The Art of Matrix Reduction How to create a super-element matrix in ANSYS ME 501 Project Michael Tonks Alan Mortensen
Summary Background Creating Super Elements in Ansys 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 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
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
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 Step 1: Create and Mesh Geometry
How to create Super Elements in Step 2: Specify Analysis type
How to create Super Elements in Step 3: Select Option to Print Stiffness Matrix Select File Name Select option to print Matrix
How to create Super Elements in Step 4: Choose Masters and Master DOF’s Choose Master Nodes Choose Master DOF’s Choose DOFs
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
How to create Super Elements in Super Element Stiffness Matrix:
How to create Super Elements in Super Element Stiffness Matrix:
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?