What is reproduced
This first version checks the critical load of the simple frame in §2.1.2, using the production engine. It also traces one imperfect path with the production corotational arc-length solver. The path is not a validated reproduction of Figure 2b.
Two 1 m members, pinned at the outer ends and rigidly joined at the corner. E = 21 MPa, A = 0.01 m², J = 10⁻⁴/12 m⁴. A downward 1 kN reference load acts at the corner. The path adds a +0.001 kN·m reference moment; there are 10 elements per member.
Published reference
§2.1.2, pages 4–5: closed-form (λ₁, α, β) = (2.43; 0.3805; 0.1421); numerical (2.4313; 0.382; 0.1436). Figure 2b is on page 4. These are reference values, not computed coefficients.
Evidence and limitations
The production linear buckling load is compared with the paper. Every element energy partial derivative through order four is checked by central differences at three states. These checks validate derivatives of the production-style beam energy; they do not validate Koiter coefficients.
With 10 elements per member, |λ₁ − 2.4313| = 5.568E-5, below the 1E-4 tolerance. The maximum scaled derivative discrepancy is 3.08E-8, below 2E-5. These are checks of the implemented subset only.
A scaled linear displacement and linear buckling mode do not satisfy the nonlinear critical-point equations in the initial probe. No coefficients or Koiter prediction are displayed from that rejected calculation. The critical state and modal normalization must be resolved first.
Not yet reproduced: α, β, the second-order displacement correction, closed-form post-buckling coefficients, and near-bifurcation agreement between Koiter and arc-length paths. Optimisation, multiple modes, larger assemblies and experimental validation are outside this first version.
Questions for the authors
Could you share the minimal §2.1.2 input, mesh and beam formulation; the precise normalization and sign mapping from ξ to corner rotation; and the reference α, β and arc-length arrays? Please clarify the reported coefficient error percentages, which differ from arithmetic on the rounded values.
Cite this
Stabileo Research, “Roorda frame: reproduction in progress”, reproduction of Federico Ferrari, Ole Sigmund (2025), doi:10.1002/nme.70082. Implementation: research/stability/ferrari-sigmund-2025 at commit 417d112f9493. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.