[cig-commits] r11333 - short/3D/PyLith/trunk/examples/twocells/twoquad4

[willic3 at geodynamics.org]

Author: willic3
Date: 2008-03-05 13:45:31 -0800 (Wed, 05 Mar 2008)
New Revision: 11333

Added:
   short/3D/PyLith/trunk/examples/twocells/twoquad4/README.tractions
Modified:
   short/3D/PyLith/trunk/examples/twocells/twoquad4/README
   short/3D/PyLith/trunk/examples/twocells/twoquad4/axialtract.cfg
Log:
Modified README to include traction problem, and included another README
describing the analytical solution. Also increased quadrature order for
tractions, even though it's not needed for constant applied tractions.



Modified: short/3D/PyLith/trunk/examples/twocells/twoquad4/README
===================================================================
--- short/3D/PyLith/trunk/examples/twocells/twoquad4/README	2008-03-05 21:15:02 UTC (rev 11332)
+++ short/3D/PyLith/trunk/examples/twocells/twoquad4/README	2008-03-05 21:45:31 UTC (rev 11333)
@@ -21,6 +21,15 @@
     - axialdisp.cfg:  Parameter settings.
     - axialdisp.spatialdb: Database of Dirichlet BC values.
 
+  * axialtract
+
+    A constant normal traction is applied to the right edge of the mesh.
+    The left edge is pinned in the x-direction, and the bottom edge is
+    pinned in the y-direction.
+
+    - axialtract.cfg:  Parameter settings.
+    - axialtract.spatialdb: Database of Neumann BC values.
+
   * sheardisp: 
 
     The left and right edges of the mesh are pinned in the
@@ -48,6 +57,7 @@
 To run the examples, you can type:
 
   pylith axialdisp.cfg
+  pylith axialtract.cfg
   pylith sheardisp.cfg
   pylith dislocation.cfg
 

Added: short/3D/PyLith/trunk/examples/twocells/twoquad4/README.tractions
===================================================================
--- short/3D/PyLith/trunk/examples/twocells/twoquad4/README.tractions	                        (rev 0)
+++ short/3D/PyLith/trunk/examples/twocells/twoquad4/README.tractions	2008-03-05 21:45:31 UTC (rev 11333)
@@ -0,0 +1,37 @@
+The traction example is a simple problem to demonstrate the usage of
+Neumann (traction) boundary conditions. A constant traction of 4.0e8 Pa
+is applied to the right edge of the mesh, the left edge is pinned in x,
+and the bottom edge is pinned in y. The constant normal traction yields
+a constant stress field within the domain, where the xx-component is equal
+to the applied traction. The yy and xy components are both zero. The
+corresponding strain field is:
+
+exx = (1 - nu^2) * N/E
+eyy = -nu * (1 + nu) * N/E
+exy = 0
+
+where nu is Poisson's ratio (0.25 for this problem), E is Young's modulus
+(75 GPa for this problem), and N is the applied normal traction (400 MPa
+for this problem). Integrating the strain-displacement relations and using
+the applied displacement BC, the corresponding displacement field is:
+
+u = (1 - nu^2) * N * (x - x0)/E
+v = nu * (1 + nu) * N * (y0 - y)/E
+
+where x0 and y0 are the minimum x and y-values respectively, along which
+displacements are fixed. Using the mesh, properties, and boundary conditions
+for this problem, the solution should be:
+
+exx = 5.0e-3
+eyy = -1.66667e-3
+exy = 0.0
+
+(-2,-1): u = 0.0,  v = -0.003333
+(-2, 1): u = 0.0,  v =  0.0
+( 0,-1): u = 0.01, v = -0.003333
+( 0, 1): u = 0.01, v =  0.0
+( 2,-1): u = 0.02, v = -0.003333
+( 2, 1): u = 0.02, v =  0.0
+
+Users should compare the computed solution to the analytical solution to
+insure that everything is computed correctly.

Modified: short/3D/PyLith/trunk/examples/twocells/twoquad4/axialtract.cfg
===================================================================
--- short/3D/PyLith/trunk/examples/twocells/twoquad4/axialtract.cfg	2008-03-05 21:15:02 UTC (rev 11332)
+++ short/3D/PyLith/trunk/examples/twocells/twoquad4/axialtract.cfg	2008-03-05 21:45:31 UTC (rev 11333)
@@ -70,7 +70,7 @@
 quadrature = pylith.feassemble.quadrature.Quadrature1Din2D
 quadrature.cell = pylith.feassemble.FIATLagrange
 quadrature.cell.dimension = 1
-quadrature.cell.quad_order = 1
+quadrature.cell.quad_order = 2
 
 # Boundary conditions to be applied to the bottom boundary of the mesh.
 [pylithapp.timedependent.bc.y_neg]