Status: not-run
Nonlinear benchmarks / NL7
Trace the equilibrium path of a pinned right-angle frame through buckling and postbuckling, including load reversal.
Equal 1.2 m centerline arms join at right angles. B=(0,0), elbow=(0,1.2 m), C=(1.2 m,1.2 m), and load point A=(0.24 m,1.2 m). The rectangular cross section has in-plane depth 0.02 m and transverse width 0.03 m.
Elastic material with E=71.74 GPa and ν=0.
Pin B and C against both in-plane translations without fixing section rotation. Apply a downward dead load at A.
Quasistatic, planar response with large rotations; no plasticity, gravity or contact.
Body-fitted AM-DT C3D8R solids replace the reference beam model. The arms share a finite-size square joint. Pin and load resultants are distributed along transverse centerlines. Zero transverse displacement is compatible with the zero Poisson ratio and planar response. Unlike beam kinematics, the solid model permits local joint and load-introduction deformation; refinement and reference agreement must both pass. The production finite-strain elastic law is Saint Venant–Kirchhoff. A shared sparse bordered pseudo-arc-length solver follows the equilibrium branch; no reference deformation is imposed.
Measure downward displacement at A averaged across its transverse load line. Follow the documented interpolation: recover PL²/EI at the first crossing of downward displacement/L=0.407, and displacement/L at the final ascending load PL²/EI=31.887. This avoids inverting the almost horizontal force curve at its first limit point. Interpolate adjacent accepted states only. Require actual load reversal and retain every scalar path point. I=width×depth³/12.
AM-DT acceptance policy, not NAFEMS certification: the normalized load and displacement checkpoints must each agree within 2%, with less than 2% change under simultaneous spatial/path-step refinement. Failure is retained rather than relaxing these thresholds or skipping a checkpoint.
loadFactorAtDownwardDisplacement0_407 = 18.552 1
downwardDisplacementAt31_887_over_L = 0.784 1