Analytical Benchmarks — Exact Solutions for FEM & CFD Verification
Timoshenko beam, Lame cylinder, Hertz contact, Stokes flow, and other closed-form solutions used as verification benchmarks for simulation codes.
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Quick Explainer
Why use analytical solutions for verification rather than experimental data?
Experimental data has measurement uncertainty and mixes numerical error with physical modeling error. Analytical solutions are exact for the mathematical problem — no experimental noise, no model error, just numerical discretization error. If your FEM disagrees with an analytical solution, the error is definitively numerical, not physical.
What is the Lame cylinder solution and why is it a standard FEM benchmark?
The Lame solution gives exact stress and displacement in a thick-walled cylinder under internal and external pressure — non-trivial, with stress varying with radius and concentration at the inner wall. It tests element performance under bending-dominated stress states, boundary condition application on curved surfaces, and convergence rate. FEM results should converge cleanly to the Lame solution as mesh refines.