The Art of Matrix Reduction
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The Art of Matrix ReductionHow to create a super-element matrix in ANSYS
ME 501 ProjectMichael TonksAlan Mortensen
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Summary
• Background– Matrix Reduction– Substructure Analysis
• Creating Super Elements in Ansys
• Leading Edge Example
• Conclusions
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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
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Create Super Element Matrices
boundary nodes
interior nodes
• Matrix reduced to create equivalent super-element matrixSmall and easy to analyzeContains all important information
• The equivalent stiffness matrix is condensed by eliminating interior nodes that have no loads
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Create Super Element Matrices
Reduced stiffness matrix:Kr = Kbb - Kbi Kii
-1 Kib
Kbb
Kib Kii
Kbi *b
*i
Fb
Fi
interior DOF’s
coupled DOF’s
coupled DOF’s
boundary DOF’s
• Matrix reduced to create equivalent super-element matrixSmall and easy to analyzeContains all important information
• The equivalent stiffness matrix is condensed by eliminating interior nodes that have no loads
![Page 6: The Art of Matrix Reduction](https://reader036.fdocuments.us/reader036/viewer/2022062304/56812a71550346895d8df5bd/html5/thumbnails/6.jpg)
Substructure Analysis
• Large structures divided into sections
• Each separate section analyzed to find stiffness matrix
• Super elements created and reassembled for full structural analysis
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How to create Super Elements in
• Step 1: Create and Mesh Geometry
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• Step 2: Specify Analysis type
How to create Super Elements in
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• Step 3: Select Option to Print Stiffness Matrix
Select File Name
Select option to print Matrix
How to create Super Elements in
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• Step 4: Choose Masters and Master DOF’s– Choose Master Nodes– Choose Master DOF’s
Choose DOFs
How to create Super Elements in
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• 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
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• Super Element Stiffness Matrix:
How to create Super Elements in
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• Super Element Stiffness Matrix:
How to create Super Elements in
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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
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Meshed Part
• Skin meshed using Shell Elements
• Shells given thickness of actual part
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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
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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
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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
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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
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Questions?