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 –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 Matrix reduced to create equivalent super-element matrix  Small and easy to analyze  Contains all important information The equivalent stiffness matrix is condensed by eliminating interior nodes that have no displacement

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

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

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

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

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

10. 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 How to create Super Elements in Ansys

11. Super Element Stiffness Matrix: How to create Super Elements in Ansys

12. Example Leading Edge Skin –Supplied by Boeing Phantom Works –Modeled in Pro/E –Imported as IGES into Ansys Actual PartPro/E ModelAnsys Model

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

14. 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

15. 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

16. 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

17. 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

18. Questions?