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The following four-article series was published in a newsletter of the American Society of Mechanical Engineers (ASME). It serves as an introduction to the analysis discipline known as the finite element method (FEM). The author is Steve Roensch, an engineering consultant and expert witness specializing in finite element analysis.
Last in a four-part series.
Previous: Finite Element Analysis (FEA): Solution
The Post-processing Phase
After a finite element model has been prepared and checked, boundary conditions have been applied, and the model has been solved, it is time to investigate the results. This activity is known as the post-processing phase.
1. Verification and Sanity Checks
Post-processing begins with a thorough check for problems that may have occurred during solution.
- Log Files: Most solvers provide a log file which should be searched for warnings or errors. It provides a quantitative measure of how well-behaved the numerical procedures were.
- Reaction Loads: As a "sanity check," reaction loads at restrained nodes should be summed and examined. For a linear static analysis, reaction loads must closely balance the applied load. Significant discrepancies cast doubt on the validity of all other results.
- Error Norms: Quantities like strain energy density and stress deviation among adjacent elements can be reviewed, typically to target subsequent adaptive remeshing.
2. Visualization Techniques
Once the solution is verified, the quantities of interest may be examined using various display options:
- Displacement: The model's overall displacement is often displayed by superposing the deformed shape over the undeformed shape. Animation capabilities are crucial for understanding the deformation pattern.
- Stresses: Since stress is a tensor quantity, derived quantities are extracted for display.
- Principal Stress Vectors: Displayed as color-coded arrows indicating direction and magnitude.
- Von Mises Stress: A scalar failure stress displayed as colored bands (contour plots). When treated as a 3D object with light sources, this is a shaded image stress plot.
3. Advanced Capabilities: Adaptivity and Optimization
Adaptive Remeshing: Rapidly gaining popularity, this technique uses error norms to automatically remesh the model. It places a denser mesh in regions needing improvement and a coarser mesh in areas of overkill. This works best when boundary conditions are applied directly to the underlying CAD geometry.
Optimization: The model is modified automatically to satisfy performance criteria.
- Scalar Optimization: Modifies beam cross-sections, shell thicknesses, or material properties to meet stress or deflection constraints.
- Shape Optimization: Modifies the actual 3D boundaries using driving dimensions as parameters.
Future Trends and Integration
A clear trend is the integration of FEA with multi-body dynamics packages. The long-term goal is real-time computation of stresses in systems undergoing large displacement motion, accounting for friction and fluid flow.
Conclusion
The finite element method has matured into a vital tool for structural and thermal analysis. With the cost of technology dropping and software capabilities expanding, the question has moved from "Why apply FEA?" to "Why not?"
The method is fully capable of delivering higher quality products in a shorter design cycle with a reduced chance of field failure, provided it is applied by a capable analyst.
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