Convert a 1-D Cubic Hermite Mesh into a 2-D Mesh

Description

• In this example, you start by making a circular 1-D mesh using four cubic Hermite elements. Then the four 1-D elements are converted to one 2-D bi-cubic Hermite element, which is then converted to a cubic-linear element.
• The nodal coordinates and element connectivities are read from tab-delimited spreadsheets.

Start Continuity

• Launch the Continuity Client

• On the About Continuity startup screen

  • leave the mesh checkbox checked under Use Modules:

• Click OK to bring up the main window

Create circular mesh with four 1-D cubic Hermite elements

• Mesh→Edit→Coordinates…

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

  • Click OK to submit Coordinate Form

• Mesh→Edit→Basis…

  • Choose Hermite Basis Function→1D→Cubic

  • Click Add Cubic

  • Click OK to submit Basis Form

• Mesh→Edit→Nodes…

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

    • Continuity Table Manager→File→Open…

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

      • Continuity Table Manager→File→Close and update form

  • Click OK to submit Node Form

• Mesh→Edit→Elements…

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

    • Continuity Table Manager→File→Open…

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

      • Continuity Table Manager→File→Close and update form

  • Click OK to submit Element Form

• File→Send

• View→EditDimensions…

  • Click Accept marked recommendations and click OK

• Mesh→Calculate Mesh…

• Mesh→Render→Nodes…

• Mesh→Render→Elements…

  • Click the lines radio button

  • Click Render to display mesh

  

Convert to one cubic-cubic Hermite 2-D circular element

Now we’ll take the 4 1D cubic elements and turn them into the edges of a 2-D cubic-cubic hermite element.

• Mesh→Edit→Elements…

  • For elements 2,3 and 4, select each element then click the Delete Element button below to remove each element

  • For the remaining one element, enter 4,3,1,2 as the nodes

  • Click OK

• Mesh→Edit→Basis…

  • Choose Hermite Basis Function→2D→Cubic-Cubic

  • Click Add Cubic-Cubic

  • Click OK to submit Basis Form

• Mesh→Edit→Nodes…

  • Select Cubic-Cubic under Coordinate 1 and Coordinate 2

  • Modify the derivatives based on the table below
    

  • Click OK to submit Node Form

• File→Reset…

  • Select the Save, reset, and reload radio button on the bottom

  • Click OK

• File→Send

• View→EditDimensions…

  • Click Accept marked recommendations and click OK

• Mesh→Calculate Mesh…

• Mesh→Render→Elements…

  • Click the lines radio button

  • Click Render to display mesh

Convert to linear-cubic interpolation

• Mesh→Edit→Basis…

  • Choose Hermite Basis Function→2D→Linear-Cubic

  • Click Add Linear-Cubic

  • Click OK to submit Basis Form

• Mesh→Edit→Nodes…

  • Select Linear-Cubic under Coordinate 1 and Coordinate 2

  • Click OK

• File→Send

• Mesh→Calculate Mesh…

• Mesh→Render→Elements…

  • Click the lines radio button

  • Click Render to display mesh

Pre-built model

This cont6 file contains all data and parameters for this problem: 1d_circle_arclength_derivs.cont6