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
  • On the About Continuity startup screen

    • leave the mesh checkbox checked under Use Modules:

  • Click OK to bring up the main window

Create initial mesh

Calculate nodal derivatives with respect to local coordinates

  • Mesh→Refine...

    • 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

  • Mesh→Edit→Nodes...

    • 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

  • File→Save→Model...

    • Enter LocalDerivs.cont6 next to File Name:

  • File→Send

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

  • Mesh→Calculate Mesh...

    • 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

  • Mesh→Refine...

    • 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

  • Mesh→Edit→Nodes...

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

Render the mesh

Refine the mesh four-fold and re-render

Pre-built model

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