Create and Refine a 1-D Cubic Hermite Element Mesh

Description

• These step-by-step instructions will guide you through creating, refining and rendering a mesh of one-dimensional linear Lagrange elements.
• The nodal coordinates and element connectivities are read from simple Excel spreadsheets.
• An automated script that runs this tutorial is included in the Continuity installation: examples\mesh10\1d_example.py. To run it, click File→Scripts→Read script→Python or session script

Start Continuity

• Launch the Continuity Client
• leave the mesh checkbox checked under Use Modules:

• Click OK to bring up the main window

Create initial mesh

• Select rectangular cartesian in the Global Coordinates: pop-up menu

• Click OK to submit Coordinate Form

• Choose Lagrange Basis Function→1D→Linear

• Click Add Linear

• Choose Hermite Basis Function→1D→Cubic

• Click Add Cubic

• Verify that the list of basis functions now contains:
• Linear Lagrange 3
• Cubic Hermite 3
• Click OK to submit Basis Form

• Click Import/Export/Graph button to open Continuity Table Manager

• Select tab-delimited nodes file (nodes.xls)

• You should now have nodes numbered 1-2
• Click OK to submit Node Form

• Click Import/Export/Graph button to open Continuity Table Manager

• Select tab-delimited elements file (elems.xls)

• You should now have only one element in the list
• Click OK to submit Element Form

• If the Dimensions Form appears, simply click Apply Marked Recommendations and then OK

• Click OK to submit

Calculate nodal derivatives with respect to local coordinates

• Enter 1 for the xi1, xi2, and xi3 fields under New Element per old element in

• Select the Local coordinates radio button under New nodal derivatives with respect to:

• Click OK to submit

• Verify that you still have only 2 nodes
• Select Cubic Hermite 3 under Coordinate 1, Coordinate 2, and Coordinate 3

• Click OK to submit Node Form

• Enter LocalDerivs.cont6 next to File Name:

• If the Dimensions Form appears, simply click Apply Marked Recommendations and then OK

• Click OK to submit

• Return to the Nodes Form and note that derivatives wrt xi(1) are no longer zero

Convert to nodal derivatives with respect to arc length coordinates

• Enter 1 for the xi1, xi2, and xi3 fields under New Element per old element in

• Select the Arc lengths radio button under New nodal derivatives with respect to:

• Click OK to submit

• Verify that you still have only 2 nodes
• Verify that the derivatives are now 0.8 and 0.6

Render the mesh

• Leave the Open Mesh, Client, and Server checkboxes checked

• Click OK

• Locate and select the LocalDerivs.cont6 saved earlier (or whatever you named it)

• Click Open

• Click the lines radio button

• Click Render to display mesh

• The mesh should now look similar to the first screenshot above.
• Click on Node 1 under Node List

• Change wrt s(1) to 0.0 under Coordinate 1

• Click on Node 2 under Node List

• Change wrt s(1) to 0.0 under Coordinate 2

• Click OK to submit Node Form

• Click the lines radio button

• Click Render to display mesh

Refine the mesh four-fold and re-render

• Enter 4 for xi1, 1 for xi2, and 1 for xi3 under New Element per old element in

• Select the Local coordinates radio button under New nodal derivatives with respect to:

• Click OK to submit

• Click the lines radio button

• Click Render to display mesh

• The mesh should now look like the second screenshot

Pre-built model

This cont6 file contains all data and parameters for this problem: mesh2.cont6