1. The Art of Matrix Reduction
How to create a super-element matrix in ANSYS
ME 501 Project
Michael Tonks
Alan Mortensen

2. Summary Background Creating Super Elements in Ansys
Matrix Reduction
Substructure Analysis
Creating Super Elements in Ansys
Leading Edge Example
Conclusions

3. FEA Difficulties Complex parts have large stiffness matrices
Analyses with large parts are cumbersome
Large Number of nodes
Many DOFs
Large matrices
Difficult to invert
Take up large disk space

4. Create Super Element Matrices
The equivalent stiffness matrix is condensed by eliminating interior nodes that have no loads
Matrix reduced to create equivalent super-element matrix
Small and easy to analyze
Contains all important information

5. Create Super Element Matrices
The equivalent stiffness matrix is condensed by eliminating interior nodes that have no loads
Matrix reduced to create equivalent super-element matrix
Small and easy to analyze
Contains all important information

6. Substructure Analysis
Large structures divided into sections
Each separate section analyzed to find stiffness matrix
Super elements created and reassembled for full structural analysis

7. How to create Super Elements in
Step 1: Create and Mesh Geometry

8. How to create Super Elements in
Step 2: Specify Analysis type

9. How to create Super Elements in
Step 3: Select Option to Print Stiffness Matrix
Select File Name
Select option to print Matrix

10. How to create Super Elements in
Step 4: Choose Masters and Master DOF’s
Choose Master Nodes
Choose Master DOF’s
Choose DOFs

11. How to create Super Elements in
Step 5: Solve in Current LS
Super Element Saved in .sub file
Super Element Matrix retrieved in List file
Menu Path: List – Other – Superelem – Data
Choose file name
Select
Full contents

12. How to create Super Elements in
Super Element Stiffness Matrix:

13. How to create Super Elements in
Super Element Stiffness Matrix:

14. Example Leading Edge Skin Supplied by Boeing Phantom Works
Modeled in Pro/E
Imported as IGES into Ansys
Actual Part
Pro/E Model
Ansys Model

15. Meshed Part Skin meshed using Shell Elements
Shells given thickness of actual part

16. Master DOF’s Chosen Part rigidly constrained along bottom edge
Master DOF’s chosen along one side
Location for spar
In X, Y, Rot Z
Master DOF’s

17. Super Element Matrix Problem solved in Ansys
Stiffness Matrix Shown in Ansys List File
Originally 683 Nodes, 2049 DOF’s
Reduced to 24 Nodes, 72 DOF’s

18. Conclusions Ansys can be used to do Substructure Analysis
Make complex problems easier to solve
Ansys can output the super element stiffness matrix
Useful for other types of analysis

19. Future Research
Investigate different data output methods for super-element matrix
Develop Matlab program to format super-element matrix for linear algebra
Combining super-elements in assemblies for FEA analysis

20. Questions?