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The Art of Matrix Reduction

The Art of Matrix Reduction. How to create a super-element matrix in ANSYS. ME 501 Project Michael Tonks Alan Mortensen. Summary. Background Matrix Reduction Substructure Analysis Creating Super Elements in Ansys Leading Edge Example Conclusions. FEA Difficulties.

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The Art of Matrix Reduction

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  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 • 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 Select File Name Select option to print Matrix • Step 3: Select Option to Print Stiffness Matrix

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

  11. How to create Super Elements in Choose file name Select Full contents • 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

  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?

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