NAFEMS Benchmarks — Standard Tests for FEM Code Qualification
NAFEMS LE1 through LE10 linear elastic benchmarks, free vibration reference problems, nonlinear reference solutions, and using NAFEMS results for solver qualification.
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Quick Explainer
What are the NAFEMS benchmarks and why are they important?
NAFEMS published benchmark problems in the 1980s-1990s with reference solutions for linear and nonlinear FEM. The LE series tests basic stress analysis elements — LE1 is a thin plate with a central hole in tension. Every major FEM code documents convergence to NAFEMS results as quality assurance. They cover specific stress states where element formulations can fail subtly.
What does the MacNeal-Harder test in NAFEMS expose?
The MacNeal-Harder tests use deliberately distorted elements and pure bending cases to expose locking — where low-order elements become pathologically stiff in bending. A simple Q4 element under pure bending can be 4x too stiff (shear locking). These tests drove development of reduced integration and incompatible mode elements that are now standard in all production FEM codes.