh()
material = fd.constitutivelaw.ElasticIsotrop(E, nu, name="ConstitutiveLaw")

wf = fd.weakform.StressEquilibrium(material, nlgeom=NLGEOM, name="wf")

assembly = fd.Assembly.create("wf", mesh)

# node set for boundary conditions
bottom = mesh.find_nodes("Y", mesh.bounding_box.ymin)
top = mesh.find_nodes("Y", mesh.bounding_box.ymax)

# add CD nodes
ref_node = mesh.add_virtual_nodes(2)  # reference node for rigid body motion
node_cd = [ref_node[0], ref_node[0], ref_node[1]]
var_cd = ["DispX", "DispY", "DispX"]

pb = fd.problem.NonLinear(assembly)
pb.set_nr_criterion("Displacement", err0=1, tol=1e-2, max_subiter=5)

results = pb.add_output(
    "rigid_tie_example", assembly, ["Disp", "Stress", "Strain", "Fext"]
)

pb.bc.add(fd.constraint.RigidTie2D(top, node_cd, var_cd))

pb.bc.add("Dirichlet", bottom, "Disp", 0)
pb.bc.add("Dirichlet", ref_node[1], "DispY", 0)  # to block the non used virtual dof
pb.bc.add(
    "Dirichlet", ref_node[1], "DispX", -np.pi / 4
)  # Rigid rotation of the right end

pb.nlsolve(dt=0.2, tmax=1, update_dt=True, print_info=1, interval_output=0.2)

# =============================================================
# Example of plots with pyvista - uncomment the desired plot
# =============================================================

# ------------------------------------
# Simple plot with default options
# ------------------------------------
results.plot("Stress", component="YY", data_type="Node", show=True)

# ------------------------------------
# Write movie with default options
# ------------------------------------
# results.write_movie('rigid_tie_example', 'Stress', 'vm', 'Node', framerate = 12, quality = 5)