Research / Numerical methods

DaDeppo–Schmidt: a deep arch at its limit

After D. A. DaDeppo, R. Schmidt, “Instability of Clamped-Hinged Circular Arches Subjected to a Point Load”, Journal of Applied Mechanics (1975), doi:10.1115/1.3423734.

Against the author’s code
First version · 0 reviews
Against the paper’s figures
Schmidt’s 2000 discussion, page 1308, explicitly quotes Table 1 of the 1975 paper: PR²/EI = 8.97. We have verified that quotation; we have not directly inspected the original table. This comparison uses the rounded published load, not a digitized curve.

Research, not a design tool. Nothing here is an engineering result.

A 215° arch, a crown load, and the production arc-length solver.

First version · 0 reviews

Research, not a design tool.

One clamped–hinged arch

A circular arch with a fixed left end and pinned right end carries a downward, fixed-direction point load at its crown. Forty straight corotational frame elements approximate the 215° opening. The asymmetric supports allow large sideways motion before the first limit point.

We use R = 1 m, EI = 1 kN·m² and EA = 10⁶ kN. The reference load is 1 kN, so the solver load factor equals PR²/EI. The often-quoted P = 897 uses R = 100 and EI = 10⁶: its normalized value is 8.97, not 897.

Limit-load comparison

Schmidt’s 2000 discussion, page 1308, explicitly quotes Table 1 of the 1975 paper: PR²/EI = 8.97. We have verified that quotation; we have not directly inspected the original table. This comparison uses the rounded published load, not a digitized curve.

Read Schmidt’s quoted values

The production Crisfield arc-length solver traces equilibrium beyond the peak using the existing corotational frames. The comparison uses the largest converged load among 400 steps, with a fixed 1% relative tolerance. The model is very stiff axially but is not exactly inextensible. The viewer uses true displacement scale.

Replay frames are endpoint results from repeated runs of the same solver, stopped every twenty steps. The live worker repeats those runs because the production API returns full nodal displacements only at the endpoint. The curve shows every converged step; its horizontal axis is step number, not crown displacement.

Not yet

  • Mesh and step-size convergence study; exact limit-point interpolation.
  • Full published equilibrium curve and second limit point.
  • Other opening angles, out-of-plane buckling, contact or material nonlinearity.
  • Independent reviews and direct inspection of the original 1975 table.

Cite this

Stabileo Research, “DaDeppo–Schmidt: a deep arch at its limit”, reproduction of D. A. DaDeppo, R. Schmidt (1975), doi:10.1115/1.3423734. Implementation: research/benchmarks/dadeppo-arch-1975 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.