60
edits
Fem-fenics: Difference between revisions
Jump to navigation
Jump to search
no edit summary
No edit summary |
No edit summary |
||
| Line 255: | Line 255: | ||
plot(u) | plot(u) | ||
interactive() | interactive() | ||
</syntaxhighlight>}} | |||
</div> | |||
</div> | |||
<div style="clear:both"></div> | |||
=== Mixed Formulation for Poisson Equation === | |||
This time we compare the code with the c++ version of DOLFIN. | |||
{{Code|HyperElasticity Problem: the ufl file|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
# Function spaces | |||
element = VectorElement("Lagrange", tetrahedron, 1) | |||
# Trial and test functions | |||
du = TrialFunction(element) # Incremental displacement | |||
v = TestFunction(element) # Test function | |||
# Functions | |||
u = Coefficient(element) # Displacement from previous iteration | |||
B = Coefficient(element) # Body force per unit volume | |||
T = Coefficient(element) # Traction force on the boundary | |||
# Kinematics | |||
I = Identity(element.cell().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 | |||
mu = Constant(tetrahedron) | |||
lmbda = Constant(tetrahedron) | |||
# 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 - inner(B, u)*dx - inner(T, u)*ds | |||
# 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) | |||
</syntaxhighlight>}} | |||
<div style="width: 100%;"> | |||
<div style="float:left; width: 48%"> | |||
{{Code|Define Poisson problem|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
</syntaxhighlight>}} | |||
</div> | |||
<div style="float:right; width: 48%"> | |||
{{Code|Define Poisson problem|<syntaxhighlight lang="c++" style="font-size:13px"> | |||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||