The Correct Way to Interpret FEM/CFD Analysis Results — From the Pitfalls of Contour Plots to Report Preparation
Theory and Physics — Why "How to Interpret Results" is Important
The Contour Plot Trap — The Pitfall of Auto-Scaling
Professor, is just looking at the contour plot not enough for interpreting analysis results? When I see pretty colors, I think "It's done!"...
That's the one people stumble on the most in actual work. If the maximum value of the contour plot's color bar is auto-scaled, it gets pulled by the stress singularity, making the whole thing completely blue and burying the information you really want to see.
Huh, completely blue...? Doesn't that mean "low stress, so safe"?
No, no. For example, if there's a 90-degree sharp edge at a bolt hole, the stress there increases without limit as you refine the mesh—the so-called stress singularity. With auto-scaling, that singular point's value becomes the color bar's upper limit, so the "stress distribution across the entire flange surface" you originally wanted to see all becomes the same color and becomes indistinguishable.
I see... So, there's something you should do before looking at the contour plot?
Yes. The correct procedure for interpreting results is fixed. Don't jump straight to the contour plot; check in this order: Deformation plot → Energy balance → Point probe. Just following this order dramatically reduces the risk of drawing wrong conclusions.
Governing Equations
Wow, the talk about proper interpretation of analysis results is super interesting! Please tell me more.
Discretization Methods
How do you actually solve this equation on a computer?
We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.
We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. higher-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.
Matrix Solution Algorithms
What exactly are matrix solution algorithms?
Solve the simultaneous equations by direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). Preconditioned iterative methods are effective for large-scale problems.
| Solver | Classification | Memory Usage | Applicable Scale |
|---|---|---|---|
| LU decomposition | Direct Method | O(n²) | Small to Medium Scale |
| Cholesky decomposition | Direct Method (Symmetric Positive Definite) | O(n²) | Small to Medium Scale |
| PCG Method | Iterative Method | O(n) | Large Scale |
| GMRES method | Iterative Method | O(n·m) | Large Scale / Non-symmetric |
| AMG Preconditioning | Preprocessing | O(n) | Very Large Scale |
So if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!
Implementation in Commercial Tools
So, what software can be used to properly interpret and report analysis results?
| Tool Name | Developer/Current | Main File Formats |
|---|---|---|
| MSC Nastran / NX Nastran | MSC Nastran (Hexagon), NX Nastran (Siemens Digital Industries Software) | .bdf, .dat, .f06, .op2, .pch |
| Abaqus FEA (SIMULIA) | Dassault Systèmes SIMULIA | .inp, .odb, .cae, .sta, .msg |
| Ansys Mechanical (formerly ANSYS Structural) | Ansys Inc. | .cdb, .rst, .db, .ans, .mac |
| Ansys Fluent | Ansys Inc. | .cas, .dat, .msh, .jou |
| Simcenter STAR-CCM+ | Siemens Digital Industries Software | .sim, .java, .csv |
| COMSOL Multiphysics | COMSOL AB | .mph |
| OpenFOAM | Open Source (OpenCFD/ESI, OpenFOAM Foundation) | Dictionary files (e.g., blockMeshDict), .foam |
Vendor Lineage and Product Integration History
Are the origins of each software quite dramatic?
MSC Nastran / NX Nastran
Next is about MSC Nastran. What's the content?
Developed in the 1960s as NASA Structural Analysis (NASTRAN). Commercialized by MSC Software, later UGS (now Siemens) derived NX Nastran. MSC was acquired by Hexagon AB in 2017.
Current Affiliation: MSC Nastran (Hexagon), NX Nastran (Siemens Digital Industries Software)
Abaqus FEA (SIMULIA)
What exactly is Abaqus FEA?
Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.
Current Affiliation: Dassault Systèmes SIMULIA
Wait, wait, structural analysis... so, can it also be used for cases like this?
Ansys Mechanical (formerly ANSYS Structural)
Tell me about "Ansys Mechanical"!
Developed in 1970 by Swanson Analysis Systems Inc. (SASI). Based on APDL (Ansys Parametric Design Language).
Current Affiliation: Ansys Inc.
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