Fem-fenics: Difference between revisions

Fem-fenics (edit)

Revision as of 15:56, 6 September 2013

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 plot(u)
 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>}}