The Art of Matrix ReductionHow to create a super-element matrix in ANSYS

ME 501 ProjectMichael TonksAlan Mortensen

Summary

• Background– Matrix Reduction– Substructure Analysis

• Creating Super Elements in Ansys

• Leading Edge Example

• Conclusions

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

Create Super Element Matrices

boundary nodes

interior nodes

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 displacement

Substructure Analysis

• Large structures divided into sections

• Each separate section analyzed to find stiffness matrix

• Super elements created and reassembled for full structural analysis

How to create Super Elements in Ansys

• Step 1: Create and Mesh Geometry

• Step 2: Specify Analysis type

How to create Super Elements in Ansys

• Step 3: Select Option to Print Stiffness Matrix

Select File Name

Select option to print Matrix

How to create Super Elements in Ansys

• Step 4: Choose Masters and Master DOF’s– Choose Master Nodes– Choose Master DOF’s

Choose DOFs

How to create Super Elements in Ansys

• 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

• Super Element Stiffness Matrix:

How to create Super Elements in Ansys

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

Meshed Part

• Skin meshed using Shell Elements

• Shells given thickness of actual part

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

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

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

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

Questions?