Accuracy vs. Speed A look into mesh density IN THIS WEBINAR: PRESENTED BY: • Mesh refinement Andrew Nelson • Discussing higher order elements Stress Engineer • Examining analytical error and Structural Design and Analysis quantifying benefits aNelson@structures.aero 5/22/2012 Page 1
Mesh Refinement • Refining a mesh is a simple process • Stress concentrations • Benefits and drawbacks • Results accuracy • Computation time • We will look at a basic example 5/22/2012 STRUCTURES .AERO Page 2
Plate with Hole LINEAR Mesh Size (in) DOF Peak Stress (psi) % Error 0.2 4440 1354 32.3 0.1 16992 1705 14.75 0.05 66408 1919 4.05 0.025 262512 2006 0.3 PARABOLIC 5/22/2012 STRUCTURES .AERO Page 3
Higher Order Elements • Parabolic elements • Different that just a finer mesh • Benefit is second order shape functions • Most useful with bending • We create these elements with mid-side nodes Linear Parabolic 5/22/2012 STRUCTURES .AERO Page 4
Error Error Regression 35 LINEAR Mesh Size (in) DOF Peak Stress (psi) % Error 30 0.2 4440 1354 32.3 25 0.1 16992 1705 14.75 Percent Error (%) 0.05 66408 1919 4.05 20 0.025 262512 2006 0.3 Linear PARABOLIC 15 Parabolic Mesh Size (in) DOF Peak Stress (psi) % Error 10 0.2 12936 1586 20.7 0.1 50316 1801 9.95 5 0.05 198024 1931 3.45 0.025 785016 2006 0.3 0 0 5 10 15 20 25 30 35 40 45 Inverse of Element Size (1/in) 5/22/2012 STRUCTURES .AERO Page 5
Split Mesh • Split meshing is a technique of using two different mesh densities in a single part • Used to keep element/node/DOF count low while increasing accuracy where you need it • Most practical way to address stress concentrations in parts 5/22/2012 STRUCTURES .AERO Page 6
In Conclusion • Refining the mesh will converge the maximum stress values to the solution, kind of obvious but this simple example compounds as models increase in complexity. • Computation times may have only increased slightly in our example, but this effect will be magnified in more complex models. • Using parabolic elements, while increasing run times, will converge on the same answer much more quickly than just using linear elements, but can be situationally effective. • The best way to approach the balance between analysis run time and solution accuracy will be to split mesh according to your geometry. 5/22/2012 STRUCTURES .AERO Page 7
Structural Design and Analysis (Structures.Aero) Structural Analysis Software Sales and Support • Team of stress engineers that help our clients design lightweight and load efficient structures. • We service aerospace companies and other industries that require high level analysis. • Value added reseller providing software, training, • Specialty in composites and lightweight and support for products we use on a daily structures basis. • Tools used include hand analysis, HyperSizer, • Support Femap, NX Nastran, Simcenter 3D, Femap, NX Nastran, Fibersim, NX, Solid Edge, Fibersim, Solid Edge, and HyperSizer. Simcenter 3D, LS Dyna, and LMS. 5/22/2012 STRUCTURES .AERO Page 8
Questions ? For questions on the material covered For questions about pricing, or to see a today, please contact Andrew Nelson. demo, please contact Marty Sivic . Andrew Nelson Marty Sivic Stress Engineer Director of Sales aNelson@structures.aero msivic@structures.aero 703-935-2816 724-382-5290 5/22/2012 STRUCTURES .AERO Page 9
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