Eighty Years of the Finite Element Method (2022)

Original Article ↗ Hacker News Discussion ↗

Finite element methods (FEM) remain central to engineering simulation 80 years after their inception, but many practitioners say day‑to‑day practice has stagnated, with legacy commercial tools like ANSYS, NASTRAN, Abaqus and COMSOL still dominating. Commenters contrast these powerful but expensive and often frustrating packages with fragmented open‑source options, debate when FEM genuinely adds value versus rapid physical prototyping, and highlight emerging directions such as isogeometric analysis, physics‑informed neural networks and libraries like FEniCS and deal.II that could eventually modernize the field.

State of the FEM/FEA Industry

  • Many practitioners feel everyday FEM practice has stagnated: workflows and tools (ANSYS, NASTRAN, Abaqus) look much like they did 10–20 years ago.
  • Some describe commercial ecosystems as sales-driven “muddy death marches” with frequent licensing reshuffles and product killing to upsell tiers.
  • Others push back, citing advances such as contact elements, bolt preload, detailed composite modeling, progressive failure, thin-layer modeling, and optimization as meaningful progress.
  • COMSOL is seen as a major “new” player, though it has existed for decades; valued mainly for easy multi-physics coupling rather than best-in-class single-physics solvers.

Commercial vs Open-Source Tools

  • Dominant commercial tools mentioned: ANSYS, Abaqus, NASTRAN, LS-DYNA, COMSOL.
  • COMSOL praised for meshing, integrated geometry, scripting, and multi-physics coupling; criticism that individual physics modules are weaker than specialist tools.
  • Open-source landscape seen as fragmented and immature for industry-grade multiphysics:
    • Structural/thermal: CalculiX (buggy), Code_Aster (powerful but confusing), open NASTRAN forks.
    • PDE frameworks: FEniCS, deal.II, SELF; mostly academic, require coding.
    • CFD/fluids: OpenFOAM (powerful but “impenetrable” to newcomers), plus mentions of Elmer and OpenRadioss.
  • FreeCAD and Gmsh used as CAD/meshing front-ends; FEATool offers a GUI atop FEniCS.

Workflows, Use Cases, and Accessibility

  • Typical engineering workflow: CAD (e.g., SolidWorks) → meshing/FEA → iteration → prototype → further iteration.
  • For hobbyists, full CAD–mesh–solve–postprocess pipeline is described as a high barrier to entry.
  • Example hobby/industry domains: electronics/EMI, antennas, aerodynamics, rocketry, machining, robotics, 3D-printing/topology optimization, graphics.

Understanding and Teaching FEM

  • Several participants find deriving FEM via Galerkin/variational methods difficult; others outline a conceptual pipeline: strong form → weak form → discretization → element integrals → global system → solve.
  • One view: in practice, many users skip derivations and rely on textbook element formulations.
  • Recommendations for deeper understanding include finite difference methods as a starting point, university FEM courses, and coding with libraries like deal.II or FEniCS.

Debate on FEM’s Role in Design

  • One camp: FEM is best as a “unit test” or verification tool; rapid physical prototyping and iteration can be more effective, especially for mechanisms and tolerances.
  • Counterpoint: what works for exceptional engineers or small prototypes does not scale to large or safety-critical structures (bridges, large aerospace/automotive structures, crashworthiness).
  • Strong disagreement over claims like “you can’t design crash-resilient structures without FEM”:
    • Historical argument: major structures and vehicles were designed pre-FEM, so it’s not strictly necessary.
    • Modern argument: complexity and performance expectations now make high-fidelity simulation essential to meet requirements, reduce testing cost, and satisfy certification.

Limitations, Validation, and “Next-Gen” Methods

  • Experienced analysts emphasize that “garbage in, garbage out”: misunderstanding models or parameters leads to wildly wrong results; hand checks and fundamentals remain crucial.
  • Reports that many “next generation” FEM ideas work on simple benchmark problems but fail to validate on complex real-world cases; industry focus has shifted toward Verification & Validation standards (e.g., ASME V&V).
  • Physics-informed neural networks, neural operators, and ML-based solvers are being explored:
    • Early impressions: very fast and directionally correct, but not yet accurate enough for final design; may serve as pre-screening tools.

Isogeometric Analysis (IGA) and Meshing Pain Points

  • IGA (using spline-based CAD functions as shape functions) highlighted as a promising direction:
    • Claims of better accuracy per degree of freedom, larger stable timesteps, improved stability for problems like incompressible solids, and immersed/trimmed methods that greatly ease meshing.
  • Skeptical view: IGA’s core idea—reusing CAD splines for shape functions—has existed for years, with limited industrial impact and questionable benefit over classical p-refinement.
  • Proponents respond that modern spline technology, hierarchical refinement, and trimming-based immersed methods do offer real gains, particularly by reducing meshing effort while retaining good convergence.