Hello all,
I am trying to calculate the reaction forces at all nodes in my mesh. I used the hyperelasticity demo to test out my approach:
from dolfin import *
from ufl import nabla_div
# Optimization options for the form compiler
parameters["form_compiler"]["cpp_optimize"] = True
ffc_options = {"optimize": True, \
"eliminate_zeros": True, \
"precompute_basis_const": True, \
"precompute_ip_const": True}
# Create mesh and define function space
mesh = UnitCubeMesh(24, 16, 16)
V = VectorFunctionSpace(mesh, "Lagrange", 1)
# Mark boundary subdomians
left = CompiledSubDomain("near(x[0], side) && on_boundary", side = 0.0)
right = CompiledSubDomain("near(x[0], side) && on_boundary", side = 1.0)
# Define Dirichlet boundary (x = 0 or x = 1)
c = Expression(("0.0", "0.0", "0.0"), degree=1)
r = Expression(("scale*0.0",
"scale*(y0 + (x[1] - y0)*cos(theta) - (x[2] - z0)*sin(theta) - x[1])",
"scale*(z0 + (x[1] - y0)*sin(theta) + (x[2] - z0)*cos(theta) - x[2])"),
scale = 0.5, y0 = 0.5, z0 = 0.5, theta = pi/3, degree=1)
bcl = DirichletBC(V, c, left)
bcr = DirichletBC(V, r, right)
bcs = [bcl, bcr]
# Define functions
du = TrialFunction(V) # Incremental displacement
v = TestFunction(V) # Test function
u = Function(V) # Displacement from previous iteration
B = Constant((0.0, 0.0, 0.0)) # Body force per unit volume
T = Constant((0.0, 0.0, 0.0)) # Traction force on the boundary
# Kinematics
d = u.geometric_dimension()
I = Identity(d) # Identity tensor
F = I + grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
# Invariants of deformation tensors
Ic = tr(C)
J = det(F)
# Elasticity parameters
E, nu = 20.0, 0.3
mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))
# Stored strain energy density (compressible neo-Hookean model)
psi = (mu/2)*(Ic - 3) - mu*ln(J) + (lmbda/2)*(ln(J))**2
# Total potential energy
Pi = psi*dx - dot(B, u)*dx - dot(T, u)*ds
# Compute first variation of Pi (directional derivative about u in the direction of v)
F = derivative(Pi, u, v)
# Compute Jacobian of F
J = derivative(F, u, du)
# Solve variational problem
solve(F == 0, u, bcs, J=J,
form_compiler_parameters=ffc_options)
coords = V.tabulate_dof_coordinates() #mesh.coordinates()
x_dofs = V.sub(0).dofmap().dofs()
y_dofs = V.sub(1).dofmap().dofs()
z_dofs = V.sub(2).dofmap().dofs()
nodes = []
for index in range(0, len(coords), 3):
nodes.append([coords[index,0], coords[index,1], coords[index,2]])
RF = derivative(Pi, u, v)
f_int = assemble(RF)
bcr.apply(f_int)
Fx = []
for i in x_dofs:
Fx.append(f_int[i])
Fy = []
for i in y_dofs:
Fy.append(f_int[i])
Fz = []
for i in z_dofs:
Fz.append(f_int[i])
This approach works to calculate reaction forces on the boundary, but how can I calculate the reaction forces on nodes on the interior of the mesh?